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https://elib.uni-stuttgart.de/handle/11682/9225
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math
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Please use this identifier to cite or link to this item: http://dx.doi.org/10.18419/opus-9208
|Title:||Energy estimates for the two-dimensional Fermi polaron|
|Abstract:||This thesis is concerned with the quantum mechanical system of a single particle interacting with an ideal gas of identical fermions by point interaction. In the physics literature this system is often referred to as Fermi polaron. We investigate the two-dimensional Fermi polaron. Unlike the one-dimensional case, point interactions in two or three dimensions cannot be implemented as perturbation of the quadratic form of the Laplacian. Either they are obtained as self-adjoint extensions of the Laplacian restricted to functions that vanish when the coordinates of two particles coincide, or they are constructed by a suitable limiting process. Choosing the second approach, a many-body operator with two-particle point interaction has firstly been rigorously defined by Dell'Antonio, Figari and Teta. We consider the Fermi polaron confined to a box with periodic boundary conditions and we identify a broad class of regularization schemes that approximate the Hamiltonian of the Fermi polaron as limit operator in the strong resolvent sense. The Hamiltonian is not given by a closed form, which could be conveniently used in standard variational principles. We establish a novel variational principle that characterizes all bound states, i.e. all energy eigenstates below the bottom of the spectrum of the kinetic energy. This variational principle turns out to be very useful for the following purposes. The ground state of the Fermi polaron is expected to be well approximated by the polaron and the molecule ansatz in the regime of weak and strong coupling between the impurity and the Fermi gas, respectively. In the physics literature, these two classes of trial states are used for variational computations with the (ultraviolet) regularized Hamiltonian. Although the implicit expressions for the minimal energy of both classes allow for the removal of the ultraviolet cutoff, it remains unclear whether the results are upper bounds to the ground state energy of the Fermi polaron. We show that the minimization of energy over polaron and molecule trial states can be reformulated in a natural way with the help of our variational principle. By doing so, the classes of trial states simplify considerably, and since there is no reference to regularized quantities, we can prove that the expressions for the polaron and the molecule energy in the physics literature are indeed upper bounds to the ground state energy of the Fermi polaron. As a further application of the variational principle, we prove analytically that to first order in a particle-hole expansion the molecule ansatz yields a better approximation to the ground state energy than the polaron ansatz if the coupling between the impurity and the Fermi gas is strong enough. So far, this had only been done numerically. The concluding chapter is devoted to the derivation of a lower bound to the ground state energy of the Fermi polaron in two-dimensional space. We show that the ground state energy can be bounded from below by a quantity that does not depend on the number of fermions in the Fermi gas. This result is correct under the assumption that the ratio of the mass of the impurity and the mass of a fermion exceeds 1.225. We also present a method which might yield a similar result for lower mass ratios. This method gives an estimate for the quadratic form of the regularized Hamiltonian in position space representation. In this connection, we present an inequality that bounds a singular potential of a two-dimensional Fermi gas depending only on the minimal distance between two fermions by the kinetic energy of the Fermi gas uniformly in the number of fermions. This inequality also applies to a potential with singularity 1/r^2, for which the Hardy inequality does not hold in two dimensions. Therefore, the full antisymmetry of the wave function has to be taken into account.|
|Appears in Collections:||08 Fakultät Mathematik und Physik|
Files in This Item:
|Energy_estimates_for_the_2D_Fermi_Polaron.pdf||667,16 kB||Adobe PDF||View/Open|
Items in OPUS are protected by copyright, with all rights reserved, unless otherwise indicated.
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| 4,298 | 7 |
http://www.123rf.com/stock-photo/in_size.html
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https://www.chegg.com/homework-help/questions-and-answers/1500-w-heater-designed-plugged-120v-outlet-125a-r-96ohms-long-take-raise-temperature-air-g-q3798379
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math
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A 1500-w heater is designed to be plugged into a 120v outlet. I=12.5A R=9.6ohms How long does it take to raise the temperature of the air in a good-sized living room (3.00m x 5.00m x 8.00m) by 10.0 degrees C? Note that the specific heat of air is 1006J/(kg x degrees C) and the density of air is 1.20kg/ m^3 Express your answer numerically in minutes, to three significant figures
This problem has been solved!
Get more help from Chegg
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| 435 | 3 |
https://books.google.com/books/about/The_Elements_of_Euclid.html?id=ch06AQAAMAAJ
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math
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What people are saying - Write a review
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The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ...
Robert Simson,Robert Euclid
No preview available - 2015
ABC is given ABCD altitude angle ABC angle BAC base BC BC is equal bisected Book XI centre circle ABC circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC line BC multiple º º opposite parallel parallelogram parallelogram AC perpendicular point F polygon prisms PROP proportionals proposition pyramid radius ratio of BC rectangle contained rectilineal figure right angles segment sides BA similar solid angle solid parallelopiped sphere square of AC straight line AB straight line AC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
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| 1,028 | 7 |
http://e-booksdirectory.com/details.php?ebook=10589
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math
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A First Course in Ordinary Differential Equations
by Norbert Euler
Publisher: Bookboon 2015
Number of pages: 232
The book consists of lecture notes intended for engineering and science students who are reading a first course in ordinary differential equations and who have already read a course on linear algebra, including general vector spaces and integral calculus for functions of one variable.
Home page url
Download or read it online for free here:
by R.S. Johnson - Bookboon
This text provides an introduction to all the relevant material normally encountered at university level: series solution, special functions, Sturm-Liouville theory and the definition, properties and use of various integral transforms.
by Simon J.A. Malham - Heriot-Watt University
From the table of contents: Linear second order ODEs; Homogeneous linear ODEs; Non-homogeneous linear ODEs; Laplace transforms; Linear algebraic equations; Matrix Equations; Linear algebraic eigenvalue problems; Systems of differential equations.
by Mohammed K A Kaabar
The book covers: The Laplace Transform, Systems of Homogeneous Linear Differential Equations, First and Higher Orders Differential Equations, Extended Methods of First and Higher Orders Differential Equations, Applications of Differential Equations.
by Michael F. Singer - arXiv
The author's goal was to give the audience an introduction to the algebraic, analytic and algorithmic aspects of the Galois theory of linear differential equations by focusing on some of the main ideas and philosophies and on examples.
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| 1,548 | 15 |
https://www.physicsforums.com/threads/solve-for-smallest-theta-for-slider-to-reach-a.156972/
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math
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k = 40 N/m
mass of slider = 200 g
EDIT r = 0.3 m
Hoop is VERTICAL, undeformed length of the spring is when spring is in position AB, slider NOT attached to spring.
Find smallest value for theta such that the slider will pass through D and reach A (see picture).
s = r*theta
1/2 k * x^2
The Attempt at a Solution
I set up the initial and final energy equations but couldn't figure out how to solve them. =P
Denoting @ as theta:
mgr(1-cos(@)) + 1/2*k(r@)^2 = mg*2r
After plugging in numbers and rearranging, I found:
mgcos(@) + 0.0018277@^2 = 1.962
I don't know how to solve for @ in that equation. Also, in the spring term of 1/2kx^2, I replaced x by r@ (s = r@) and multiplied @ by pi/180 to convert to radians for that term.
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| 725 | 14 |
https://www.jiskha.com/display.cgi?id=1344621753
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math
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posted by Paul .
Evaluate the following definite integral:
integral at a = -1, b=2
Would I have to separate them in 3 terms as:
-4 ∫1/9x^2 + ∫1/30x + ∫1/25
resulting in: -4/(3x^3)+ (15x^2)+ C?
and from there I can replace a and b
f(a) - f(b)?
1/(a+b+c) is NOT 1/a + 1/b + 1/c
What you need to do is let
u = 3x+5 and you have
du = 3 dx, so dx = du/3
x in [-1,2] means u in [2,11]
∫[2,11] -4/u^2 du/3
-4/3 ∫[2,11] u^-2 du
That should be ever so simple.
THanks Steve, but why 3x+5??
because you have 9x^2 + 30x + 25 = (3x+5)^2
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https://www.coursehero.com/file/6528829/Critique-of-Pure-Reaso6/
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math
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Critique of Pure Reason Lecture notes, January 27, 1997: Metaphysical Deduction Before picking up the thread of my previous lecture, I will answer a couple of questions put forward by the class. Q: If space is an a priori form of intuition, how can Kant claim that it has empirical reality as at A28/B44? A: Space is a priori in that its source is human sensibility, not experience. But space is empirically real in the sense that it is a component of the world of experience, as the mind's contribution to experience. Q: What does Kant mean when he says that space is an infinite given magnitude (A25/B39)? A: Kant uses the infinitude of space to show that space is not a general concept, but an intuition , and hence a "given" magnitude. General concepts have an infinite number of possible things under them (in their "sphere"). The concept 'body' comprehends potentially infinitely many bodies. But the infintude of space is that of infinitely many spaces together making up one space. Q: If space is an intuition, why does Kant refer to it as a concept? A: Space is indeed
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This note was uploaded on 11/09/2011 for the course PSY PSY2012 taught by Professor Scheff during the Fall '09 term at Broward College.
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https://www.kominkiskandynawskie.pl/crusher-mills/Dec-10_33305.html
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math
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Jan 20, 2021 Calculating Crushed Stone by Weight. A final calculation is if you need to figure out the weight in tons of your crushed stone. You might not need to figure this out, but its handy to know. Most gravel weighs about 1.5 tons per cubic yard. So, for the examples above, 2.45 cubic yards of gravel weighs 3.68 tons or 7,350 pounds.
Apr 09, 2020 Sometimes crushed stone is sold by the ton.To figure out the how many tons you will need is not hard to do. You will have to know that the standard weight contractors use for crushed stone is 2700 pounds per cubic yard. Multiply the
1.5 Tonne. How many cubic meters are in a ton of gravel? Given a weight of 32 tons and a density of between 1 and 1.4 ton/m3 , and doing the arithmetic, you get an answer of approximately 23 to 32 cubic meters, depending on the composition of the gravel.
The result is 2,835 pounds per cubic yard of gravel. Thereof, how many tons is a yard of stone dust? Most gravel and crushed stone products have similar weights per ton. A general rule of thumb when converting cubic yards of gravel to tons is to multiply the cubic area by 1.4. For your reference, gravel typically weighs 2,800 pounds per cubic yard.
Aug 15, 2018 By the ton, the costs of crushed limestone will vary anywhere from 20 to as much as 30. 1.5 tons can cover one cubic yard. Youngs Sand and Gravel, a landscape supply company located in Ohio, charges 20 a ton for all limestone,
According to imperial or US customary measurement system, a cubic yard of crushed limestone can weighs around 2600 pounds or 1.3 short tons, in this regard, How many tons of crushed limestone are in a cubic yard, so there are 1.3 short tons are in a cubic yard. 1 litre paint coverage in square meter square feet.
A cubic yard of sand equal as 2700 pounds and A short tons weighs around 2000 lbs, so number of tons, 2700/ 2000 1.35 short tons, in this regard, how many tons per cubic yard of sand, so, generally there are 1.35 short tons per cubic yard of sand. This is standard weight of sand in tons per cubic yard used for billing purpose.
May 15, 2020 Crushed stone is quoted at a weight of 2700 pounds per cubic yard. Your stone dealer tells you he has a truck that can deliver 20 tons of stone per load. You need to know who many cubic yards that comes out to.
How many tons is 4 yards pea gravel? (A single cubic yard of pea gravel weighs about 1.3 short tons.) The general range for a cubic yard of plain pea gravel is about $30 to $35, and a ton will cost about $40 to $45.
Calculate 57 Granite Stone. Type in inches and feet of your project and calculate the estimated amount of Granite Stone in cubic yards, cubic feet and Tons, that your need for your project. The Density of 57 Granite Stone 2,410 lb/yd or 1.21 t/yd or 0.8 yd/t.
Mar 02, 2020 Also know, how many cubic yards are in a ton of crushed gravel? One 20-ton truckload of crushed stone will yield 14-15 cubic yards of crushed stone. One may also ask, how much does a cubic yard of crushed stone weigh? 2400 lbs . Just so, how many cubic yards are in a ton? A cubic yard is equal to 27 cubic feet.
Mar 17, 2021 How much does a cubic yard of stone weigh? Most gravel and crushed stone products have similar weights per ton. Gravel and sand typically weighs 2,200-2,700 pounds per cubic yard. In addition, there are 2,000 pounds to a ton. Certain products, like washed gravel, weigh more like 2,835 pounds per cubic yard.
Oct 08, 2020 57 stone is generally sold by the ton, and there are approximately 1.4 tons in each cubic yard of this material. Most crushed stone and gravel products have similar weights per ton. How Many Cubic Yards Does A Ton Of 57 Stone Cover? The number of cubic yards that a ton of this gravel will cover depends on the depth at which it will be laid. Generally speaking,
Apr 09, 2020 To figure out the how many tons you will need is not hard to do. You will have to know that the standard weight contractors use for crushed stone is 2700 pounds per cubic yard. Multiply the number of cubic yards by 2700 and divide by 2000. This is thoroughly answered here.
It all depends on the stone varieties involved.Roughly, one cubic yard will equal approximately 2781 lbs, which is around 1.25 tonnes in the UK and 1.35 tonnes in the US, based on their short tonne measurement.
Jan 10, 2020 To figure out the how many tons you will need is not hard to do. You will have to know that the standard weight contractors use for crushed stone is 2700 pounds per cubic yard. Multiply the number of cubic yards by 2700 and divide by 2000. This value is the number of tons that you will need.
One cubic yard of 3/4-inch red crushed stone weighs 1.3 tons. Companies may sell the stone by ton or by cubic yard. One cubic yard covers about 10 feet by 10 feet for a depth of 3 inches and one ton covers about the same area at a 2-inch depth.
Type in inches and feet of your project and calculate the estimated amount of Base material in cubic yards, cubic feet and Tons, that your need for your project. The Density of Crusher Run 2,410 lb/yd or 1.21 t/yd or 0.8 yd/t
Rectangular Area with Crushed Gravel (105 lb/ft) and Price Per Unit Mass Lets say I need crushed gravel for part of my driveway which measures 4ft long, 2ft wide and 9in (0.75ft) deep. Lets also say that the selected gravel costs $50 per ton.
Sep 30, 2021 Crushed stone is costlier at about $55 per cubic yard and $65 per ton. Buying pea gravel in bulk may reduce costs , but different finishes, like gravel with color, will add anywhere from $20 to $50 to the price per unit.
Stone Tonnage Calculator rohrers-admin 2018-06-06T155108-0400 Tonnage calculations are based on averages and should be used as estimates. Actual amounts needed may vary.
Ceramic Tile, loose 6 x 6 1 cubic yard 1,214 lbs Concrete, Scrap, Loose 1 cubic yard 1,855 lbs Glass 1 cubic yard 2,160 lbs Gypsum, Dry Wall 1 cubic yard 3,834 lbs Metals 1 cubic yard 906 lbs Plastic 1 cubic yard 22.55 lbs Soil, Dry 1 cubic yard 2,025 lbs Soil, Wet 1 cubic yard 2,106 lbs Stone or Gravel 1 cubic yard 2,632.5 lbs
A cubic yard is a measurement by volume (Or most simply put, a measurement by size) 2. A ton is a measurement by weight. 3. A / sign means per, so 1.5 TONS/CY reads 1.5 TONS per Cubic yard which simply means there are 1.5 tons per (for) every cubic yard of material. Fortunately, a cubic yard of material has a conversion factor (unit ...
Jul 26, 2021 Use this formula to determine how much crushed stone you will need for your project (LxWxH) / 27 cubic yards of crushed stone needed. In the construction world, most materials are measured in cubic yards. Multiply the length (L), in feet, by the width (W), in feet, by the height (H), in feet, and divide by 27.
CUBIC YARDAGE CALCULATION SHEET Height of Sides ... Material Weight Pounds per Cubic Yard Asphalt 2,700 lb. Iron (wrought) 13,100 lb. Brush/Branches ... Crushed Stone 2,700 lb. Plywood Sheets 800 lb. Earth (loose) 2,050 lb. Roofing Debris 450 lb. to 750 lb.
Our Stone calculator will help you estimate how many Cubic Yards of Stone you need for your desired coverage area. The crushed stone calculator offers 4 Box area fields and 2 Circular area fields for you to calculate multiple areas simultaneously (back
Jul 08, 2011 One cubic yard of vacuum has a mass of 0 kilograms. One cubic yard of osmium has a mass of approx 5756 tons per cubic yard. Take your pick between these two extremes. Of course, a cubic yard of a neutron stars material would be much, much greater.
1 cubic foot of Stone, crushed weighs 100.00959 pounds lbs Stone, crushed weighs 1.602 gram per cubic centimeter or 1 602 kilogram per cubic meter, i.e. density of stone, crushed is equal to 1 602 kg/m. In Imperial or US customary measurement system, the density is equal to 100.0096 pound per cubic foot lb/ft, or 0.92601 ounce per cubic ...
3. Estimation of the total gravel mass needed either in tons or kilograms, by transforming the volume as follows Metric - tons - 1 cubic feet 0.0520833333 tons - 1 cubic yard 1.388888888 tons - 1 cubic meter 1.8365 tons. English - lbs - 1 cubic feet 114.823958333 lbs - 1 cubic yard 3105.0985915 lbs - 1 cubic meter 4048.789445 lbs. 4.
Per Cubic Yard 53 same as 4 but with limestone dust for easy packing 1-2 in size with half lime dust. Quantity 53 Driveway Stone - Crushed Limestone quantity. Add to cart. Compare. SKU 34986d8dc5f4. Category Shop Driveway Stone. Share on facebook . twitter . google-plus
Tile. 2970. 1.43. Trap stone. 5849. 2.52. Most of Harmony Sand Gravels products will weight approximately 2,840 pounds per cubic yard or about 1.42 tons per cubic yard. For estimating purposes, most Contractors consider the yield to be 3,000 pounds per
FTruck Body Pricing BrochuresExcelCubic_Yardage_Chart DCubic_Yardage_Chart D Rev A 6/9/2015 AGGREGATE TYPE
Jul 28, 2021 1 cubic yard of concrete weighs about 3915 pounds or 1.96 US tons. 1 cubic yard of sand (dry) weighs about 2700 pounds or 1.35 US tons. 1 cubic yard of sand (wet) weighs about 3240 pounds or 1.62 US tons. 1 cubic yard of mulch (bark) weighs about 506 pounds or 0.25 US tons. 1 cubic yard of mulch (woodchip) weighs about 674 pounds or 0.34
Calculate 57 Limestone Gravel. Type in inches and feet of your project and calculate the estimated amount of Gravel Stone in cubic yards, cubic feet and Tons, that your need for your project. The Density of 57 Limestone Gravel 2,410 lb/yd or 1.21 t/yd or 0.8 yd/t. A
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http://math.stanford.edu/~ryzhik/stanf_sem.html
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math
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Wednesdays at 4:15 PM in 384H.
We consider an integro-PDE model for a population structured by the spatial variables and a trait variable which is the diffusion rate. Competition for resource is local in spatial variables, but nonlocal in the trait variable. We show that in the limit of small mutation rate, the solution concentrates in the trait variable and forms a Dirac mass supported at the lowest diffusion rate. Hastings and Dockery et al. showed that for two competing species, the slower diffuser always prevails, if all other things are held equal. Our result suggests that their findings may well hold for a continuum of traits. This talk is based on joint work with King-Yeung Lam.
Abstract: Ray mappings are the fundamental objects of geometrical optics. We shall consider canonical problems in optics, such as phase retrieval and beam shaping, and show that their solutions are characterized by certain ray mappings. Existence of solutions and some properties of them can be established through a variational method - the Weighted Least Action Principle - which is a natural generalization of the Fermat principle of least time.
This is a joint work with D.Burago and S.Ivanov. As avid anglers we were always interested in the survival chances of fish in turbulent oceans. In this talk I will address this question mathematically, and discuss some of its consequences. I will show that a fish with bounded aquatic locomotion speed can reach any point in the ocean if the fluid velocity is incompressible, bounded, and has small mean drift.
We begin with the elementary observation that the $n$-step descendant distribution of any Galton-Watson process satisfies a discrete Smoluchowski coagulation equation with multiple coalescence. Using this we study certain CSBPs (continuous state branching processes), which arise as scaling limits of Galton-Watson processes. Our results provide a clear and natural interpretation, and an alternate proof, of the fact that the Lévy jump measure of certain CSBPs satisfies a generalized Smoluchowski equation. (This result was previously proved by Bertoin and Le Gall in 2006.) We also prove the existence of Galton-Watson processes that are universal, in the sense that all possible (sub)critical CSBPs can be obtained as a sub-sequential scaling limit of this process.
Fluid-structure interaction problems with composite structures arise in many applications. One example is the interaction between blood flow and arterial walls. Arterial walls are composed of several layers, each with different mechanical characteristics and thickness. No mathematical results exist so far that analyze existence of solutions to nonlinear, fluid-structure interaction problems in which the structure is composed of several layers. In this talk we will summarize the main difficulties in studying this class of problems, and present an existence proof and a computational scheme based on which the proof of the existence of a weak solution was obtained. Our results reveal a new physical regularizing mechanism in FSI problems with multi-layered structures: inertia of the thin fluid-structure interface with mass regularizes evolution of FSI solutions. Implications of our theoretical results on modeling the human cardiovascular system will be discussed. This is a joint work with Boris Muha (University of Zagreb, Croatia), Martina Bukac (U of Notre Dame, US) and Roland Glowinski (UH). Numerical results with vascular stents were obtained with S. Deparis and D. Forti (EPFL, Switzerland). Collaboration with medical doctors Dr. S. Little (Methodist Hospital Houston) and Dr. Z. Krajcer (Texas Heart Institute) is also acknowledged.
We prove that weak solutions of the inviscid SQG equations are not unique, thereby answering an open problem posed by De Lellis and Szekelyhidi Jr. Moreover, we show that weak solutions of the dissipative SQG equation are not unique, even if the fractional dissipation is stronger than the square root of the Laplacian. This talk is based on a joint work with T. Buckmaster and S. Shkoller.
We discuss traveling front solutions u(t,x) = U(x-ct) of reaction-diffusion equations u_t = Lu + f(u) in 1d with ignition reactions f and diffusion operators L generated by symmetric Levy processes X_t. Existence and uniqueness of fronts are well-known in the cases of classical diffusion (i.e., when L is the Laplacian) as well as some non-local diffusion operators. We extend these results to general Levy operators, showing that a weak diffusivity in the underlying process - in the sense that the first moment of X_1 is finite - gives rise to a unique (up to translation) traveling front. We also prove that our result is sharp, showing that no traveling front exists when the first moment of X_1 is infinite.
We discuss two models of random walk in random environment, one from stochastic homogenization of composite materials, and the other from interacting particle systems. The goal is to explore the quantitative aspects of the invariance principle, i.e., to quantify the convergence of the properly rescaled random walk to a Brownian motion. The idea is to borrow PDE/analytic tools from stochastic homogenization of divergence form operator and apply them in the context of interacting particle systems. In particular, we will explain the proof of a diffusive heat kernel upper bound on the tagged particle in a symmetric simple exclusion process.
In this talk, we will discuss recent advances towards understanding the regularity hypotheses in the theorem of Mouhot and Villani on Landau damping near equilibrium for the Vlasov-Poisson equations. We show that, in general, their theorem cannot be extended to any Sobolev space for the 1D periodic case. This is demonstrated by constructing arbitrarily small solutions with a sequence of nonlinear oscillations, known as plasma echoes, which damp at a rate arbitrarily slow compared to the linearized Vlasov equations. Some connections with hydrodynamic stability problems will be discussed if time permits.
Nuclear magnetic resonance (NMR) spectroscopy is the most-used technique for protein structure determination besides X-ray crystallography. In this talk, the computational problem of protein structuring from residual dipolar coupling (RDC) will be discussed. Typically the 3D structure of a protein is obtained through finding the coordinates of atoms subject to pairwise distance constraints. RDC measurements provide additional geometric information on the angles between bond directions and the principal-axis-frame. The optimization problem involving RDC is non-convex and we present a novel convex programming relaxation to it by incorporating quaternion algebra. In simulations we attain the Cramer-Rao lower bound with relatively efficient running time. From real data, we obtain the protein backbone structure for ubiquitin with 1 Angstrom resolution. This is joint work with Amit Singer and David Cowburn.
The question addressed here is how fast a front will propagate when a line, having a strong diffusion of its own, exchanges mass with a reactive medium. More precisely,we wish to know how much the diffusion on the line will affect the overall front propagation. This setting was proposed (collaboration with H. Berestycki and L. Rossi) as a model of how biological invasions can be enhanced by transportation networks. In a previous series of works, we were able to show that the line could speed up propagation indefinitely with its diffusivity. For that, we used a special type of nonlinearity that allowed the reduction of the problem to explicit computations. In the work presented here, the reactive medium is governed by nonlinearity that does not allow explicit computations anymore. We will explain how propagation speed-up still holds. In doing so, we will discuss a new transition phenomenon between two speeds of different orders of magnitude. Joint work with L. Dietrich.
For questions, contact
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s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698541187.54/warc/CC-MAIN-20161202170901-00296-ip-10-31-129-80.ec2.internal.warc.gz
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CC-MAIN-2016-50
| 7,959 | 13 |
https://studenttheses.uu.nl/handle/20.500.12932/19547
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math
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Dynamic programming on Nice Tree Decompositions
Graaff, L.W. van der
MetadataShow full item record
Connectivity problems such as the Steiner Tree Problem are NP-hard problems that are fixed parameter tractable in the treewidth of the input graph. In this thesis a dynamic programming algorithm on nice tree decompositions is discussed. Based on observations on nice tree decomposition diversity and experiment results, a number of optimization heuristics are proposed to speed up computation. By restructuring the nice tree decomposition, all tested input graphs show a considerable improvement both in amount of processed partial solutions as well as computation time. Furthermore a number of different data structures are analyzed, that allow for various constant time operations for graphs of low treewidth.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296816863.40/warc/CC-MAIN-20240414002233-20240414032233-00756.warc.gz
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CC-MAIN-2024-18
| 810 | 4 |
https://nrich.maths.org/public/topic.php?code=5039&cl=2&cldcmpid=13349
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math
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Try entering different sets of numbers in the number pyramids. How does the total at the top change?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?
We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4
The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?
Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .
Can you explain the strategy for winning this game with any target?
A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?
A card pairing game involving knowledge of simple ratio.
Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?
Can you discover whether this is a fair game?
Meg and Mo still need to hang their marbles so that they balance, but this time the constraints are different. Use the interactivity to experiment and find out what they need to do.
A game for two people that can be played with pencils and paper. Combine your knowledge of coordinates with some strategic thinking.
A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!
The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.
A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
An interactive activity for one to experiment with a tricky tessellation
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .
A generic circular pegboard resource.
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
A train building game for 2 players.
Train game for an adult and child. Who will be the first to make the train?
A simulation of target archery practice
Mo has left, but Meg is still experimenting. Use the interactivity to help you find out how she can alter her pouch of marbles and still keep the two pouches balanced.
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
Here is a chance to play a version of the classic Countdown Game.
A game for 1 person to play on screen. Practise your number bonds whilst improving your memory
Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?
An animation that helps you understand the game of Nim.
Use the interactivity or play this dice game yourself. How could you make it fair?
Work out the fractions to match the cards with the same amount of money.
Meg and Mo need to hang their marbles so that they balance. Use the interactivity to experiment and find out what they need to do.
Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?
Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?
Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
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s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496669276.41/warc/CC-MAIN-20191117192728-20191117220728-00296.warc.gz
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CC-MAIN-2019-47
| 5,918 | 49 |
http://panasonicapac.mynewsdesk.com/blog_posts/tag/corporate
|
math
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Blog posts • Nov 03, 2015 14:32 +08
As smart cities are becoming more and more prevalent around the world, we also see an increasing number of new innovations in design and technology. However, it is often easy to simply associate ‘smart’ with buildings or cities that run in automation or with robotics and provide connection to data and services in order to improve services and eco-friendliness.
Blog posts • Aug 12, 2015 10:00 +08
As the technology for generating and managing renewable energy sources becomes more sophisticated, a rising number of governments, companies and private consumers are waking up to the possibilities of sustainable alternatives to fossil fuels. But one of the main criticisms that persist is their lack of aesthetic appeal. How is this evolving and winning over customers in society today?
Blog posts • Aug 05, 2015 11:17 +08
Modern advancements in digital technology, have steadily reduced the need for obtrusive physical barriers and there is a growing trend towards ultra-discreet security systems and low-profile personal safety solutions among Asia’s wealthy.
Blog posts • Jul 15, 2015 17:19 +08
Energy needs pose various challenges for ASEAN countries as economic development reaches unprecedented growth in the past 25 years. Read how each country has been looking at opportunities in renewable resources.
Blog posts • Jul 01, 2015 13:00 +08
Though there may be some who continue to debate its very existence, it is difficult to deny that climate change is one of the defining issues of our time. And while tackling the problem relies largely on governments making changes at a global level, increased awareness of the causes of climate change has led to a seismic shift in mindset at the consumer level.
Blog posts • Jun 25, 2015 09:30 +08
Billed as the future of urban living, “smart” cities have been on the horizon—and the drawing board—for more than a decade. But this new breed of digitally integrated metropolis, in which embedded technology is used to enhance standards of living and sustainability, is no longer a mere pipe dream as the first wave of “smart” cities has come to fruition in a variety of locations around the world.
Blog posts • Jun 19, 2015 09:07 +08
In a society where technology is ubiquitous, we often think little of electrical outlets or how we access electricity to power modern conveniences. However, to technicians and home builders, safe and high quality wiring devices remain top concerns.
Blog posts • Jun 08, 2015 15:00 +08
Recent flooding in Malaysia and Indonesia highlight the need for improvements in water management systems. We take a look home water management systems which can be used to mitigate the effects of heavy rainfall and also make water available for use in times of drought.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583514497.14/warc/CC-MAIN-20181022025852-20181022051352-00245.warc.gz
|
CC-MAIN-2018-43
| 2,821 | 16 |
https://www.jiskha.com/display.cgi?id=1381203607
|
math
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physics mechanical energy and power
posted by carlo .
A car m = 1850 kg is traveling at a constant speed of v = 30 m/s. The car experiences a force of drag (air resistance) of Fd = 300 N.
Write an expression for the power the car must produce Pi to maintain its speed.
Part (b) What is the power in HP?
No Attempt No Attempt Part
(c) The car encounters an incline which makes an angle of θ = 12 degrees with respect to the horizontal. The cruise control kicks in and increases the cars power to maintain its speed. What is the new power (in HP) required to maintain a constant speed?
P(i)=F(d) •v =300 •30=9000 W=12.07 hp
=(300+1850•9.8•sin12) •30 =
=18231.3 W=24.45 hp
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s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886110792.29/warc/CC-MAIN-20170822143101-20170822163101-00554.warc.gz
|
CC-MAIN-2017-34
| 680 | 10 |
http://hermeneutics.stackexchange.com/questions/tagged/isaiah+satan
|
math
|
Biblical Hermeneutics Meta
to customize your list.
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Why is Isaiah 14:12-15 interpreted by some to refer to Satan?
Is 14:12 “How you are fallen from heaven, O Lucifer, son of the morning! How you are cut down to the ground, You who weakened the nations! 13 For you have said in your heart: ‘I will ...
Jan 18 at 16:24
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s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997873839.53/warc/CC-MAIN-20140722025753-00118-ip-10-33-131-23.ec2.internal.warc.gz
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CC-MAIN-2014-23
| 2,325 | 53 |
http://maths.york.ac.uk/www/PhysicsPublications
|
math
|
A full list of publications by all members of the Department is also available.
Asymptotically thermal responses for smoothly switched detectors. XIV Marcel Grossmann Meeting.. Submitted.
A 3D spinorial view of 4D exceptional phenomena. SIGMAP, Proceedings in Mathematics and Statistics Series.. In Press.
Characterization of local observables in integrable quantum field theories. Communications in Mathematical Physics.. In Press.
Quantum Measurements Constrained by Symmetries. The XXIXth International Colloquium on Group-Theoretical Methods in Physics.. In Press.
Time, chance and quantum theory. Probing the Meaning and Structure of Quantum Mechanics: Superpositions, Semantics, Dynamics and Identity.. In Press.
Von Neumann entropy and majorization. Journal of Mathematical Analysis and Applications.. In Press.
The birth of $E_8$ out of the spinors of the icosahedron. Proceedings of the Royal Society A.. 2016.
Algebraic quantum field theory in curved spacetimes. Advances in Algebraic Quantum Field Theory. :pp125-189.. 2015.
Clifford algebra is the natural framework for root systems and Coxeter groups. Group theory: Coxeter, conformal and modular groups. Advances in Applied Clifford Algebras.. 2015.
Lax Operator for Macdonald Symmetric Functions. Letters in Mathematical Physics. 105(7):901-916.. 2015.
Locally covariant quantum field theory and the problem of formulating the same physics in all spacetimes. Phil. Trans. R. Soc. A. 373:1-16.. 2015.
Department of Mathematics, University of York, Heslington, York, UK. YO10 5DD
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s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701166261.11/warc/CC-MAIN-20160205193926-00299-ip-10-236-182-209.ec2.internal.warc.gz
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CC-MAIN-2016-07
| 1,542 | 13 |
https://honestlyaine.com/skin-diseases/how-do-you-find-the-moles-of-a-solution.html
|
math
|
How do you find moles of solute in a solution?
The number of moles of solute = mass of solute ÷ molar mass of solute, where mass is measured in grams and molar mass (defined as the mass of one mole of a substance in grams) is measured in g/mol.
How do you find the moles of particles in a solution?
Calculating the number of particles
- The number of particles in a substance can be calculated using:
- Number of particles = Avogadro constant × the amount of substance in mol.
- Calculate the number of water molecules in 0.5 mol of water.
- Number of water molecules = Avogadro constant x amount of substance in mol.
How do you find the moles of a solution with molarity?
The molarity (M) of a solution is the number of moles of solute dissolved in one liter of solution. To calculate the molarity of a solution, you divide the moles of solute by the volume of the solution expressed in liters.
What is the mole formula?
Avogadro’s number is a very important relationship to remember: 1 mole = 6.022×1023 6.022 × 10 23 atoms, molecules, protons, etc. To convert from moles to atoms, multiply the molar amount by Avogadro’s number. To convert from atoms to moles, divide the atom amount by Avogadro’s number (or multiply by its reciprocal).
How do you find the number of moles in a liquid?
MOLES FROM VOLUME OF PURE LIQUID OR SOLID
Multiply the volume by the density to get the mass. Divide the mass by the molar mass to get the number of moles.
How many moles are in a solution?
To calculate the number of moles in a solution given the molarity, we multiply the molarity by total volume of the solution in liters. How many moles of potassium chloride (KCl) are in 4.0 L of a 0.65 M solution? There are 2.6 moles of KCl in a 0.65 M solution that occupies 4.0 L.
How do you find the particles in a solution?
Divide the number of moles by the volume of solution in liters (L). If, for instance, the solution is 1.5 L — 1.32 ÷ 1.5 = 0.88. This is the solution’s particle concentration, measured in molarity (M), or moles per liter.
How do you find the number of moles in a substance?
So in order to calculate the number of moles of any substance present in the sample, we simply divide the given weight of the substance by its molar mass. Where ‘n’ is the number of moles, ‘m’ is the given mass and ‘M’ is the molar mass.
How do you find moles from liters and molarity?
Molarity is a unit of concentration, measuring the number of moles of a solute per liter of solution.
To calculate molarity:
- Find the number of moles of solute dissolved in solution,
- Find the volume of solution in liters, and.
- Divide moles solute by liters solution.
How do you find moles when given molarity and liters?
Compute the volume of a solution in liters, given the number of moles and molarity, by dividing the number of moles by the molarity in units of moles per liter. For example, a solution containing 6.0 moles and a having a molarity of 3.0 moles per liter has a volume of 2.0 moles per liter.
How do you calculate moles from molarity and ML?
The equation for calculating Molarity from the moles and volume is very simple. Just divide moles of solute by volume of solution.
How do you calculate moles step by step?
How to find moles?
- Measure the weight of your substance.
- Use a periodic table to find its atomic or molecular mass.
- Divide the weight by the atomic or molecular mass.
- Check your results with Omni Calculator.
How do you calculate 1 mole of oxygen?
Calculate the number of oxygen atoms in 1 mole of O2. Solution — 1 molecule of O2 = 2 oxygen atoms So, 1 mole of O2 = 2 mole oxygen atoms = 2 × 6.022 × 1023 = 12.044 ×1023 oxygen atoms.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030334855.91/warc/CC-MAIN-20220926082131-20220926112131-00217.warc.gz
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CC-MAIN-2022-40
| 3,677 | 39 |
https://testmaxprep.com/lsat/community/100005103-how-is-the-answer-a
|
math
|
on November 20, 2019
I read the passage a few times and can't really understand why the answer is A. We know the results were positive and the studies were flawed, so the treatment is probably not effective.
Answer choice A says that the judges did not have uniform criteria. Is this the parallel methodological flaw we found in the passage? So, because the judges did not have uniform criteria, their winner (treatment) is flawed, or is a bad one?
Thanks in advance.
Irina on November 20, 2019
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710237.57/warc/CC-MAIN-20221127105736-20221127135736-00825.warc.gz
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CC-MAIN-2022-49
| 494 | 5 |
http://www.i-maps.com/hotel-locator/usa/poi/4113.html
|
math
|
Welcome to I-Maps Hotel Locator
Launch the map to get a list of hotels near Community General Hospital. The list will adjust to match the hotels shown on the map each time you zoom or center the map.
The map's hotel list uses the format shown on the right. The annual average rates are shown in small text above the latest observed rates. Check the difference to identify low rates.
Enter your dates on the left to set the rate links on the hotel list. Use the rate links to get the current available rates and reserve rooms. more info...
See Hotel Price Categories below for hotel classification price breaks.
See the Discount Hotels Page for the best deals.
Use the Rate Table on the Syracuse, NY page to compare rates for all Syracuse hotels. Check the high and low rates for below average values.
Syracuse, NY Hotel Rate Information
Hotel Price Categories for Syracuse, New York
The hotels on the map are grouped into color coded price categories based on their average room rates. The average rate for each hotel is calculated from the average of it's high and low room rates observed over a period of one year.
The latest hotel rate analysis for Syracuse, NY was performed on April 7, 2009. The analysis is based on the average room rates for hotels within Syracuse, NY and adjacent towns forming the Syracuse, NY Metropolitan Statistical Area. The current classification breaks based on this analysis are as follows:
Deluxe Hotels (Magenta) :
Moderate Hotels (Cyan) :
Budget Hotels (Green) :
average room rate > $154
average room rate is $80 to $154
average room rate < $80
See Hotel Rate Analysis and Classification Details on the Syracuse, NY page for a detailed explanation of the classification breaks.
Hotel Search and Rate Comparison
Use the map to reduce the list of hotels to the area you are interested in. As you zoom in, the list of hotels on the sidebar will adjust to match the hotels you see on the map.
The map's hotel list includes the annual average rates, the latest observed rates, and hyperlinks associated with each hotel.
The average high and low rates are presented for comparison to the latest observed rates. The average rates are displayed in small text ( low | high ) above the latest observed rates.
The lastest observed rates are presented in bold text on the hotel list. The observed rates are updated daily.
The current rates and availability for each hotel may be accessed through the rate links on the map's hotel list. The rate links may be set to retrieve rates and availabilty for a specific number of occupants on specific dates by setting values in the above Set Rate Requests selection box.
See the Rate Table on the Syracuse, NY page for more information on rates and links to graphs showing the rate history of each hotel.
A list of room rates for all currently available Syracuse, NY Hotels may be accessed through the following link:
For more information about the map, see the help link below.Open Help Window: Locator Map Help
United States : New York
Syracuse, NY Hotels
Cities Near SyracuseAuburn
Airport - TransportationSyracuse Hancock International Airport (SYR)
Art Galleries & DealersMinette Porcelain Wildlife
Beech Street Gallery
Hospitals & Medical Care FacilitiesCommunity General Hospital
Hutchings Psychiatric Center
Madison Irving Surgery Center
St. Joseph's Hospital Health Center
US Veterans Medical Center
Van Duyn Home and Hospital
MuseumsEverson Museum of Art
Museum of Automobile History
Ner-A-Car Museum of Syracuse
Onondaga Historical Society
Parke S Avery Historical House
Science Centers - Nature CentersDiscovery Center of Science
Stadiums - Arenas - Athletic FieldsAli Brandi Stadium
P and C Stadium
Carrier Dome - Syracuse University
War Memorial at Onecenter
Universities & CollegesLe Moyne College
Onondaga Community College
St Joseph's School of Nursing
Upstate Medical University
Syracuse Hotel ChainsBest Western
Courtyard by Marriott
Historic Hotels of America
Historic Hotels Of America
Holiday Inn Express
Red Roof Inns
Renaissance Hotels and Resorts
Residence Inn by Marriott
Sheraton Hotels and Resorts
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https://www.clutchprep.com/chemistry/practice-problems/102675/if-the-gas-inside-the-flask-is-cooled-so-that-its-pressure-is-reduced-from-797-3
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math
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🤓 Based on our data, we think this question is relevant for Professor Williams' class at GS.
Recall that when the height of the gas in an open end arm is higher compared to the one next to the gas:
Pinitial = Patm + height difference (Pgas = Pinitial)
If the gas inside the flask is cooled so that its pressure is reduced from 797.3 torr to a value of 715.7 torr what will be the height of the mercury in the open-end arm? (Hint: The sum of the heights in both arms must remain constant regardless of the change in pressure.)
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| 528 | 4 |
https://research.tue.nl/en/publications/support-for-problem-solving-in-manpower-planning-problems
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math
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In this paper we describe the construction of problem solving strategies in the context of a well-defined decision situation in which various problem situations are of interest, such as in manpower planning situations. The problem solving component of the system consists of a set of basic mathematical algorithms that can be combined to solution strategies to the stated problems. An analysis process is needed that converts the stated problem to a set of subproblems that can be solved by the available mathematical algorithms. The analysis process consists of an aggregation stage and a decomposition stage. The aim of aggregation is to decrease the size of the problem by neglecting the irrelevant information. The aim of decomposition is to be able to solve rather complex problems by the separation into sets of subproblems.
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https://math.answers.com/Q/How_do_you_factor_the_trinomial_6b2-13bs-63s2
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math
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That trinomial is unfactorable (the roots are not integers).
just like factoring any other trinomial.
That is the linear part.
Change all the signs in the trinomial and then proceed as normal.
(y10 + 2y5z3 + 4z6)
That's not a trinomial, but it factors to x(x + 19)
Take a trinomial. 2x2 - 3x - 2 Factor it. (2x + 1)(x - 2) Repeat as necessary.
You would factor out -1 (a) from a trinomial in an equation such as -a^2 +30a - 2a + 60 after the middle term has been separated. The final answer of this trinomial would then be (a-30) (a-30).
A factor of a perfect square trinomial is eithera number that is a factor of each term of the trinomial,a binomial that is a factor of the trinomial, ora product of the above two.For example, consider 4x2 + 8x + 4It has the factors2 or 4,(x + 1) or2x+2 = 2*(x+1) or 4x+4 = 4*(x+1)
It's not enough to copy the question off the test. If you don't tell us what the trinomial is, we can't factor it for you.
x + 8orx - 4
(3x - y)(3x - 5y) and (2x + 1)(2x + 11)
bobo ka kasi patal
The factors of that trinomial are (x - 13) and (x + 3) . Neither of them appears below.
factor the trinomial 16x^2+24x+9
To factor a trinomial square take the square roots of the end terms and join them with a plus sign if the middle term is preceded by a plus or with a minus if the middle term is preceded by a minus.
(x + 1)(x - 4)
. x + 4
x - 12
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http://www.omnilexica.com/?q=-Manifold
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math
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On this page:
Definition of the noun -Manifold
What does -Manifold mean as a name of something?
- [mathematics] A manifold of the specified number of dimensions.
Printed books with definitions for -Manifold
Click on a title to look inside that book (if available):
by R. H. Bing
An n-manifold is a metric space each of whose points has a neighborhood homeomorphic with Euclidean n-space En. Each point of an n- manifold with boundary has...
Hence, an n-manifold is an n-manifold with boundary but not conversely.
Foundations of Topology (2012)
by C. Wayne Patty
A topological n-dimensional manifold or n-manifold is a second count- able Hausdorff space in which each point has a neighborhood that is homeomorphic to the open disc . A 1-manifold is called a curve and a 2- manifold is called a surface.
Online dictionaries and encyclopedias with entries for -Manifold
Click on a label to prioritize search results according to that topic:
Quotes about -Manifold
I think most of us sense that it is a responsibility of the humanities to try to help better the conduct of human beings in their lives and manifold professional activities. (J. Irwin Miller)
more quotes about -manifold...
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Go to the usage examples of -Manifold to see it in context!
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https://tyjizukykazavo.elizrosshubbell.com/systems-of-incongruences-in-a-proof-on-addition-mod-m-book-3879mi.php
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math
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2 edition of Systems of incongruences in a proof on addition mod m found in the catalog.
Systems of incongruences in a proof on addition mod m
Santiago Sologuren P.
Written in English
|Statement||by Santiago Sologuren P.|
|The Physical Object|
|Pagination||, 59 leaves, bound ;|
|Number of Pages||59|
Credits and distribution permission. Other user's assets All the assets in this file belong to the author, or are from free-to-use modder's resources; Upload permission You can upload this file to other sites but you must credit me as the creator of the file; Modification permission You are allowed to modify my files and release bug fixes or improve on the . By the way we constructed D from E, E*D = 1 (mod (P -1)*(Q -1)), so M ED (mod N) = M. Try working with this cipher yourself, using the RSA secret-sharing worksheet. Final Thoughts. Now, if you ever hear anything in the news about a large number being .
x 2 + 3q(mod 5): You should read the proofs of Theorem and Theorem very carefully. These proofs actually show you the necessary techniques to solve all linear congru-ences of the form ax b(mod n), and all simultaneous linear equations of the form x a(mod n) and x b(mod m), where the moduli nand mare relatively prime. Main article: Divisibility Rules Divisibility rules are efficient shortcut methods to check whether a given number is completely divisible by another number or not. These divisibility tests, though initially made only for the set of natural numbers (N), (\mathbb N), (N), can be applied to the set of all integers (Z) (\mathbb Z) (Z) as well if we just ignore the signs and employ our.
This article is intended for troubleshooting the PlayStation 4 and Nintendo Switch versions of Minecraft. If you are experiencing any issues with lagging, crashing, and hanging on the Switch and PS4 platfor. This book is full of worked out examples. We use the the notation “Solu-tion.” to indicate where the reasoning for a problem begins; the symbol is used to indicate the end of the solution to a problem. There is a Table of Contents that is useful in helping you find a .
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Systems of incongruences in a proof on addition mod m Public Deposited. Analytics × Add Author: Santiago Sologuren P. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in A familiar use of modular arithmetic is in the hour clock, in which the.
Proof. Since a b(mod m) and c d(mod m), by the Theorem above there are integers s and t Systems of incongruences in a proof on addition mod m book b = a +sm and d = c +tm. Therefore, The operation +m is defined as a +m b = (a +b) mod m.
This is addition modulo m. The operation m is defined as a m b = (a b) mod m. This is multiplication modulo m. r we have a ” r (mod m)".This is perfectly fine, because as I mentioned earlier many texts give the intuitive idea as a lemma.
The number r in the proof is called the least residue of the number a modulo m. Exercise 1: Find the least residue of (a) mod 3, (b) (c) and (d) mod Congruences act like equalities in many ways. Most downloaded worksheets. Ones to thousands ( KiB, 6, hits); Integers - hard ( MiB, 5, hits); Solving word problems using integers ( KiB, 4, Contents Preface vii Introduction viii I Fundamentals 1.
Sets 3 IntroductiontoSets 3 TheCartesianProduct 8 Subsets 11 PowerSets 14 Union,Intersection,Difference > Microwave And Rf Design Of Wireless Systems by David M.
Pozar > An Introduction to Signals and Systems,1ed, by John Stuller > Control Systems Engineering, 4th Edition,by Norman S.
Nise > Physics for Scientists and Engineers,5ed,A. Serway,vol1 > Laser Fundamentals,2ed, by William T. Silfvast. Modular arithmetic is a system of arithmetic for integers, which considers the remainder. In modular arithmetic, numbers "wrap around" upon reaching a given fixed quantity (this given quantity is known as the modulus) to leave a remainder.
Modular arithmetic is often tied to prime numbers, for instance, in Wilson's theorem, Lucas's theorem, and Hensel's lemma, and. The goal of this book is to bring the reader closer to this world. The reader is strongly encouraged to do every exercise in this book, checking their answers in the back (where many, but not all, solutions are given).
Also, throughout the text there, are examples of calculations done using the powerful free open source mathematical software system. a≡b (mod m) is read as "a is congruent to b mod m". In a simple, but not wholly correct way, we can think of a≡b (mod m) to mean "a is the remainder when b is divided by m".
For instance, 2≡12 (mod 10) means that 2 is the remainder when 12 is divided by (j +k) of m. In symbols, we have: a+c ⌘ b+d (mod m), (68) as desired.
A similar proof can be used to show that if a ⌘ b (mod m) and c ⌘ d (mod m), then ac ⌘ bd (mod m). These two results allow us to treat all numbers that are congruent modulo m as identical when adding and subtracting numbers.
If we know that a ⌘ 3. Mod [m, n] gives the remainder of m divided by n. Mod [m, n] is equivalent to m-n Quotient [m, n]. For positive integers m and n, Mod [m, n] is an integer between 0 and n Mod [m, n, d] gives a result such that and. NASA SYSTEMS ENGINEERING HANDBOOK viii Preface S ince the initial writing of NASA/SP in and the following revision (Rev 1) insystems engineering as a discipline at the National Aeronautics and Space Administration (NASA) has undergone rapid and continued evolution.
Changes include using Model-Based Systems Engineering to improve. Books at Amazon. The Books homepage helps you explore Earth's Biggest Bookstore without ever leaving the comfort of your couch.
Here you'll find current best sellers in books, new releases in books, deals in books, Kindle. Modulo Challenge (Addition and Subtraction) Modular multiplication. Practice: Modular multiplication. Modular exponentiation. Fast modular exponentiation.
Fast Modular Exponentiation. Modular inverses. The Euclidean Algorithm. Next lesson. Primality test. Addition, subtraction, multiplication are binary operations on Z. Addition is a binary operation on Q because Division is NOT a binary operation on Z because Division is a binary operation on Classi cation of binary operations by their properties Associative and Commutative Laws DEFINITION 2.
A binary operation on Ais associative if. m and Complete Residue Systems 43 17 Addition and Multiplication in Z 21 Probabilistic Primality Tests 55 22 Representations in Other Bases 57 23 Computation of aN mod m 59 24 Public Key Cryptosystems 63 A Proof by Induction 67 B Axioms for Z 69 C Some Properties of R Chapter 1 Divisibility In this book, all numbers are integers, unless.
Proof Marks, Arsenal & Inspector Marks. In addition to arsenal marks, you will find other marks or stampings. These include the date, serial number and property marks as well as various acceptance and proof marks.
I have not been able to locate an authoritative resource for identifying the acceptance and proof marks as it appears, many. Me×d ≡Me×d (mod φ(n)) ≡M (mod n) •The result shown above, which follows directly from Euler’s theorem, requires that M and n be coprime.
However, as will be shown in Sectionwhen n is a product of two primes p and q, this result applies to all M, 0 ≤M. m!n!(m+ n). is an integer. 2 IMO /3 A Show that the coe cients of a binomial expansion (a+ b)n where nis a positive integer, are all odd, if and only if nis of the form 2k 1 for some positive integer k.
A Prove that the expression gcd(m;n) n n m is an integer for all pairs of positive integers (m;n) with n m 1. Putnam A. In programming language theory and proof theory, the Curry–Howard correspondence (also known as the Curry–Howard isomorphism or equivalence, or the proofs-as-programs and propositions-or formulae-as-types interpretation) is the direct relationship between computer programs and mathematical proofs.
It is a generalization of a syntactic analogy between systems .The system x a k modm k, k 1, 2,n has a unique solution modulo M m 1 m 2 m n. Proof. First we prove that the system has a solution.
Proceeding as in the above example, we define solution to each equation as y k a k modm k y k 0 mod m j, k j Combining them together yeilds the equation V. Adamchik 9.notion of ordering mod m.
In R you know x2 = y2)x= y, but it is false that a2 b2 mod m)a bmod m in general. Consider 42 12 mod 15 with 4 6 1 mod In R you are used to x3 = y3)x= y. But 23 13 mod 7 and 2 6 1 mod 7. When we add and multiply modulo m, we are carrying out modular arithmetic.
That addition and multiplication can be carried out on.
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https://www.coursehero.com/file/153490/Quiz-5-Solns/
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math
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Phys320 – Spring 2004 (Baski) Quiz #6: Nuclear Physics April 21, 2004 Name: ___SOLUTIONS_____ Complete both of the following problems. Show all of your work for full credit. Problem 1: Radioactivity The counting rate from a radioactive source is initially 4 million decays per second, and it decreases to 500,000 s–1after 6 seconds. Find the τand half-life of this source in seconds. Also, find the counting rate after 20 seconds has elapsed. Solving for τin the decay equation R = Roe– t/τgives: ( 29( 291/2656116s2.885 sandln2(2.885)(0.693)2.0s410lnln510exp(410)exp20s2.885s3,903soottttRRRRtst--======
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http://jbessayyktw.ultimatestructuredwater.info/how-much-should-i-charge-to-proofread-a-thesis.html
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math
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How much should i charge to proofread a thesis
Professional english proofreading and editing services trusted by thousands of esl speakers dissertation/thesis proofreading and editing services dissertation/thesis proofreading and editing services if you are looking for a cheap. Academic proofreading for students and tutors thesis and coursework proofreading excellent service and value for money. What is a reasonable rate to charge for editing someone else's thesis up vote 5 down vote favorite i'm a phd student in engineering should i charge entry for a public lecture 1 how do i get editing help for technical (mathematic/statistic. I can correct grammatical errors and make sure the thesis has a clear structure however, i' how much should i charge most proof readers charge for every page they check for spelling/gramatical errors. 'thank you for doing such a phenomenal job i was unsure whether i should spend the money to have my thesis edited but you have made it worth my while all editing prices are based on the length of your document and how soon you would like it returned all. Faq have a question that isn't answered here we provide the right editor to get the job done, whether it's dissertation editing, thesis editing, book editing we'll be happy to check them for no additional charge. A startling fact about how much should i charge to proofread a thesis, honesty is the best policy story essay meaning, bosch ppr 250 essay, trees essay in telugu uncovered.
Discussion among translators, entitled: rate for proofreading/editing a phd dissertation forum name: proofreading / editing / reviewing terminology kudoz help network ™ term search but should i really try to charge that much this time. Proofreading agencies are filling an academic support gap in uk universities up to universities to create proofreading policies says: i once had a phd student whose thesis was so much better than her command of english led me to expect. Editing and proofreading rates portrait of m diego martelli by federico zandomeneghi, 1879 there will be an additional charge, as the editing process takes much longer to complete with the pdf editing tools available. Scribendicom answers the popular question: how much does editing cost english dissertation, thesis english is not my first language i need english editing and proofreading so that i sound like a native speaker. He said it has been edited in the past as well but would like me to go over it again i have proofread some of his shorter papers (for free) in the past how much should i charge also, do i charge by the hour or by the page.
Again, this is just in my experience a note of caution: i would only charge a job rate if i had a lot of experience with the material at hand and knew that i could work through it pretty quickly what to charge for proofreading, copyediting, writing, etc written by yuwanda, site editor. Premium nigerian website design company and online advertising agency/digital marketing. Beyond the basics how much should i charge by lynn wasnak i f you're a beginning freelance writer, or don't know many other freelancers, you may.
How much should you charge/pay for proofreading or editing as an editor - how much should you charge as a writer, how much should you pay unfortunately there is no standard 'going rate' for editing editors have unique styles and services. 113 responses to how should you charge for freelance editing vitaeus says: i'm so glad i found this site as i have been asked how much i would charge to proofread by a brand new author i'm not working so i have been known to read all day long. How much does online thesis writing help cost other services that may come at an additional cost: editing, proofreading, formatting and/or revisions keep in mind that if you write your own paper, the cost may be lower depending on the company. If i am to research (conduct interviews for a psychology thesis), and then write 50-60 pages of a masters thesis, how much should i expect to get paid.
How much should i charge to proofread a thesis
I am in the beginning stages of writing and would like any thoughts on hiring someone to proofread my thesis my school offers little help in or do you plan to hire a thesis/dissertation proofreader sign many editors charge by the page or the hour i was amazed at how.
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Have your thesis or dissertation proofread and edited by our highly experienced native english speaking editors 24/7 support, 365 days per year. English dissertation, thesis, or proposal editing how much does proofreading cost if you pay by the word it is much easier to know ahead of time how much proofreading will cost if you choose a proofreader that charges by the word or by the page. Should i get an editor for my thesis july 16 the market sets the rate editors can charge, and as with the economy in general but if i were to start writing my thesis and would want an editor to proofread it. So a colleague of mine, for whom english is not a native language, has asked me to edit and proofread their master's thesis, with monetary.
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https://www.jiskha.com/display.cgi?id=1512614256
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posted by Dee
I have a 3 part question that I have the answers for but I am still having issues understanding it. Looking for help with the explanation / steps on how you would get the answer.
1) The width of a rectangular field is 3h yards and it's length is 3 yards longer than the width. The field has a fence around it's perimeter with a gate 4 yards wide.
A) Write an expression for the perimeter of the rectangular field in terms of h, excluding the width of the gate.
(12 h + 2 ) yards
B) It costs $28 per yard to fence the field, excluding the gate. Write an expression that represents the cost of fencing the field.
The cost is 28 (12h + 2 ) dollars
C) If h = 5, find the cost of the fencing, excluding the gate.
The cost is $1,736
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http://redwoodsmedia.com/multiplying-and-dividing-radicals-worksheet/
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math
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multiplying and dividing radicals worksheet
Here is the Multiplying And Dividing Radicals Worksheet section. Here you will find all we have for Multiplying And Dividing Radicals Worksheet. For instance there are many worksheet that you can print here, and if you want to preview the Multiplying And Dividing Radicals Worksheet simply click the link or image and you will take to save page section.
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https://malevus.com/history-of-geometry/
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math
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What is the history of geometry? The term “geometry” is derived from the ancient Greek word “geometria,” which means measurement (-metria) of earth or land (geo), but this branch of mathematics covers much more than mapping. Geometry explains the relationship between shape and size, and also the nature of mathematics and numbers. Find out more about the invention and history of geometry, as well as the pioneers of geometry and the groundbreaking discoveries they made that have shaped the field.
Discovery and Origin of Geometry
Ancient civilizations in places like the Indus Valley and Babylonia roughly 3000 BC are credited with laying the groundwork for geometry. Geometry first appeared in the ancient world as a set of rules and formulas suitable for planning, constructing, astronomy, and solving mathematical problems. These principles included length, area, angle, and volume. Cubic and spherical Indus weights and measures were crafted from chert, jasper, and agate.
Beginning around the 6th century BC, the Greeks expanded this knowledge and, using it, developed the conceptual field currently recognized as “geometry.” Greek philosophers such as Thales (624-545 BC), Pythagoras (570-490 BC), and Plato (428-347 BC) realized the fundamental relationship between the nature of space and geometry and reinforced geometry as an important field of study belonging to mathematics.
Euclid (325-265 BC), who was probably Plato’s student and worked as a teacher in Alexandria, summed up the early Greek geometry in his magnificent work, “Elements,” written in 300 BC, and created scientific principles for geometric models using a handful of simple rules and axioms. The Elements became a standard geometry textbook for over 2000 years.
Let no one ignorant of geometry enter.Plato, Greek philosopher, and mathematician
The Turning Point in the History of Geometry
Throughout the Middle Ages, mathematicians and philosophers from different cultures continued to use geometry to create a model of the universe. But the next major milestone came with the work of the French mathematician and philosopher René Descartes (1596-1650), who lived in the 17th century. Descartes developed coordinate systems to define the positions of the points in two-dimensional and three-dimensional space led to the birth of the field of analytical geometry, a new tool of mathematical algebra to solve and define geometry problems.
Descartes’ work also led to the emergence of far more exotic forms of geometry. Mathematicians had long known that there were regions, such as the surface of a sphere, where the axioms of Euclidean geometry did not apply. The discovery of non-Euclidean geometry helped clarify many more fundamental principles that combined numbers and geometry. In 1899, German mathematician David Hilbert (1862-1943) developed new and more generalized axioms. Throughout the 20th and 21st centuries, these axioms were applied to a wide variety of mathematical cases.
Timeline of the History of Geometry
The timeline of geometry begins with the birth of practical geometry and concludes with fractal geometry.
3000 BC – Practical Geometry
The history of geometry first arose in the Indus Valley and Babylonian civilizations from the need to solve problems such as calculating the volume of material required to build a pyramid. The level of sophistication of some of these early concepts is so high that a contemporary mathematician can struggle to deduce them without resorting to calculus.
300 BC – Spherical Geometry
The Greek astronomer Theodosius of Bithynia (169-100 BC) compiled “spherics” in a book that consolidated the earlier work by Euclid (325-265 BC) and Autolycus of Pitane (360-290 BC) on spherical astronomy. In his Elements book, which was regarded as authoritative all the way up to the early 19th century in the history of geometry, Euclid provided the foundation for geometry.
The spherical geometry allowed calculating areas and angles on spherical surfaces, such as star or planet positions in the imaginary sky sphere used by astronomers, or the locations of points on a map. However, this system does not follow Euclidean rules. In spherical geometry, the sum of a triangle’s angles is more than 180 degrees, and lines that run parallel to each other eventually meet. Euclid is considered the “father of geometry.”
500 BC – Pythagoras
The Greek philosopher named the “Pythagoras theorem”, which calculates the hypotenuse (the longest side) of a right-angled triangle from the lengths of the other edges. The theory that a triangle’s angles would sum to 180 degrees, or two right angles, is attributed to Pythagoras of Samos.
He said that the sum of the squares of the other two sides of a right triangle equals the square of the hypotenuse (the side opposite the right angle). Whenever the ancient engineers knew the lengths of two sides of a right triangle and needed to figure out the third, they used this theorem to do so, just like we do today.
The idea of similar triangles, whereby two triangles are similar if they have the same form but need not have the same size, was also created by Pythagoras (570-490 BC). Pythagoras is remembered as a pivotal figure in the development of geometry.
4th Century BC – Geometric Tools
Since the geometric tools have been around for thousands of years in the history of geometry, their precise historical beginnings are difficult to ascertain. However, the use of geometric instruments to measure, sketch, and build geometric forms and constructions may be traced back to at least the ancient Egyptians and Greeks. The Egyptians employed geometric tools in the building of their pyramids. The Greeks founded the science of geometry and wrote extensively on the use of geometric tools. They have undergone significant changes throughout the time.
The Greek philosopher Plato (428-347 BC) stated that the tools of a true geometer should be limited to a straightedge and a compass, thereby establishing geometry as a science rather than a practical mastery. Euclid (325-265 BC), the “father of geometry,” and subsequent geometers defined the method of creating geometrical forms using certain tools. The ancient Greeks were the first to present building challenges using just a straightedge and compass. Some examples are building a line that is twice as long as another line or a line that divides an angle into two equal halves.
360 BC – Platonic Solids
Plato introduced the concept of the Platonic solids first in his dialogue “Timaeus.” The Platonic solids are known as the five regular convex polyhedra (polygonal bodies), but Plato also combined them with his ideas about the structure of matter in 360 BC. The Platonic solids include five shapes that can be formed by joining similar faces along the edges. The tetrahedron has four faces, the cube has six, the octahedron has eight, the dodecahedron has twelve, and the icosahedron has twenty faces.
In this “Timaeus,” Plato equated the five Platonic solids with the classical elements (earth, air, fire, and water) and the fifth element of the universe, which he named the “quintessence.”
In the history of geometry, mathematicians and philosophers have always had a healthy respect for and fascination with the Platonic solids. They have also found applications in the fields of art, design, and architecture, and have served as inspiration for the development of several additional three-dimensional forms. The Platonic solids are still widely studied and admired for their symmetry and elegance, making them an integral element of modern geometry.
240 BC – Archimedean Solids
The Greek mathematician Pappus of Alexandria (who flourished in 320 AD) described 13 convex polyhedrons, which are uniform polygons with similar edges and corners. In all, there are 14 Archimedean solids, 13 of which are attributed to Archimedes. In his 240 BC book, “Measurement of a Circle,” he detailed his study on these solids. The value of pi was approximated in this book by the Greek mathematician using the Archimedean solids.
Archimedean solids are a class of polyhedra. To qualify as one of these solids, each of the faces of an object must be a congruent regular polygon, and there must be vertices at which two or more polygons intersect. Archimedean solids differ from Platonic solids in that their vertices do not always have the same number of faces meeting.
9th Century – Islamic Geometry
Mathematicians and astronomers of the Islamic world explored the possibilities of spherical geometry. The geometric models used in Islamic decoration during this period are similar to modern fractal geometry.
Geometric principles and the recurrence of geometric patterns are central to Islamic geometry, which is known for its ornate and aesthetically pleasing forms. Stars, polygons, and both regular and irregular tessellations are common components of these patterns.
During the Islamic Golden Age (about the 8th to 13th centuries), Islamic geometry emerged as its own culture. Structures, tiles, textiles, and other ornamental arts all made use of these patterns and designs.
1619 – Kepler’s Polyhedron
German mathematician Johannes Kepler (1571-1630) discovered a new class of polyhedra, known as the star polyhedron. In his 1619 treatise “Harmonices Mundi,” Kepler described a set of four polyhedra. These “Kepler-Poinsot polyhedra” are the small stellated dodecahedron, the great stellated dodecahedron, the great dodecahedron, and the great icosahedron.
The Platonic and Archimedean solids, which are likewise polyhedra but have regular polygons for faces, are closely linked to Kepler’s polyhedra. Kepler’s polyhedra differ from these solids in that not all of their vertices are shared by the same number of faces. In Kepler’s mind, these geometric patterns reflected the underlying structure of the cosmos and hence had a cosmic meaning.
1637 – Analytical Geometry
“La Geométrie,” a fascinating book by the French mathematician and philosopher René Descartes, explains how points in space can be measured by coordinate systems and geometric structures can be described by equations. This is called “analytical geometry,” and it is a field of study.
The study of geometric forms and their attributes is the domain of analytical geometry, often referred to as coordinate geometry or Cartesian geometry. Many consider René Descartes to be the “father” of analytical geometry because of his work in this area.
Prior to the advent of analytical geometry, the measurement and qualities of physical objects and forms were at the center of the geometry field. Descartes’ ideas made possible the abstract analysis and description of geometric forms and their attributes using algebraic techniques.
In addition, he proposed the use of equations to define geometric forms and curves, which allowed for a more accurate and rigorous investigation of these objects and their attributes. Today, many disciplines rely on the tools and techniques developed in analytical geometry, making it an indispensable branch of mathematics in the history of geometry.
1858 – Topology
During the 19th century, mathematicians began to be fascinated by topology, or geometric edges and surfaces rather than specific shapes. The visualized Möbius strip above is an object with a single surface and a single continuous edge.
Topology is the mathematical study of the features of geometrical objects and spaces that remain unchanged while they are continuously deformed. It can be deformed by stretching, bending, and twisting, but not by ripping or gluing.
Leonard Euler, a Swiss mathematician who flourished in the 18th century, is considered the father of modern topology. Using what would become known as graph theory, Euler investigated the topology of polyhedra. Graph theory is the study of networks made up of points and lines.
The notion of the Möbius strip, a surface with just one side and one border, was established by August Ferdinand Möbius and Johann Benedict Listing, who contributed to the advancement of topology in the 19th century. To explore various mathematical objects and structures such as manifolds, knots, and topological spaces, topology evolved into a more abstract and generic discipline in the 20th century.
1882 – The Discovery of the Klein Bottle
German scientist Felix Klein (1849-1925) discovered a shape that has a one-sided surface without any surface borders, which proves to be a geometry with more than three dimensions. Felix Klein initially characterized it in the 19th century as a tool for investigating the characteristics of non-orientable surfaces.
The Klein bottle is not characterized by its geometric form but rather by its attributes and connections to other things, making it a topological entity. It is a mathematical description of a surface with no obvious boundaries, and it may be thought of as a loop that has been twisted and linked to itself.
One of the fascinating features of the Klein bottle is that it can’t be immersed in three-dimensional space without crossing over into itself. Because of this feature, the Klein bottle is notoriously hard to draw to scale, prompting the creation of a number of computer techniques for studying and understanding its features.
20th Century – Fractal Geometry
Our ability to use computers has led to the discovery of fractals, which are equations of detailed models that repeat each other at different scales and produce shapes like the well-known Mandelbrot set and display them in a graphical form.
Mathematically speaking, fractal geometry is the study of the characteristics of geometric objects with both self-similarity and a non-integer dimension. Many definitions of fractals focus on the fact that they are geometric forms with “fractional dimension,” or a dimension that is between a whole number and a fraction.
The French mathematician Henri Poincaré used the word “fractal” to characterize things having a “fractional dimension” in the early 20th century. However, the German mathematician Georg Cantor researched the idea of self-similarity, a central aspect of fractals, far earlier, in the 19th century.
Benoit Mandelbrot, a mathematician born in Poland, is widely recognized as the pioneer of fractal geometry. He made significant contributions to the area in the 1970s. Mandelbrot used the term “fractal geometry” to characterize the emerging area of study he established by using computer graphics to show and analyze the characteristics of fractals.
Fractal geometry has relevance in many modern disciplines, such as physics, biology, and computer science. It’s also used in the development of computer graphics as well as the research of chaotic systems.
The computer’s power allowed us to solve problems such as the four-color theorem, which distinguishes the various regions within a complex map using nothing but four colors in such a way that no two adjacent regions on the map have the same color.
Francis Guthrie introduced the four-color theorem in 1852, then in 1976, Kenneth Appel and Wolfgang Haken used computer systems to verify it. Extensive computer computations were used to prove the four-color theorem, which states that every map can be colored using just four colors.
Useful in many disciplines, including cartography and computer science, the four-color theorem is worth studying. It’s used to make comprehensible maps, and it’s spawned new computational and mathematical methods for investigating and comprehending the characteristics of maps and other spatial systems.
Types of Geometry
Euclidean geometry is analyzing shapes in two dimensions and three dimensions according to the rules established by Euclid, an ancient Greek mathematician. One defining feature of Euclidean geometry is that its definitions and theorems are grounded in axioms, or universally accepted facts.
Euclidean geometry, named after the ancient Greek mathematician who developed it, is one of the most widespread kinds of geometry. Axioms, or fundamental principles, form the foundation of Euclidean geometry. For example, it is an axiom that any two straight lines will meet at a single point. This branch of geometry is very applicable since it explains the behavior of solid forms and objects in the physical world.
This branch of geometry is distinguished from Euclidean geometry by its use of various axioms. Two examples of non-Euclidean geometries are hyperbolic geometry, which uses a different set of axioms for parallel lines, and elliptic geometry, which uses a different set of axioms for the sum of the angles in a triangle.
Some of the assumptions of Euclidean geometry are rejected in non-Euclidean geometry. Hyperbolic geometry, one of the most well-known types of non-Euclidean geometry, is predicated on the premise that two lines can meet in more than one place. This branch of geometry is often used in the investigation of cosmological structure and space-time characteristics.
The focus here is on geometric shapes and transformations that keep length-to-width ratios (the ratios of distances) the same. Perspective drawings and other forms of graphics can be analyzed using projective geometry.
Projective geometry is the study of the characteristics of figures and forms when they are projected onto a two-dimensional plane, making it the third type of geometry. Creating perspective and the appearance of depth on a two-dimensional surface is made possible using this form of geometry, making it useful in art, architecture, and photography.
The fourth type of geometry is topological geometry, which investigates the features of geometric objects that remain the same under continuous deformations like stretching or bending. This geometry is often used in the investigation of sub-atomic structures and cosmological characteristics.
Preserved features of geometric forms during continuous deformations like stretching or bending are the focus of this field of research. Deformable forms have interesting qualities that can be investigated using topology.
Differential geometry is a calculus-based research field in geometry. Curves and surfaces in three dimensions can be analyzed with the help of differential geometry. Numerous branches of science and technology rely heavily on the concepts and methods of differential geometry, such as physics, engineering, and computing. It is used in the investigation of spatial phenomena and the properties of dynamic physical systems.
It is a tool used in physics to learn more about the nature of space-time and how particles and fields behave. Manifolds are high-dimensional spaces used to simulate physical processes and investigate their characteristics.
This type of geometry has many applications in engineering, including the study of surface qualities and the design and analysis of complex systems like airplanes and cars. In computer science, it is used to study data structures and algorithms and what makes them work the way they do.
In algebraic geometry, we apply algebraic concepts and methods to the study of geometry. This field of study focuses on the qualities of shapes whose characteristics can be expressed in terms of equations. This type of geometry studies Algebraic curves, Algebraic surfaces, Algebraic varieties, and also manifolds. These are curves, surfaces, objects, and high-dimensional spaces that can be defined using algebraic equations such as parabolas, planes, ellipsoids, lines, circles or the curvature of space-time.
In general, geometry is a fascinating and intricate mathematical field with several practical applications. Geometry is essential to our knowledge of the world around us, whether we’re trying to figure out how the cosmos formed or conjure up some impressive optical illusions.
- Ray C. Jurgensen, Alfred J. Donnelly, and Mary P. Dolciani. Editorial Advisors Andrew M. Gleason, Albert E. Meder, Jr. Modern School Mathematics: Geometry. Houghton Mifflin Company, ISBN 0-395-13102-2.
- Frits Staal, 1999, “Greek and Vedic Geometry”, Journal of Indian Philosophy, doi:10.1023/A:1004364417713, S2CID 170894641
- Nineteenth Century Geometry – Stanford Encyclopedia of Philosophy
- Rosenfeld, B. A., 1988. A History of Non-Euclidean Geometry: Evolution of the Concept of a Geometric Space, New York: Springer.
- Euclides, Elementa, I. L. Heiberg (ed.), Leipzig: B. G. Teubner, 5 volumes., 1883–88.
- Mathematics Department, University of British Columbia, The Babylonian tabled Plimpton 322.
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https://www.willamette.edu/cla/math/colloquia/index.html
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math
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Calendar of upcoming talks available here
The Mathematics Colloquia is a series of talks by the Willamette University Math Department and visiting speakers. These talks are aimed at faculty and undergraduate math students and will introduce the audience to fun, interesting applications of undergraduate mathematics, as well as more advanced topics in mathematics research. Unless otherwise noted, Colloquium talks will be held Thursdays at 4:00pm in Ford Room 102. Refreshments will be provided. We hope you can join us! If you would like more information, please contact Prof. Erin McNicholas.
Colloquium Schedule 2013-2014
Thursday, March 6th, Ford Hall 102 at 4:10pm
A Prime Producing Polynomial
To me, prime numbers are interesting. Although there are not as many practical applications like in statistics, physics, and engineering; there is a certain mystery and challenge in their study. My study of prime numbers has revealed many unsolved problems. For example, although it is known that many linear functions with integer coefficients and integer input variables will produce a sequence with an infinite number of prime numbers in it (Dirichlet’s Theorem), it is not known if this is the case for polynomials of degree 2 or more. This is the Bouniakowsky Conjecture. This talk will focus on a quadratic polynomial, namely x^2 + x + 41. It is my finding that many restrictions on x will yield an infinite sequence of composite numbers.
Past 2013-14 Talks
2/27 Glencora Borradaile, Oregon State University, School of Electrical Engineering & Computer Science
Min Cuts, Shortest Cycles and Planar Graphs, oh my!
2/20 K. Tucker (a.k.a k-TUCK)
Enumeration and Projection Dependence of 1-Singular Knots
2/20 R. Robinson (a.k.a Ray-Robins)
Convergence of Sequences of Polygons
12/5 Jordan Purdy, Mathematics Dept
Spatial Statistics - Logistic Regression, the Autologistic Model and Mountain Pine Beetle
12/4 Samantha Reynolds, Willamette University '14
College Entrance Exam Firms, Nonprofit Efficiency, and Testing Fees
11/14 Professor Inga Johnson, Mathematics Dept
Topology, Homology and Applications to Data
10/31 Jeff Schreiner-McGraw and Will Agnew-Svoboda
10/24 Nancy Ann Neudauer, Pacific University
What is a Matroid? Investigations of asymptotic enumeration in matroids
10/3 Yumi Li, Math Major
Put Your Thinking CAPS On (Exploring Finite Geometry in the Card Game SET®)
9/19 Ryan Wright, Janrain Inc.
Computing the Coming Robot Apocalypse: The math behind Artificial Intelligence and Machine Learning
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http://www.ck12.org/algebra/Fractional-Exponents/lesson/user:support/Fractional-Exponents/r2/
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math
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If an exponent usually tells you the number of times to multiply the base by itself, what does it mean if the exponent is a fraction? How can you think about and calculate ?
A fraction exponent is related to a root. Raising a number to the power of is the same as taking the square root of the number. If you have , you can think about this expression in multiple ways:
All of these ideas can be summarized as the following rule for fractional exponents:
Simplify the following:
The cube root of 125 is ‘5’.
Evaluate the denominator.
Simplify the following:
The rational exponents represent the exponent and the index of the base. The numerator is the exponent and the denominator is the index.
a) State the following using radicals:
b) State the following using exponents:
Concept Problem Revisited
To determine the value of , there are several methods that can be applied.
‘3’ is the exponent and ‘2’ is the index. Remember the index tells what root to find. The ‘2’ is understood and is never written when the operation is to take the square root of a number or term.
- In an algebraic expression, the base is the variable, number, product or quotient, to which the exponent refers. Some examples are: In the expression , ‘2’ is the base. In the expression , ‘’ is the base.
- In an algebraic expression, the exponent is the number to the upper right of the base that tells how many times to multiply the base times itself. Some examples are:
- In the expression , ‘5’ is the exponent. It means to multiply 2 times itself 5 times as shown here:
- In the expression , ‘4’ is the exponent. It means to multiply times itself 4 times as shown here: .
- Laws of Exponents
- The laws of exponents are the algebra rules and formulas that tell us the operation to perform on the exponents when dealing with exponential expressions.
1. Use the laws of exponents to evaluate the following:
2. Simplify the following using the laws of exponents.
3. Use the laws of exponents to evaluate the following:
- Apply the law of exponents for rational exponents .
- Apply the law of exponents for negative exponents .
- Apply the law of exponents for rational exponents to and . To , apply the law for negative exponents and then the law for rational exponents.
- Numerator divided by denominator:
Express each of the following as a radical and if possible, simplify.
Express each of the following using exponents:
Evaluate each of the following using the laws of exponents:
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https://www.physicsforums.com/threads/impulses-of-squids.269695/
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math
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1. The problem statement, all variables and given/known data Squids and octopuses propel themselves by expelling water. They do this by taking the water into a cavity and then suddenly contracting the cavity, forcing the water to shoot out of an opening. A 6.50 kg squid (including the water in its cavity) that is at rest suddenly sees a dangerous predator. If this squid has 1.75 kg of water in its cavity, at what speed must it expel the water to suddenly achieve a speed of 2.50 m/s to escape the predator? Neglect any drag effects of the surrounding water. 2. Relevant equations m dv/dt=-Vex dm/dt v-vo- -vex loge (m1/m0) 3. The attempt at a solution vex= V/ log (m1/M0) = -2.5 m/s / (log ((6.5-1.75)6.5) = 7.9704 m/s Now I figured out this problem based on the equations that i have and this is the only solution that i keep getting. Am I using the wrong equation or am I entering the numbers wrong? Thanks for the help!
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http://talks.cam.ac.uk/talk/index/40440
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math
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|COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring.|
Dehn twists and free subgroups of the symplectic mapping class group
If you have a question about this talk, please contact Ivan Smith.
Given two Lagrangian spheres in an exact symplectic manifold, we present conditions under which the Dehn twists about them generate a free non-abelian subgroup of the symplectic mapping class group. This extends a result of Ishida for Riemann surfaces. The proof generalises the categorical version of Seidel’s long exact sequence to arbitrary powers of a fixed Dehn twist. Time allowing, we construct families of examples containing such spheres.
This talk is part of the Differential Geometry and Topology Seminar series.
This talk is included in these lists:
Note that ex-directory lists are not shown.
Other listsCultures of the Digital Economy (CoDE) Research Institute, Anglia Ruskin University Computer Laboratory Programming Research Group Seminar Cambridge Neuroscience Seminar, 2011
Other talks1848 in Germany and Austria Towards a more realistic subjective decision theory Meet the Authors Mackenzie-Stuart Lecture 2017 Pre-Publication Considerations: Publishing your Research Effectively (for STEM PhD Students) Post-war Politics in Southern Europe
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http://causeofyou.net/find/variational-methods-in-statistics-mathematics-in-science-engineering/
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math
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Variational Methods In Statistics Mathematics In Science Engineering PDF EPUB Download
Variational Methods In Statistics Mathematics In Science Engineering also available in docx and mobi. Read Variational Methods In Statistics Mathematics In Science Engineering online, read in mobile or Kindle.
There is a resurgence of applications in which the calculus of variations has direct relevance. In addition to application to solid mechanics and dynamics, it is now being applied in a variety of numerical methods, numerical grid generation, modern physics, various optimization settings and fluid dynamics. Many applications, such as nonlinear optimal control theory applied to continuous systems, have only recently become tractable computationally, with the advent of advanced algorithms and large computer systems. This book reflects the strong connection between calculus of variations and the applications for which variational methods form the fundamental foundation. The mathematical fundamentals of calculus of variations (at least those necessary to pursue applications) is rather compact and is contained in a single chapter of the book. The majority of the text consists of applications of variational calculus for a variety of fields.
Distributions, Hilbert Space Operators, and Variational Methods
Author: Philippe Blanchard
Publisher: Springer Science & Business Media
Physics has long been regarded as a wellspring of mathematical problems. Mathematical Methods in Physics is a self-contained presentation, driven by historic motivations, excellent examples, detailed proofs, and a focus on those parts of mathematics that are needed in more ambitious courses on quantum mechanics and classical and quantum field theory. Aimed primarily at a broad community of graduate students in mathematics, mathematical physics, physics and engineering, as well as researchers in these disciplines.
Variational Methods in Image Processing presents the principles, techniques, and applications of variational image processing. The text focuses on variational models, their corresponding Euler–Lagrange equations, and numerical implementations for image processing. It balances traditional computational models with more modern techniques that solve the latest challenges introduced by new image acquisition devices. The book addresses the most important problems in image processing along with other related problems and applications. Each chapter presents the problem, discusses its mathematical formulation as a minimization problem, analyzes its mathematical well-posedness, derives the associated Euler–Lagrange equations, describes the numerical approximations and algorithms, explains several numerical results, and includes a list of exercises. MATLAB® codes are available online. Filled with tables, illustrations, and algorithms, this self-contained textbook is primarily for advanced undergraduate and graduate students in applied mathematics, scientific computing, medical imaging, computer vision, computer science, and engineering. It also offers a detailed overview of the relevant variational models for engineers, professionals from academia, and those in the image processing industry.
Introduction to Variational Methods in Control Engineering focuses on the design of automatic controls. The monograph first discusses the application of classical calculus of variations, including a generalization of the Euler-Lagrange equations, limitation of classical variational calculus, and solution of the control problem. The book also describes dynamic programming. Topics include the limitations of dynamic programming; general formulation of dynamic programming; and application to linear multivariable digital control systems. The text also underscores the continuous form of dynamic programming; Pontryagin's principle; and the two-point boundary problem. The book also touches on inaccessible state variables. Topics include the optimum realizable control law; observed data and vector spaces; design of the optimum estimator; and extension to the continuous systems. The book also presents a summary of potential applications, including complex control systems and on-line computer control. The text is recommended to readers and students wanting to explore the design of automatic controls.
This book contains the proceedings ofthe meeting on "Applied Mathematics in the Aerospace Field," held in Erice, Sicily, Italy from September 3 to September 10, 1991. The occasion of the meeting was the 12th Course of the School of Mathematics "Guido Stampacchia," directed by Professor Franco Giannessi of the University of Pisa. The school is affiliated with the International Center for Scientific Culture "Ettore Majorana," which is directed by Professor Antonino Zichichi of the University of Bologna. The objective of the course was to give a perspective on the state-of the-art and research trends concerning the application of mathematics to aerospace science and engineering. The course was structured with invited lectures and seminars concerning fundamental aspects of differential equa tions, mathematical programming, optimal control, numerical methods, per turbation methods, and variational methods occurring in flight mechanics, astrodynamics, guidance, control, aircraft design, fluid mechanics, rarefied gas dynamics, and solid mechanics. The book includes 20 chapters by 23 contributors from the United States, Germany, and Italy and is intended to be an important reference work on the application of mathematics to the aerospace field. It reflects the belief of the course directors that strong interaction between mathematics and engineering is beneficial, indeed essential, to progresses in both areas.
The book includes lectures given by the plenary and key speakers at the 9th International ISAAC Congress held 2013 in Krakow, Poland. The contributions treat recent developments in analysis and surrounding areas, concerning topics from the theory of partial differential equations, function spaces, scattering, probability theory, and others, as well as applications to biomathematics, queueing models, fractured porous media and geomechanics.
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http://www.newyorklawjournal.com/id=1377601548311
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math
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Advice for the Lawlorn: Are Your Interviewing Basics Making You Look Bad?
A point on a prior column (regarding researching your interviewers). As someone who often interviews candidates, I sometimes find it a little creepy when the candidate lets me know that (s)he's researched me—there is a stalker aspect to that.
I think the candidate should feel free to ask a litigator about a case the litigator worked on while at the current firm (or the equivalent question of a corporate lawyer). It is not appropriate, however, to ask an interviewer a question that doesn't relate specifically to the work, i.e., "So I saw that you went to XXX law school. How did you like that?"
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http://www.astronomy.net/forums/god/messages/31611.shtml
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math
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But you are not me!
I thought you agreed with that!
By the way:
seen "2001. A Space Odyssey"?
Remember that "black monolith"?
"Planck's constant" appears to be "the scale of scale": a holographic "monolith" projected by repeatedly mixing two reference frames giving the impression of a floating fixed "plank" as a door to "outer space" where the outer space is all the other reference frames that are mixed through the repeat iterations of the initial two.
But the real door is I understand Jesus Christ where God meets man so cushions the shock of man meets God...
Speed of light constant:
this is apparantly "speed of speed":
from the perspective of "any other perspective outside two initial reference frames":
consider a series of sentences each containing the words "mile" and "hour":
1. The car travelled 50 miles in 1 hour
2. The boat travelled 40 miles in 3 hours
3. The bike travelled 15 miles in 1 hour.
and so on
From the perspective of "assignment of definitions" to quote Dr. Dick;
A whole lot of such sentences in themselves (without even defining what number is) could be thought of as defining a constant meeting place for "mile" and "hour";
If you did define what number is you could then connect this constant "mile:hour" space with "number" to get your plank constant (like a piece of 4 by 2: like Chris Langan's "conspansive duality" and "info-cognition": you get the mile: hour in NUMBER and the NUMBER in mile:hour:
try to get a handle on this and you collapse the lot into you (like a big bang) with a cosmic background radiation (consisting of particles of "big bang" with space-time strings attached?):
and six quarks for your chosen two-world perspective:
quark top: number (in mile: hour)
quark up: mile in the above (chose what comes up)
quark down: hour in first (top) quark
quark strange: mile: hour (pick which) in number
quark charm: mile: hour (pick the now chosen (other) one in number
quark beauty/ bottom: number perspective of mile: hour in number
The patterns of theoretical physics can occur in any measurement?
In the set of sentences example:
what sheds "light" on the collection?
Light does: light as true free meeting.
This generates "logical consistency" which becomes mass (room to move within an agreed reference frame)?
the localised collapse of "space-time" on each perspective:
in my sentences example:
each sentence has a "plank mass" being "every way the other sentences can meet in that sentence's space without breaking it...
So a minimum definition of the curvature of the sentences-space (the space in space)
one sentences space meets another: all the others might attach strings to this meeting say:
the minimum definition of the concept "direction" requires two sentences mutual agreement on defining "mile" and defining "hour":
and agreeing on a direction (a variation that points to the other sentences (what Dr. Dick calls "adding unknown data" but he has used a math seive it seems and ended out with "noodles" (or pasta) (which Chroot calls a "straw metric"?)
Take every way a three can meet with respect to every other way (as in Heaven: every voice gets a hearing) in our sentences and we get a minimum definition limits for "threesome" giving "planck length" as "the limit on our ability to define length here"
Speed of light constant:
One thing meets another:
call this "speed" but how calibrate it?
Super calli fragilistic expi alla docious?
Over callibrate (so "super") requires overshooting so overlapping sets;
So is it supposedly fragile? (how overlap can happen? requires input of others)
expi: expedience: mathematics uses numbers and claims togetherness which sticks things together
but with what do they stick together? (a la....)
forbidden fruit? Bits of us? Since numbers are not defined you have to cobble together bits of the original things you were trying to calibrate in order to calibrate them?
I am aware of the wildly metaphorical nature of the above play....
Maybe the fall of man was about getting hung up on number? Subjecting himself to number? An illusion that we are stuck ...?
Something wrong in the above somewhere it may ....?
This may help:
Jesus referred to bread and wine as His body and blood; said that "man does not live on bread alone but on every word that comes from the mouth of God" and that "no one comes to the Father except through Me" (Jesus) and that "he who believes that Jesus Christ is the Son of God has already overcome the world".
The Catholic Mass celebrates coming together; there is a way of understanding all this and physics is right in the middle it seems?
Returning to speed of light:
Every way "three can happen" with respect to every other way:
gives "light (three as one) from light (three as one) as a constant background of light (three as one)? But what is three and what is one?
We are told God is three and God is One...
A local minimum definition of number meets "every way three can be three" or time can be space and space can be time: gives an apparent fixed speed if you interact with math:
In the sentences example:
any two definitions of "mile" and "hour" that agree with each other and with every other logical possibility there; are BOUND by the minimum/maximum definitional freedom of a four-way split (Michelson Morley experiment!) of two items ("mile" and "hour").
The Michelson Morley experiment is "rigged" in that it cannot detect direction: it mixes it up?
If one looks at it without assuming a rigid space upon which it is constructed.....?
Or you could break it up into mini-MM's called "axions" that seem to be conscious of each other (they by definition know each others limits in defining their mutual space in this simplified pattern perspective here)?
Dr. Dick's maths seems to generate a space full of little crosses (Dirac delta functions) that collectively appear to project a universal Dirac delta function (a cross sees a cross while considering other crosses: you get a delta function attached to one cross's perspective?)
The more you iterate the meeting of two crosses; the third one perspective on this seems to fan out (delta) in a way functional to the other crosses?
His conclusion seems logical:
the universe operating on a quantum system he does not understand?
Because a universal Dirac Delta function is going to involve a lot of fuzzy deltas all muddled up?
But math did that......
You can see the deltas: the number pyramids that numbers are built of.....
But beyond number....
Heaven is all around us......
God invites us to sign in.........
Did I make a mistake somewhere?
Your view of "I" would not be fixed because it is a matter of our agreeing on a space where you can be and I can be....
but my own "I" is fixed by definition or how could I question if it is fixed without a constant me that knows he is using a logically consistent space?
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s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030338213.55/warc/CC-MAIN-20221007143842-20221007173842-00249.warc.gz
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CC-MAIN-2022-40
| 6,818 | 77 |
https://www.preprints.org/manuscript/201711.0120/v1
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math
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Preserved in Portico This version is not peer-reviewed
The Generating Function of the Catalan Numbers and Lower Triangular Integer Matrices
: Received: 18 November 2017 / Approved: 20 November 2017 / Online: 20 November 2017 (07:20:26 CET)
In the paper, by the Faά di Bruno formula, several identities for the Bell polynomials of the second kind, and an inversion theorem, the authors simplify coefficients of two families of nonlinear ordinary differential equations for the generating function of the Catalan numbers and discover inverses of fifteen closely related lower triangular integer matrices.
simplification; coefficient; nonlinear ordinary differential equation; generating function; Catalan number; inverse matrix; lower triangular integer matrix; Faά di Bruno formula; Bell polynomial of the second kind; inversion theorem
Computer Science and Mathematics, Computational Mathematics
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
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CC-MAIN-2023-50
| 1,281 | 9 |
https://ristoranteilgattoelavolpe.com/online-casino-geld-verdienen/scharfschgtze-spiele.php
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math
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Calculus math solver
This calculus math solver makes learning math enjoyable and rewarding. Students who use will see a big improvement in their math skills. Mathematics can be a difficult subject for many students.
The Best Calculus math solver
Newton and Leibniz founded the theory of calculus at the same time in the 17th century. Agnesi, known as the mother of calculus, summarized the mathematical methods of these two enemies for the first time in his analysis handout (left), which has been popular in Europe for more than 60 years. The problems caused by the introduction of infinitesimal quantities in calculus triggered the second mathematical crisis in history. The strict mathematical basis of calculus was finally established by Karl Weierstrass (1815-1897), the late German mathematician who was the father of modern analysis until the 19th century, which finally made the description of mathematical analysis truly accurate. By the way, Lao Wei was said to be a physical education teacher before he became a mathematician. Nowadays, when people satirize someone's poor mathematics, they often say that the person's mathematics is taught by a physical education teacher. It seems that this can't be said casually. Although Newton and Leibniz had different methods of studying calculus, they came to the same goal by different paths. They independently completed the great cause of creating calculus, laid the foundation of calculus, and made groundbreaking and pioneering contributions to the rise and development of variable mathematics. The glory should be shared by them. However, there was a fierce debate about the priority of inventing calculus in history Most master of mathematics programs do not require students to be majoring in mathematics, but generally require applicants to have a foundation of mathematics related courses, including advanced calculus, linear algebra, complex variables, partial calculus and constant calculus equations, probability theory, etc. If the undergraduate is a student with a non mathematical background, it is recommended to check and make up the prerequisite courses required by the target institution in advance. Leibniz's research interests are very broad. His knowledge covers more than 40 fields, including philosophy, history, language, mathematics, biology, geology, physics, machinery, theology, law, diplomacy and so on, and he has made outstanding achievements in each field However, because he created calculus and carefully designed very ingenious and concise calculus symbols, he became famous as a great mathematician (2) Undergraduate professional background requirements: high quantitative background is required, such as computer science, mathematics, electrical engineering or physical science. Relevant work experience will also be considered. The applicant should be familiar with linear algebra, calculus and other undergraduate mathematics courses Primary school is to learn some very simple basic mathematics. Junior high school and senior high school begin to deepen mathematics and extend it to more difficult content. All three systems will learn high-order calculus Advanced mathematics includes number series, limit, calculus, spatial analytic geometry and linear algebra, as well as basic subjects of engineering, science and finance graduate examinations. This subject is a college course, so it is often called higher mathematics and calculus in textbooks. 1 find out the important function keys. Scientific calculators have several function keys, which are very important for learning algebra, trigonometry, geometry, calculus, etc. Find the following function keys on your calculator: AA - Mathematics: analysis and methods focuses on abstract concepts of mathematics, including functional formulas, trigonometry and calculus. Students can scientifically study regularity, explore guess and dig direct evidence. IB math exam has strict requirements on the setting of calculators. If the invigilator clears the setting of calculators during the exam, you need to be able to quickly change it to the original mode. Therefore, it is also necessary to spend some time doing calculator exercises. If you can't, you can ask pineapple's online teacher to demonstrate it to you.
Instant help with all types of math
best app for bright students. It's one of the best apps you may ever see. Really helpful. but bit hard to understand first time. so, you should give some instructions when someone open it for the first time. Make the camera quality better and most important thing your scanning time is too fast love that. but don't like that sound after scene change it.
The app is excellent, it does all that it's supposed to do and works very well. It has a variety of ways to solve equations and it also shows you how is solved it so you are able to understand it. My only problem with it is that when you try to take a photo, the resizer is a bit restrictive but that could easily be fixed
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CC-MAIN-2022-49
| 4,975 | 7 |
https://nigerianscholars.com/tutorials/quantitative-aspects-chemical-change/stoichiometric-calculations-2/
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math
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Earlier, you learnt how to write balanced chemical equations and started looking at stoichiometric calculations. By knowing the ratios of substances in a reaction, it is possible to use stoichiometry to calculate the amount of either reactants or products that are involved in the reaction.
The following figure highlights the relation between the balanced chemical equation and the number of moles:
Earlier, we explored some of the concepts of stoichiometry. We looked at how to calculate the number of moles of a substance and how to find the molar mass. We also looked at how to find the molecular and empirical formulae of substances. Now we will explore more of these concepts such as limiting reagents, percent purity and percent yield.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363125.46/warc/CC-MAIN-20211204215252-20211205005252-00409.warc.gz
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CC-MAIN-2021-49
| 742 | 3 |
https://play.google.com/store/apps/details?id=com.rkayapps.compoundinterestcalculator
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math
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Where is ur simple interest calculator? If u don't have that , then y have u mentioned in the name of the app that it's a simple & compound interest calculator?
To develop my financial credit also I will be good agent for promoting the loan & interest calculator
This is a very useful app which helps almost everybody in day to day life to ascertain ones position.
Love this app, easy to use. Nice to know in advance what payments and interest will be.
I like this app to improve my business but let me try it
Excellent app for interest calculation
Updated Compound Interest Calculator with the following features.
(1) You can calculate compound interest for the given number of "days". For example, calculate compound interest for 100 days.
(2) The regular deposit term now supports "days". For example, you can deposit 10 bucks daily for 50 days
EMI Calculator works as great Financial Planner and very useful Loan Calculator
EMI Calculator / Loan Calculator / Mortgage Calculator / Home Loan Eligibility
Loan EMI Calculator with Amortized Analysis, Payment Schedule, Loan Profile
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s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891812880.33/warc/CC-MAIN-20180220050606-20180220070606-00774.warc.gz
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CC-MAIN-2018-09
| 1,082 | 12 |
https://blogs.warwick.ac.uk/news/entry/google_results/
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math
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I'm writing some notes for a presentation about blogging at Warwick. One of the things I'm interested in is blog entries which become highly visible to search engines. Does anyone have any interesting examples of Google searches which return a Warwick Blogs entry somewhere in the first ten results?
I should clarify what I mean by "interesting", perhaps:-
- Results for something other than someone's name are interesting (so "crystalography" would be more interesting than "John Smith").
- Results about a subject other than someone's life are interesting (so "Plato" would be more interesting than "John Smith party fifteen pints").
- Results which are ranked number one are more interesting than results ranked number ten.
- Results which point to posts which are in some sense serious – they are reflective or critical or analytical – are more interesting than results which point to rants or rambles or funnys.
None of which is to say, of course, that there's anything wrong with blogging about your life, or ranting, or being funny. But if you know of any Google searches which meet one or more of the above criteria, it'd be very helpful if you could leave a comment. Thanks.
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CC-MAIN-2024-18
| 1,187 | 7 |
http://www.unc.edu/~tparent/validityhandoutLOGIC.html
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math
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An Overview of Arguments in Logic
An argument is a set of statements one of which (the conclusion) is taken to be supported by the remaining statements (the premises). [Note that a “statement” can either be a whole sentence, or an independent clause within a sentence.]
Five types of Arguments: Inductive, Deductive, Abductive, Practical, and Other.
An Inductive argument is an argument where the premises register the known cases of a certain phenomenon, and the conclusion suggests that unknown cases will be like the known cases.
(P1) The sun rose today.
(P1) Everyone in my family has been stung by
(P2) The sun rose yesterday. (C) So, absolutely everyone has been stung by a bee.
(P3) The sun rose the day before
(P4) The sun rose the day before
the day before yesterday.
(C1) So, the sun will rise tomorrow.
Of course, the premises in each argument do not guarantee the truth of the conclusion. Still, an argument can be a good inductive argument to the degree that the conclusion is likely given the premise(s). (In assessing its likelihood, sometimes people talk of the “inductive strength” of the argument.)
A Deductive argument, on the other hand, is an argument where (roughly) the truth of the premises would guarantee the truth of the conclusion.
Official Definition: An argument is deductive if and only if [abbreviation: “iff”] it is not possible for the premise(s) to be true and the conclusion false.
Example of a deductive argument:
(P1) Jim likes either Coke or Pepsi.
(P2) Jim does not like Pepsi.
(C) So, Jim likes Coke.
So with a deductive argument, if we get you to accept the premises, then you must accept the conclusion too. Why? ‘Cause in a deductive argument there’s no way for both the premises to be true and the conclusion false.
Unfortunately, most of the time a deductive argument is called (misleadingly) a ‘valid argument’. The label is misleading, since you can have a “valid” argument which is nonetheless a bad argument, all things considered. That’s because the premises might be totally implausible. Yet the argument still counts as “valid” if it is the kind of argument where if you granted the premises, the conclusion would be guaranteed.
So if you hear a logician call an argument “valid,” that does not mean that it is ultimately a good argument. Conversely, if an argument is “invalid,” that also does not mean it is ultimately a bad argument. Consider for instance that all inductive arguments are invalid, technically speaking, i.e., they are non-deductive. Still, as we saw, there can be good inductive arguments. Thus, if you say that an argument is “invalid,” you’re saying that the premises do not guarantee the conclusion, though the premises may still make the conclusion very likely for all that.
The term ‘valid’ is also misleading in that “validity” concerns a relationship between premise(s) and conclusion. It is not directly concerned with whether the statements in the argument are actually true. This is contrary to how we use the word ‘valid’ outside the logic classroom: Ordinarily, we sometimes say that someone has made a “valid point” or that someone’s perspective is “valid” when we mean that s/he made a true statement. But this is NOT how logicians use ‘valid’—they only say that arguments are “valid.” (Consequently, logicians do not speak of a point or a perspective as “valid,” though they can say instead that someone has a good point or has a legitimate perspective, etc.)
Of course, not every argument is deductive (= valid). Here’s one example:
(P1) Jim likes either Coke or Pepsi.
(P2) Jim does not like Mountain Dew.
(C) So, Jim likes Coke.
In this, it is possible for the premises to be true, and the conclusion false. That’s not to say the premises are actually true or the conclusion is actually false. Rather, it’s just to say that this combination of truth and falsity is possible. N.B., A non-deductive (= invalid) argument is also sometimes called a non-sequitur—it is an argument where the conclusion “does not follow” from the premise(s).
Some deductive arguments are also SOUND: An argument is sound iff it is deductive AND every premise is true. Thus, an argument is unsound iff it is some premise is false or is not deductive.
So, to check that an argument is sound, you have to verify that the argument is deductive and that every premise is true.
Example of a sound argument:
(P1) If a thing is a rectangle, then it’s not a circle.
(P2) This page is a rectangle.
(C) So, this page is not a circle.
This argument is sound, since it is deductive, and all of its premises are true.
Example of an unsound argument:
(P1) If Bill Gates is poor, then I’m a monkey’s uncle.
(P2) Bill Gates is poor.
(C) So I’m a monkey’s uncle.
This argument is unsound: Although it is deductive, it is not true that Bill Gates is poor.
NOTE: Truth and Falsity are NOT properties of arguments, but of statements. Thus, we do not say that a deductive argument is “true;” rather, we say that it is valid or sound. Or, if we want to talk of “true” and “false,” we can evaluate the statements in the argument as true or false.
An Abductive argument is an argument that is neither deductive nor inductive, where the conclusion stands as an explanation of facts given in the premises.
(P1) I can’t get online from my computer.
(P1) I have a
(P2) There’s nothing wrong with my hardware or (C) So, my head is shrinking
(C) So, the University network must be down.
Note that in the first example, the conclusion does not explain (P2) in isolation. (The network being down wouldn’t explain why there’s nothing wrong with my hardware/software.) So the conclusion of an abductive argument is not one that explains why each premise is true individually; rather, it explains why the premises are jointly true, true all at once.
Consequently, in the first example, the conclusion is best seen NOT as an explanation of why I can’t get online per se. (That would just be an explanation of the first premise.) Rather, it’s best seen as an explanation of why I can’t get online despite my functioning hardware/software.
Confusingly, some inductive and deductive arguments also have conclusions which (in some sense) explain the premise(s). The second example I gave of an inductive argument is one where the conclusion (in some sense) explains the premise. Moreover, the conclusion is explanatory in the following deductive argument:
(P1) This figure is a triangle.
(C) Hence, this figure is a closed, three-sided figure.
After all, if the figure is a closed three-sided figure, that “explains” why it is a triangle. But still, the argument is deductive, because the truth of the premise would guarantee that the conclusion is true.
Thus, in order to be certain that an argument is abductive, you must first show that the argument is neither deductive nor inductive.
Like an inductive argument, however, an argument is a good abductive argument to the degree that the conclusion is likely given the premise(s). (Since abduction and induction are both evaluated by the probability of the conclusion, oftentimes logic books will call both types of argument “induction.”) N.B., If the conclusion of an abductive argument is the most likely explanation out of all the explanations available, then the abductive argument is sometimes called an inference to the best explanation.
A Practical argument is an argument where the conclusion is a statement of what should or ought to be done, yet the argument is not deductive, not inductive, and not abductive.
(P1) Stocks are low right now (P1) I need to make money.
(P2) The economy will recover soon. (P2) Kidnapping children makes money.
(C) So, I should buy stocks right now. (C) So, I should start kidnapping children.
As should be clear, these two arguments are not deductive. Re: the first argument, even if stocks are low and the economy is expected to recover, it is still possible that I should NOT buy stocks right now. After all, I might have barely enough money to feed my family.
Still, the first example can be a good practical argument if we’re talking about someone who has expendable income. But even in that case, it remains possible for the premise to be true and the conclusion false for different reasons. So the argument is still non-deductive.
When is a practical argument a good practical argument? NOBODY KNOWS. That is still debated vigorously among ethicists. However, there is a sub-type of practical argument, called a decision-theoretic argument, and it is known what makes these arguments good or bad (under certain assumptions). Very briefly, you have a good decision-theoretic argument when the conclusion recommends an action that is expected to “maximize profit” among the available options. (No need to go into more detail at this point...)
Note: Some arguments with a “should” or “ought to” conclusion are NOT practical arguments. Consider the following inductive and deductive arguments (respectively):
(P1) I shouldn’t have played the lottery today. (P1) Thou shalt not steal.
(P2) I shouldn’t have played the lottery yesterday. (C) I should not steal this ipod.
(P3) I shouldn’t have played the lottery the day before that.
(C) I shouldn’t play the lottery tomorrow.
(Arguably, there are also abductive arguments with “should” or “ought to” conclusions as well.) So remember that the term ‘practical argument’ is reserved for an argument that is NOT any of the previous three types of argument—AND has a “should” or “ought to” conclusion.
Other arguments exist besides the previous four types. Some arguments in the “other” category are “mixtures” of the previous types of arguments. Consider, for instance:
(P1) My car is usually out of gas.
(P2) My car currently isn’t running.
(C) So, my car is currently out of gas.
The conclusion here seems to be inductively and abductively inferred. Consider that if the argument just consisted of (P1) and (C), it would plausibly be inductive. But if the argument just consisted of (P2) and (C), then it would look abductive. Yet since you’ve got both premises, it looks like inductive and abductive reasoning is being used.
A different kind of “other” argument is an enthymeme: In these arguments, too much is left unsaid for us to classify the reasoning more precisely. For instance, consider:
(P1) The Democrats took control of the Congress and the White House.
(C) So, predictably, the economy stopped its downward slide.
How exactly is (C) supported by (P1) in this case? Are we making an induction based on past cases (which aren’t explicitly mentioned)? Or are we deducing the conclusion from a suppressed premise like “whenever the Democrats are in control, the economy improves”? It’s impossible to say. So when an argument is enthymematic to this degree, we put it in the “other” category.
Relatedly, some arguments can’t be classified more precisely, simply because they are just plain awful. Consider:
(P1) I have ten toes.
(P2) Penguins live in
(C) So, Obama’s economic plan will fail.
Observe that out of context, these three sentences would not seem to be an argument at all. But here, they indeed constitute an argument since one statement is marked as the conclusion, and other statements are marked as premises. So in this case, the three statements here are an argument; it’s just that it’s a really bad argument. Because of that, it’s not at all clear how the premises are meant to support the conclusion; hence, the argument goes in the “other” category.
Finally, some arguments in the “other” category are arguments by analogy. Here’s a famous example:
(P1) A watch has a designer.
(P2) The universe is like a watch.
(C) So, the universe has a designer.
Note that the truth of the premises would not guarantee the conclusion; hence, the argument is not deductive. Moreover, the conclusion is not meant to explain why the premises are jointly true. So it isn’t abductive either.
Some logic books, however, classify arguments by analogy a type of inductive argument. I myself think this is backwards: Inductive arguments are a type of argument by analogy, if induction assumes that the unknown cases will be like the known cases. But even ignoring that, it seems best not to classify arguments by analogy as inductive. That’s because normally when logicians speak of induction, they do not have analogical reasoning in mind. (And conversely, they are not normally thinking of induction when they talk of analogical reasoning.)
Thus, I’ve put arguments by analogy in the “other” category. But unlike the just-plain-awful arguments, it is not obvious whether the watch-argument (for example) is a bad argument. Its worth would depend on how appropriate the analogy is in (P2)—and specifically, whether the universe is similar in the right way to a watch. I’ll let the theologians among you decide that one. But generally, an argument by analogy is a good argument to the extent that the analogy is a “tight” one (to put it roughly).
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http://physics.stackexchange.com/questions/43087/cause-of-buoyant-force/43089
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math
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Can you explain to me what causes the buoyant force? Is this a result of a density gradient, or is it like a normal force with solid objects?
It is the result of a dependence of the pressure with growing depth, due to the gravitational field (i.e. the weight of the water).
You may do an easy calculation with some simple geometrical form, e.g. a cylinder totally submerged in water, to quickly understand how it works. The force due to pressure in each surface element of the curved wall of the cylinder is proportional to the depth of that element, and has the normal direction to the wall, i.e. towards the axis of the cylinder. After an easy integration in polar coordinates, you can see that the resultant force points upwards. That is because the forces in the upper parts are smaller that the ones near the more deeply submerged part of the cylinder.
A surprising conclusion is that a golf ball submerged in a tank of water in the space station, would not go upwards... or that the bubbles in a coke in the hands of an astronaut remain where they origin... I would love to see that.
It's like a teeter-totter.
Some of the fluid is pushed up as the solid thing moves down. There energy cost of doing that is exactly the same as the energy cost of pushing down on one end of a teeter-totter.
Good answers, but let me try to make it intuitive.
Water weighs 1 gram per cubic centimeter (or 1 kilogram per Liter, a cube 10 centimeters on a side, if you prefer).
So if you have a tube 1 centimeter square, stopped up at the bottom, and you fill it with water to a height of N centimeters, then you know how much pressure there is at the bottom. It is simply the weight of the water in the tube, N grams, right?
Now take the tube, not stopped up at the bottom, and just put it in water to a depth of N centimeters. So the water in it weighs N grams, right? So, since the water stays in the tube (it doesn't run out the bottom) the outside water at the bottom of the tube has to be pushing up with a pressure equal to the weight of the water in the tube - N grams per square centimeter.
Now, with the tube still in the water, N centimeters deep, seal off the bottom of the tube with some kind of membrane, and suck the water out of the tube so it is empty. How much pressure is the outside water pushing up with against the membrane on the bottom of the tube? The same, right? N grams per square centimeter. However, since the tube doesn't have N grams of water inside it, pressing down, the tube itself is being pushed up by the N grams per square centimeter pressure at the bottom, that is not being matched by an equal weight of water in the tube pressing down.
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http://tynpnnhaf.ga/str2666-definition-of-combinational-logic-circuit.html
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math
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definition of combinational logic circuit
Shows the steps involved in designing a combinational logic circuit. Glamorous Combinational Logic Design And Analysis Lecture Notes Calculator Abaeacbdcbd. Gorgeous Sequential Logic Circuits Combinational Definition Figuredangersignimplementation. Gorgeous Combinational Logic Design Using K Maps. Introduction Logic circuits for digital systems may be combinational or sequential. A combinational circuit consists of logic gates whose outputs at any time are determined directly from the present combination of inputs without regard to previous inputs. Logic Circuits: Combinational versus Sequential Circuits. Design Procedure of Combinational Circuits.n Combinational Circuits: Output only depends on the present combination of inputs. Chapter - 5 FLIP-FLOPS AND SIMPLE FLIP-FLOP APPLICATIONS Introduction : Logic circuit is divided into two types. 1. Combinational Logic Circuit 2. Sequential Logic Circuit Definition : 1. Combinational. Combinational Logic Circuits. Always gives the same output for a given set of inputs. We will apply the knowledge of Boolean Algebra to realize these circuits. First we will look at Combinational Logic Circuit. The behavior of combinational logic circuits is most typically identified and specified by a logic equation or by a truth table. Either of these methods provides a clear, concise, and unambiguous definition of how input signals are combined to drive outputs signals. combinational logic circuit. комбинационная логическая сеть. Англо-русский словарь промышленной и научной лексики.Combinational logic — Not to be confused with combinatory logic, a topic in mathematical logic. In digital circuit theory, combinational logic (sometimes also Chapter 2 Fault Detection in Logic Circuits2.
1 test generation for combinational logic circuits2.2 testing of sequential circuitsAn Introduction to Logic Circuit Testing provides a detailed coverage of techniques for test Combinational circuits are logic circuits whose outputs respond immediately to the inputs there is no memory.Fig.2 Switch transistor response and corresponding definitions of digital output signal. The digital system consists of two types of circuits, namely: (i) Combinational circuits and (ii) Sequential circuits A combinational circuit consists of logic gates, where outputs are at any instant and are determined only by the present combination of inputs without regard to previous inputs or Lecture 6: More Complex Combinational Logic Circuits. XOR ab ab. N. B. Dodge 9/15.Definition of a Multiplexer. A multiplexer is a combinational logic circuit that has up to 2n inputs, an n-bit address, and one output. Combinational Logic Circuit Definition.
This combinational logic is in contrast compared to the sequential logic circuit in which the output depends on both present inputs and also on the previous inputs. Definition. Combinational Logic Circuit. The combinational logic circuit comprises of logic gates and thus the output obtained is directly related to the input. There are no feedback elements in case of the Combinational logic circuit. Converting Between Standard Forms. Summary. Chapter 2: Combinational Logic Circuits. 1. We can show that these axioms are true, given the definitions of AND, OR and NOT. As a final example of a combinational logic system, suppose we have been asked to design a circuit that accepts a binary digit, 0 or 1, and decodes it into a setThis operation also changes the structure of the graph by adding an arc from the node for G to the node for F and changing the definition of F. Chapter 2 Part 1 Combinational Logic Circuits. Originals by: Charles R. Kime and Tom Kamisnski Modified for course use by: Kewal K. Saluja and Yu Hen Hu.Operator Definitions. Application: Digital Logic Circuits. — Analogy between the operations of switching devices and the operations of logical connectives.— Rules for a Combinational Circuit: — Never combine two input wires.by definition of |. A combinational circuit is one where the output at any time depends only on the present combination of inputs at that point of time with total disregard to the past state of the inputs. The logic gate is the most basic building block of combinational logic. These circuits can be classified as combi-national logic circuits because, at any time, the logic level at the output depends on the combination of logic levels present at the inputs.In this chapter, we will continue our study of combinational circuits. Component define logic gates wikipedia the free all things electronic a picokit blog useful without true false.Logicblocks experiment guide learn sparkfun simplified circuit. Homework hwa. Patent us binational logic structure using pass drawing. Combinational logic is used to build circuits that produce specified outputs from certain inputs, the construction of combinational logic is generallyFollowing is a definition of one type of automaton, which attempts to help one grasp the essential concepts involved in automata theory/theories. Combinational and Sequential circuits are the most essential concepts to be understood in digital electronics. Combinational logic (sometimes also referred to as time-independent logic) is a type of digital logic which is implemented by Boolean circuits Combinational logic refers to circuits whose output is a function of the present value of the inputs only. As soon as inputs are changed, the information about the previous inputs is lost, that is, combinational logic circuits have no memory. Logic circuits for digital systems may be either combinational or sequential. A combinational circuit consists of logic gates whose outputs at any time are determined from only the present combination of inputs. Definition The combinational logic can be defined as is that logic in which all outputs are directly related to the current combination of values on its inputs.Much of logic design involves connecting simple combinational logic circuits to construct a larger circuit that performs a much more Common Combinational Logic Circuits. Adders. Subtraction typically via 2s complement addition. N inputs produce M outputs (typically N M). C. E. Stroud. Combinational Logic Circuits (10/12). 1. Definition of combinational circuit - a circuit whose output is dependent only on the state of its inputs.This paper presents an efficient formal logic verification algorithm for combinational circuits. A combinational logic circuit implement logical functions where its outputs depend only on its current combination of input values. On the other hand sequential circuits, unlike combinational logic, have state or memory. The combinational circuit consist of logic gates whose outputs at any time is determined directly from the present combination of input without any regard to the previous input.The only problem is that the definition of "as good as possible" may vary greatly. With combinational logic, the circuit produces the same output regardless of the order the inputs are changed. There are circuits which depend on the when the inputs change, these circuits are called sequential logic.That is the formal definition of a multiplexer. Adapted from Digital Logic Circuit Analysis Design, by Nelson, Nagle, Carroll, Irwin, Prentice-Hall,1995, Chapter 12, pages 739 to 757. Testing of combinational logic circuits digital logic circuit testing definitions. Included in this paper are examples of several CMOS logic circuits implemented at the transistor level along with a design method for the implementation of CMOS combinational logic circuits. Fig 1: Combinational logic circuit. For n number of input variables, there are 2n possible combinations of binary input values. This circuit can be described by m Boolean functions, one for each output. 1. Combinational LOGIC CIRCUITS: 2. Sequential. Combinational logic circuits (circuits without a memory): Combinational switching networks whose outputs depend only on the current inputs. Define Programmable Logic Device. What are the three forms of programmable logic devices? Explain how to program a PAL. Draw the PLA schematic circuit that will produce the following expression: Y AB AB AB. n Logic Gates (NOT, AND, OR, NAND, NOR, XOR, XNOR). n Combinational Logic Circuits from Boolean Functions.n Definition: Logic Basis is a minimal set of basic Boolean functions with which an arbitrary Boolean function can be represented. For a Boolean function g, we say a combinational logic circuit C computes g, if res(N) g(x, , x2, . . . . x,) where N is the output node.The width of C, denoted width(C), is the maximum of its thickness at all its levels. The definition of width in this letter is not equivalent to the one in [ 11, but we can obtain 2 Overview Objectives -Define combinational logic circuit -Analysis of logic circuits (to describe what they do) -Design of logic circuits from word definition -Minimization or Simplification of logic circuits -Mathematical Foundation of logic circuits (Boolean Algebra and switching theory). definition - COMBINATIONAL LOGIC. definition of Wikipedia. Advertizing .In digital circuit theory, combinational logic (sometimes also referred to as combinatorial logic) is a type of digital logic which is implemented by boolean circuits, where the output is a pure function of the present Analysis of Combinational Logic. Verifying the circuit is combinational No memory elements No feedback paths (connections). Secondly, obtain the Boolean functions for each output or the truth table. From the definition of the edge classification scheme, it follows that every such P ( i, j ) Q path covers edge ( i, j ). Let G2 . cover ( G ) - G1.Combinational logic circuits. 61. In actually implementing this algorithm, one could combine T1, T 2 , and T3 into a single transformation. Combinational logic is used in computer circuits to perform Boolean algebra on input signals and on stored data.Find a translation for the combinational logic definition in other languages: Select another language: - Select - (Chinese - Simplified) (Chinese - Traditional) Espaol In digital circuit theory, combinational logic (sometimes also referred to as time-independent logic ) is a type of digital logic which is implemented by Boolean circuits, where the output is a pure function of the present input only. Definition of the noun Combinational Circuit.Definitions Combinational circuits (24): Let F be a combinational circuit and C(x) the corresponding logic function, where x is an arbitrary input. Definition of Combinational Logic Circuits: In the theory of digital circuit, combinatorial logic (also called time-independent logic) is a type of digital logic that is implemented by Boolean circuits wherein the output is a function of the input only. The outputs of Combinational Logic Circuits are only determined by the logical function of their current input state, logic 0 or logic 1, at any given instant in time. The result is that combinational logic circuits have no feedback Combinational Logic circuit contains logic gates where its output is determined by the combination of the current inputs, regardless of the output or the prior combination of inputs. Basically, combinational circuit can be depicted by diagram-1 below Combinational circuit is a circuit in which we combine the different gates in the circuit, for example encoder, decoder, multiplexer and demultiplexer.Half adder is a combinational logic circuit with two inputs and two outputs. Combinational logic circuits are electronic circuits that produce outputs based on the states of the inputs. Unlike in sequential logic circuits, the previous outputs do not partly determine the next outputs.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125947421.74/warc/CC-MAIN-20180424221730-20180425001730-00226.warc.gz
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CC-MAIN-2018-17
| 11,782 | 4 |
http://math.stackexchange.com/questions/325837/discrete-math-is-the-survey-accurate/325853
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math
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A library has conducted a survey of its readers. The survey asked its $10,000$ readers about their reading habits and the number of books that they have borrowed from the library in $2012$. It has found that its readers claimed to have borrowed $75,000$ books in $2012$. The library has also reviewed the borrowing records of its books and found that on average a book was borrowed $5$ times. The library has $20,000$ books.
Is this survey accurate?
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s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257824995.51/warc/CC-MAIN-20160723071024-00068-ip-10-185-27-174.ec2.internal.warc.gz
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CC-MAIN-2016-30
| 449 | 2 |
https://nrich.maths.org/public/leg.php?code=5039&cl=2&cldcmpid=5791
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math
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Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
Can you find all the different triangles on these peg boards, and find their angles?
Investigate how logic gates work in circuits.
What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?
A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?
Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
Can you find triangles on a 9-point circle? Can you work out their angles?
An environment that enables you to investigate tessellations of regular polygons
A game in which players take it in turns to choose a number. Can you block your opponent?
Overlaying pentominoes can produce some effective patterns. Why not use LOGO to try out some of the ideas suggested here?
Can you set the logic gates so that the number of bulbs which are on is the same as the number of switches which are on?
An interactive activity for one to experiment with a tricky tessellation
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
Can you fit the tangram pieces into the outline of this telephone?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
Can you fit the tangram pieces into the outline of Little Fung at the table?
An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.
Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?
Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4
A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
Can you fit the tangram pieces into the outlines of these people?
Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?
Can you fit the tangram pieces into the outlines of the chairs?
A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.
A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.
A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The winner is the player to take the last counter.
An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .
Try this interactive strategy game for 2
A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!
Exchange the positions of the two sets of counters in the least possible number of moves
A game for two or more players that uses a knowledge of measuring tools. Spin the spinner and identify which jobs can be done with the measuring tool shown.
A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?
The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.
Two engines, at opposite ends of a single track railway line, set off towards one another just as a fly, sitting on the front of one of the engines, sets off flying along the railway line...
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s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267867493.99/warc/CC-MAIN-20180625053151-20180625073151-00297.warc.gz
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CC-MAIN-2018-26
| 6,396 | 50 |
https://gmatclub.com/forum/the-net-proceeds-increase-as-the-number-of-tickets-sold-increases-did-263866.html
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math
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The net proceeds increase as the number of tickets sold increases. Did the net proceeds exceed $80,000 on 7,600 tickets sold?
(1) The net proceeds exceeded $40,000 on 4,000 tickets sold.
(2) The net proceeds exceeded $100,000 on $7,000 tickets sold.
As we're asked about a something that looks like a range (it has 'exceeds' = 'greater than'), we'll look at the extremes.
This is a Logical approach.
(1) So 4,000 tickets gave more than $40,000. We don't know if all the tickets have the same price or not so have no idea how much money 7,600 tickets netted. Could be $41,000 and could be $100,000.
(2) Since more tickets means more money than more than 7,000 tickets means more than $100,000, so definitely more than $80,000.
(B) is our answer.
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Watch free GMAT tutorials in Math, Verbal, IR, and AWA.
GMAT test takers: Watch now the GMAC interview with the people who write the GMAT test!
We discussed the chances of improving a GMAT score; how important the first questions on the test are; what to do if you don’t have enough time to complete a whole section; and more.
You can watch all the action from the interview here.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583516123.97/warc/CC-MAIN-20181023090235-20181023111735-00210.warc.gz
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CC-MAIN-2018-43
| 1,244 | 15 |
http://mathhelpforum.com/advanced-algebra/99676-2-short-problems.html
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math
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Show us how you've done the second one and we'll comment.
Hi, it's been awhile since I've been on here but I've now officially started Linear Algebra.
There are two problems in my homework I cannot solve. They are the following:
1. Find the equation of the form that passes through points and using elementary row operations on a matrix.
2. Find the equation of the parabola that pass through (0,3), (1,9) and (2,3) using elementary row operations on a matrix.
I believe I have the second problem solved but I am unsure of my answer. Thank you for looking at this! =)
Actually, I think I may be on my way to answering them both. It's just that I don't know what to do when I get to a certain point. Here goes:
for the y = mx + b problem....
I set it up as and .
I set up a matrix that looks like:
4 1 -1
1 1 8
I then set it up in rref form using about 8 steps, until I come out to a matrix that looks like...
1 0 -3
0 1 11
However, I don't really know what this tells me. I don't know how to check it, or set it up in an equation form. I get to the same point in the quadratic problem.
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s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698540928.63/warc/CC-MAIN-20161202170900-00452-ip-10-31-129-80.ec2.internal.warc.gz
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CC-MAIN-2016-50
| 1,085 | 16 |
https://slideplayer.com/slide/268336/
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math
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Presentation on theme: "1 PythagoreanTheorem Statement 2 In a right triangle The sum of the areas of the squares on its sides equals the area of the square on its hypotenuse."— Presentation transcript:
2 In a right triangle The sum of the areas of the squares on its sides equals the area of the square on its hypotenuse.
3 Proofs There are several proofs of Pythagorean theorem. Some of them are rigorous analytical proofs. They are based on the properties of triangles, such as congruence of triangles or similarity of triangles. Some others are based on transformations.
4 Analytical Proof We will now discuss a proof based on the congruence of triangles.
5 Consider a right triangle ABC Δ ABC is right angled at C.
6 It is given that triangle ABC is right angled at C We have to prove that Area sq. ACGF + Area sq. BCHK = Area sq. ABDE.
7 Now, consider ΔABF & ΔAEC They are congruent, because AE = AB (why?) They are sides of the same square ABDE AF = AC, (why?) They are sides of the same square ACGF And also, BAF = BAC + CAF = CAB + BAE = CAE Hence by SAS, Δ ABF = Δ AEC …(i).
8 But, the area of the ΔABF is half the area of the square ACGF. Δ ABF has base AF and the altitude from B on it = CA Its area therefore equals half the area of square on the side AF area Δ ABF =½ area sq. ACGF
9 The area of the ΔAEC equals half the area of the rectangle AELM. On the other hand, ΔAEC has base AE The altitude from C = AM, (where M is the point of intersection of AB with the line CL parallel to AE) Therefore, area of ΔAEC = ½ area rectangle AELM …(iii)
10 The area of the square ACGF = the area of the rectangle AELM We have From (i), Δ ABF = Δ AEC From (ii), area of Δ ABF = ½ area of sq. ACGF And from (iii), area of Δ AEC = ½ area of rect. AELM Thus, from (i), (ii) and (iii), area of sq. ACGF =area of rect. AELM **(a).
11 In the same way, Can you establish that The area of sq. BKHC =area of rect. BDLM…?
12 O.K. -- Let us consider ΔABK & ΔDBC They are congruent, because BD = BA (why?) BC = BK, (why?) ABK = ABC + CBK = CBA + ABD = DBC Hence by SAS, Δ ABK = Δ DBC …(iv)
13 The area of the ΔABK equals half the area of the square BKHC Δ ABK has base BK The altitude from A = BC. Therefore, area of Δ ABK = ½ area of square BKHC …(v).
14 The area of the ΔBDC equals half the area of the rectangle BDLM. On the other hand, Δ BDC has base BD The altitude from C = BM, Therefore, the area of Δ BDC = ½ area of rect. BDLM …(vi).
15 Thus, the area of the square on side BC equals the area of the rectangle BDLM We now have Δ ABK = Δ DBC … (iv) area of ΔABK =half area of sq. BKHC.. (v) And area of ΔDBC =half area of rect. BDLM.. (vi) From (iv), (v) and (vi), area of sq. BKHC =area of rect. BDLM **(b).
16 Combining the results area of sq. ACGF =area of rect. AELM **(a) And also, area of sq. BKHC =area of rect. BDLM **(b).
17 Summing UP area of sq. ACGF +area of sq. BKHC =area of rect. AELM +area of rect. BDLM = area of sq. AEDB. In other words, area of sq. on side AC + area of sq. on side BC. = area of the square on hypotenuse AB.
18 Applications Integers which can form the sides of a right triangle are called Phythagorean Triplets. Like 3,4 and 5. And 5,12 and … ??? Think Calculate.
19 Teaser (an extension activity) If two sides AC and BC measure 3 and 4 units -- But if the included angle is not a right angle -- but an obtuse angle, then AB will be….. More than 5. Again, if the angle is acute, then !!!!.
20 Verification We will now see a demonstration of verification of Pythagorean theorem through transformations.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823348.23/warc/CC-MAIN-20181210144632-20181210170132-00565.warc.gz
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CC-MAIN-2018-51
| 3,589 | 20 |
https://math.answers.com/Q/What_would_you_do_if_there_are_two_numbers_in_the_middle_when_you_are_doing_the_mean_in_maths
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math
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Technically it's the same away from both numbers, in maths you would round it up to 2!
WHY ARE YOU CHEATING IN THE MATHS CHALLENGE? I am doing it AND I HAVE THE ANSWER but u DONT desreve to have the ANSWER STOP CHEATING LOOSER
You take the arithmetic mean of the two middle numbers.
The same as you would in any other language.
When you are looking for the median, you are looking for the middle. So those numbers 12377901, first you would have to put them into numerical order. Which would be 0,1,1,2,3,7,7,9. An easy way to solve it from there would be to cross out each end. Making it 1,1,2,3,7,7. Keep doing that until you either have only one number left, or you have two numbers. In this equation you would have to numbers left, so you would look for the middle of those two numbers which would be 2.5. And there you have found the median of those numbers.
Yes, it would be in the middle of the middle two
Numbers help you with almost everything. Driving, school, sport, TV channels, and many more. Numbers may seem like a boring part of maths. We use maths in everyday life and all those idiots out there who think maths sucks and maths is boring and who call people nerds and geeks because they're smart, shame on you. Think about where you would be with out numbers. It's a hard life to live.
The "mean", or "mean average" in full, is obtained by adding up all the numbers and then dividing by the number of numbers there are. It is saying that if the numbers were all the same, this is what they would be.
If there are two numbers in the middle you find the middle in between that like if you hade 40 and 50 in the midlle the median would be 45.
pic the number between the middle one's e.g 1,3,4,6,8,9 the median would be 5 because it is between the 2 middle numbers
It would be the average (mode) of the two middle numbers, possibly a decimal value.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104669950.91/warc/CC-MAIN-20220706090857-20220706120857-00525.warc.gz
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CC-MAIN-2022-27
| 1,860 | 11 |
https://team.inria.fr/apics/habilitation-of-fabien-seyfert-analytical-methods-for-the-conception-and-tuning-of-microwave-devices/
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math
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Habilitation of Fabien Seyfert, Wednesday 6th of February, 14h00, Salle Euler Violet, Inria Sophia Antipolis.
Title: Analytical methods for the conception and tuning of microwave devices.
In this presentation I will expose part of the work I’ve been pursuing since my appointment at Inria in 2001. Passive microwave devices such as filters, multiplexers, power-dividers are ruled by Maxwell equations that describes the wave scattering phenomenon at the origin of their functioning. The central mathematical object is here the scattering matrix, that describes the linear dependency between the Fourier transforms of the incoming and outcoming modal power waves propagating in the transmission lines (or wave-guides) used to feed this type of hardware. Designing or conceiving this devices amounts to determine their physical dimensions, the size of their electromagnetic cavities and coupling irises, such as to meet certain frequency specifications formulated on their scattering matrix. Tuning procedures tackle the problem of correcting these dimensional parameters at hand of harmonic measurements performed on the system.
We will present here a de-embedding procedure for filters that aim to furnish a stable rational model of given MacMillan degree, when starting from narrow band incomplete harmonic measurements of these devices. We will show why the partial nature of the frequency measurement induces an ill-posed stable rational approximation problem and naturally brings us to state an analytic completion problem, best formulated in the framework of the classical Hardy spaces of holomorphic functions. The main question we will try to answer here is: how much additional information to the harmonic measurements is needed in order to perform a completion procedure in a satisfactory manner ? Without spoiling the suspense around this question, we can roughly answer it this way: as opposed to what the analytic continuation principle may suggest, quite a lot. After introducing elementary bounded extremal problems, we will detail a mixed norm version of these, where the modulus of the transfer needs to be specified for frequencies outside the measurement band. We will explain how this led us to consider a completion problem where additional information is provided, by means of a finite dimensional description of possible extensions of the data. The latter is at heart of the dedicated software toolbox Presto-HF that was transferred to academic, as well as industrial, practitioners of the filter community.
Working in close connection with filter specialists led us to consider a preliminary stage in the manufacturing process of filters: the synthesis of an ideal frequency response. We will describe here a procedure for the computation of multiband responses, with a guaranteed optimal selectivity at fixed degree and number of transmission zeros. A specific alternation property is presented in order to characterize optimal solutions of a set of signed quasi-convex sub-problems, in terms of alternating sequences of extremal points. As compared with Achieser’s result on uniform real valued rational approximation on an interval, our approach consists in an adaptation of the latter to the multi-band case and to the solving of a Zolotariov problem of the third kind.
Deembedding techniques as well as frequency response synthesis procedures have in common that they all end up with a rational 2×2 scattering matrix that needs to be realized as a circuit to proceed further in the filter’s tuning or synthesis process. The circuit used here is the low-pass prototype, which consists of ideally coupled resonators. The coupling topology, that is the way resonators are coupled, or not, one to another is crucial here. We present here a result stating the existence of a canonical circuital realisation called the arrow form. For circuits with non-canonical coupling topologies we develop an algebraic approach for the corresponding structured realisation problem, together with an abstract framework clarifying the compatibility conditions between coupling topology and class of frequency responses. Some formal results at the crossing of circuit theory and algebraic geometry will be discussed. Software implementations relying on the Groebner bases engine FGb and the dedicated toolbox Dedale-HF will be discussed.
We will eventually discuss contributions to the classical problem of broadband matching in electronics, encountered when conceiving energy efficient multiplexers and antennas. An approach based on Nevanlinna-Pick interpolation will be presented.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496667319.87/warc/CC-MAIN-20191113164312-20191113192312-00389.warc.gz
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CC-MAIN-2019-47
| 4,597 | 7 |
http://www.maa.org/press/maa-reviews/finite-mathematics-an-applied-approach
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math
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This textbook includes chapters on linear systems, matrix algebra, linear programming, finance, combinatorics, probability, statistics, game theory, and logic. However, these topics are presented without a unifying concept. Even though the author defines finite mathematics as “the area of mathematics that deals with the study of finite sets” on p. 327, there is no attempt to use this description to tie everything together. The subtitle “An Applied Approach” does not reflect the pedagogical style of the book. At the beginning of each section, specific computational and/or conceptual objectives are listed. When each idea is encountered, a reference is given to relevant problems in the exercise set. For the most part, applications are presented only after all the nuts and bolts are in place so that the ideas appear in context. Even though a large number of applications are included, they do not drive the presentation. Some are highly imaginative, and others are routine.
The reviews provided in the appendices are concise. In order for a student to be prepared fully for this book, he or she will need to have a strong background in College Algebra. For example, the chapter on Finance makes extensive use of exponents, logarithms, geometric sequences, and recursively defined sequences. However, there are significant portions of the book that can be processed by students with only a background in Intermediate Algebra. For example, the chapter on Probability is very accessible. Thus, in order to make appropriate use of this textbook, the instructor will need to select the material to include in his or her syllabus with care.
The instructional value of the book varies noticeably from chapter to chapter. This perception might be due in part to the differing prerequisites for each topic. I found the chapter on the geometric approach to linear programming to be well written. The technical concepts are presented in detail so that less sophisticated readers can follow along, and several nice applications are given. On the other hand, the chapter on the Simplex Method demands a considerable amount of “mathematical maturity” from the reader. The steps are given for all key computations, but there are relatively few intuitive justifications. A similar dichotomy can be seen in Chapters 2 and 10. Several matrix applications are developed in these chapters. In Section 2.7, the authors clearly demonstrate the role of the inverse matrix in the Cryptography application, but there is no hint of the role of the transpose matrices in the solution to the Least Squares problem. In Section 10.3, the entries of the fundamental matrix of an absorbing Markov chain are interpreted and several examples are given, but no intuition is given to support the conclusions. On the other hand, the distinctions between pure and mixed Game Theory strategies and the justifications for the expected payoff computations in Sections 10.4 – 10.6 are clear.
A nice feature of the book is the inclusion of examples that utilize graphing utilities and spreadsheets. The authors highlight relevant syntax details. In some chapters, mathematical questions from professional exams (CPA, CMA, and Actuary Exams) are reproduced. A glossary would have been helpful for some of these questions. There are several errors and omissions that mar the exposition. The definition of echelon form in Chapter 2 is imprecise in the sense that the authors do not consider the possibility that the first column could represent a free variable. The presentation of the Open Leontief Model reverses notation between p. 131 and p. 136. The inflation model on p. 278 actually computes depreciation by a given rate, not the purchasing power. Table 20 on p. 609 is presented without explanation, and the description of indirect proof on p. 611 is much too terse. The argument in Exercise 4 on p. 612 has no conclusion. Section C.5 is listed in the contents for Appendix C on p. 621, but it is missing from the book.
Because of some pedagogical features, graded exercise sets, and extensive coverage of applications, the book can be used successfully in finite mathematics courses. Overall, however, I consider the book to be mediocre because of the deficiencies outlined above.
Jerry G. Ianni teaches at LaGuardia Community College.
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https://discussion.evernote.com/tags/deselecting%20offline%20notebooks/
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math
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Search the Community
Showing results for tags 'deselecting offline notebooks'.
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Evernote is taking up a lot of space on my Android. I may have selected too many large notebooks for use offline. I am trying to deselect them, but don't know how. I don't see anything in the Notebooks queue indicating whether a notebook has been designated as an offline notebook. I deleted EN and reinstalled it, but it still seems to be quite large.
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CC-MAIN-2020-24
| 446 | 4 |
http://www.paywizard.org/main/salary/minimum-wage/missouri
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math
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Overtime Pay Missouri: $11.55 per hour
The overtime pay rate is one and one-half (1.5) times the regular working hour rate of pay. Overtime pay is the cash compensation for the hours eligible employees work in excess of:
40 hours in a workweek (a workweek = 7x24= 168 hours).
12 hours per workday
12 consecutive hours without regard to the starting and ending time of the workday (excluding duty free meal periods)
Whichever calculation results in the greater payment of wages.
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http://scootle.edu.au/ec/viewMetadata.action?id=L7826&q=&topic=%22Backstage%22&start=0&sort=relevance&contentsource=&contentprovider=&resourcetype=&v=text&showBookmarkedResources=&showLomCommercialResources=false&field=title&field=text.all&field=topic&contenttype=all&contenttype=%22Interactive%20resource%22&contenttype=%22Tablet%20friendly%20(Interactive%20resource)%22&contenttype=%22Collection%22&contenttype=%22Image%22&contenttype=%22Moving%20image%22&contenttype=%22Sound%22&contenttype=%22Assessment%20resource%22&contenttype=%22Teacher%20guide%22&contenttype=%22Dataset%22&contenttype=%22Text%22&contenttype=%22Mobile%20app%22&commResContentType=all&commResContentType=%22App%20(mobile)%22&commResContentType=%22Audio%22&commResContentType=%22Book%20(electronic)%22&commResContentType=%22Book%20(printed)%22&commResContentType=%22Digital%20item%22&commResContentType=%22Learning%20object%22&commResContentType=%22Other%22&commResContentType=%22Printed%20item%22&commResContentType=%22Software%22&commResContentType=%22Teacher%20resource%22&commResContentType=%22Video%22&userlevel=all&userlevel=(0%20OR%201%20OR%202)&userlevel=(3%20OR%204)&userlevel=(5%20OR%206)&userlevel=(7%20OR%208)&userlevel=(9%20OR%2010)&userlevel=(11%20OR%2012)&kc=any&lom=true&scot=true&follow=true&topiccounts=true&rows=20&suggestedResources=R11593,R11112,L9673,R7395,L9497,R11493,L9778,L8751,R5669,R11253,R11592,R7604,R10723&fromSearch=true
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math
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TLF ID L7826
Observe the linear and non-linear distance–time graphs of a rocket travelling at both constant and changing velocities. Calculate the average and instantaneous velocities of the rocket over different time intervals. Notice what happens to the average and instantaneous velocities as the time intervals become smaller. Work out the relationship between these velocities and the gradients of secants and tangents. This learning object is a combination of two objects in the same series.
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http://frownage.xooit.fr/t181-Introduction-To-Algorithms-Epub-Free-100.htm
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math
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[PDF/ePub Download] introduction to algorithms eBook Download Ebook : introduction to algorithms in PDF Format.
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https://slideplayer.com/slide/4947506/
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math
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Regression Analysis. Unscheduled Maintenance Issue: l 36 flight squadrons l Each experiences unscheduled maintenance actions (UMAs) l UMAs costs $1000.
Published byModified over 6 years ago
Presentation on theme: "Regression Analysis. Unscheduled Maintenance Issue: l 36 flight squadrons l Each experiences unscheduled maintenance actions (UMAs) l UMAs costs $1000."— Presentation transcript:
95% Confidence Interval on our estimate of UMAs and costs l 60 + 2(2) = [56, 64] l low cost: 56 * $1000 * 36 = $2,016,000 l high cost: 64 * $1000 * 36 = $2,304,000
What do you want to know? l How many UMAs will there be next month? l What is the average number of UMAs ? l Is there a relationship between UMAs and and some other variable that may be used to predict UMAs? l What is that relationship?
Relationships l What might be related to UMAs? n Pilot Experience ? n Flight hours ? n Sorties flown ? n Mean time to failure (for specific parts) ? n Number of landings / takeoffs ?
Regression: l To estimate the expected or mean value of UMAs for next month: n look for a linear relationship between UMAs and a “predictive” variable n If a linear relationship exists, use regression analysis
Regression analysis: describes and evaluates relationships between one variable (dependent or explained variable), and one or more other variables (called the independent or explanatory variables).
What is a good estimating variable for UMAs? l quantifiable l predictable l logical relationship with dependent variable l must be a linear relationship: Y = a + bX
Describing the Relationship l Is there a relationship? n Do the two variables (UMAs and sorties or experience) move together? n Do they move in the same direction or in opposite directions? l How strong is the relationship? n How closely do they move together?
Correlation Coefficient l Statistical measure of how closely two variables are moving together in a coordinated fashion n Measures strength and direction l Value ranges from -1.0 to +1.0 n +1.0 indicates “perfect” positive linear relation n -1.0 indicates “perfect” negative linear relation n 0 indicates no relation between the two variables
A Word of Caution... l Correlation does NOT imply causation n It simply measures the coordinated movement of two variables l Variation in two variables may be due to a third common variable l The observed relationship may be due to chance alone
What is the Relationship? l In order to use the correlation information to help describe the relationship between two variables we need a model l The simplest one is a linear model:
Testing Model Parameters l How well does the model explain the variation in the dependent variable? l Does the independent variable really seem to matter? l Is the intercept constant statistically significant?
Basic Steps of Regression Analysis l Formulate the model l Plot scatter diagram for visual inspection l Compute correlation coefficient l Fit the regression line l Test the model
Factors affecting estimation accuracy l Sample size (larger is better) l Range of X values (wider is better) l Standard deviation of U (smaller is better)
Uses and Limitations of Regression Analysis l Identifying relationships n Not necessarily cause n May be due to chance only l Forecasting future outcomes n Only valid over the range of the data n Past may not be good predictor of future
Common pitfalls in regression l Failure to draw scatter diagrams l Omitting important variables from the model l The “two point” phenomenon l Unfounded claims of model sophistication l Insufficient attention to interval estimates and predictions l Predicting too far outside of known range
Summary l Regression Analysis is a useful tool n Helps quantify relationships l But be careful n Does not imply cause and effect n Don’t go outside range of data n Check linearity assumptions n Use common sense!
Non-linear relationship between output and cost
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http://www.chegg.com/homework-help/problems-section-103-solved-integrating-differential-equatio-chapter-10.3-problem-8p-solution-9781111577735-exc
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math
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The problems for Section 10.3 are to be solved by integrating the differential equations of the deflection curve. All beams have constant flexural rigidity EI. When drawing shear-force and bending-moment diagrams, be sure to label all critical ordinates, including maximum and minimum values.
A fixed-end beam of length L is loaded by a distributed load in the form of a cosine curve with maximum intensity q0 at A.
(a) Use the fourth-order differential equation of the deflection curve to solve for reactions at A and B and also the equation of the deflection curve.
(b) Repeat part (a) using the distributed load q0 sin(πx/L)
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https://www.terasolartisans.com/john/notes-of-a-writers/how-many-radians-are-in-an-hour/
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math
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How many radians are in an hour?
Hour angles to Radians
|1 Hour angles = 0.2618 Radians||10 Hour angles = 2.618 Radians|
|2 Hour angles = 0.5236 Radians||20 Hour angles = 5.236 Radians|
|3 Hour angles = 0.7854 Radians||30 Hour angles = 7.854 Radians|
|4 Hour angles = 1.0472 Radians||40 Hour angles = 10.472 Radians|
How do you represent minutes?
Degrees, minutes and seconds are denoted by the symbols °, ‘, “. e.g. 10° 33’ 19” means an angle of 10 degrees, 33 minutes and 19 seconds . A degree is divided into 60 minutes (of arc), and each minute is divided into 60 seconds (of arc).
How many degree make an hour?
How do you convert degrees to hours?
Convert from Degrees to Hour angles….Degrees to Hour angles.
|1 Degrees = 0.0667 Hour angles||10 Degrees = 0.6667 Hour angles||2500 Degrees = 166.67 Hour angles|
|2 Degrees = 0.1333 Hour angles||20 Degrees = 1.3333 Hour angles||5000 Degrees = 333.33 Hour angles|
|3 Degrees = 0.2 Hour angles||30 Degrees = 2 Hour angles||10000 Degrees = 666.67 Hour angles|
How do you write hours and minutes?
If you are using numerals, you would usually include both hours and minutes, although you can omit the minutes in less formal writing. For instance, all the following would be acceptable: She gets up at six in the morning every day. She gets up at 6:00 in the morning every day.
How do I write hours and minutes in Word?
When writing out the time of day in words, use a hyphen between the hour and the minutes, unless the minutes themselves are hyphenated:
- I leave for work between eight and eight-thirty.
- Megan usually leaves for work at about eight forty-five.
What is a symbol for time?
A common symbol used now is the hourglass. Although this is an object we don’t use in everyday life, the symbolism of time slipping away from one, and the common phrase “the sands of time” show that this metaphorical understanding of time pervades at least English-language thought.
How do you convert degrees to time?
1 degree of arc is define as 1/360 of a revolution. In SI units 1° is π/180 radians. 1 Minute of time (astronomical): 1 Minute of time (astronomical) is equal to 1 turn/1440.
How many hours is 45 degrees?
Hour angles to Degrees
|1 Hour angles = 15 Degrees||10 Hour angles = 150 Degrees|
|3 Hour angles = 45 Degrees||30 Hour angles = 450 Degrees|
|4 Hour angles = 60 Degrees||40 Hour angles = 600 Degrees|
|5 Hour angles = 75 Degrees||50 Hour angles = 750 Degrees|
|6 Hour angles = 90 Degrees||100 Hour angles = 1500 Degrees|
What is the symbol for an hour?
How do you write 2 hours and 45 minutes?
How to Convert Time to Decimal
- 2 hours is 2 hours * (1 hour/ 1 hour) = 2 hours.
- 45 minutes is 45 minutes * (1 hour / 60 minutes) = 45/60 hours = 0.75 hours.
- 45 seconds is 45 seconds * (1 hour / 3600 seconds) = 45/3600 hours = 0.0125 hours.
- Adding them all together we have 2 hours + 0.75 hours + 0.0125 hours = 2.7625 hours.
How do you convert degrees to minutes and seconds?
How to Convert Decimal Degrees to DMS
- For the degrees use the whole number part of the decimal.
- For the minutes multiply the remaining decimal by 60. Use the whole number part of the answer as minutes.
- For the seconds multiply the new remaining decimal by 60.
How do you write time in words?
For novels (fiction and non-fiction), the general rule is to spell out time. When expressing time in words instead of numerals, you should use a hyphen, as in five-fifteen. But when a hyphen is necessary in the expression of minutes, only hyphenate the minutes, as in five forty-five.
Can an angle be negative?
Angle measure can be positive or negative, depending on the direction of rotation. Rotation is measured from the initial side to the terminal side of the angle. Positive angles (Figure a) result from counterclockwise rotation, and negative angles (Figure b) result from clockwise rotation.
What is the radian measure between arms of watch at 5 pm?
At 5 PM , the arms of a 12-hour clock are separated by 5/12 of a full circle. Thus the angle between them is 5/12 of 2π radians = 5/6 π radians or roughly 2.618 radians.
How do you convert degrees minutes to radians?
To convert degrees to radians, first convert the number of degrees, minutes, and seconds to decimal form. Divide the number of minutes by 60 and add to the number of degrees. So, for example, 12° 28′ is 12 + 28/60 which equals 12.467°. Next multiply by π and divide by 180 to get the angle in radians.
What is the symbol for hours and minutes?
While the unit s , seconds is an SI standard, the symbols h for hours and min for minutes are accepted for use with SI standards although they are not SI standard units of measure, being integrals of the basic accepted standard, s.
How many degrees is a triangle?
How is 1 degree 60 minutes?
1 degree can be equal to 60 parts which should be called seconds not minutes. And 60 minutes forms 360 degree .
How many seconds are present in 2 degree?
Please share if you found this tool useful:
|1 Degrees to Seconds Of Time = 240||70 Degrees to Seconds Of Time = 16800|
|2 Degrees to Seconds Of Time = 480||80 Degrees to Seconds Of Time = 19200|
|3 Degrees to Seconds Of Time = 720||90 Degrees to Seconds Of Time = 21600|
How do you write 1 minute?
To write an abbreviated version of minutes, you can use the following: min. ‘ (informally)…Abbreviations for Minutes
- 1 min.
- 5 min.
- 45 min.
How do you convert from radians to hours?
Convert Radians to Hour Angles One full turn is 2π radians. 1 Hour Angle: 1 Hour angle is 1 turn/24 or 15°. In terms of SI units an hour angle is π/12 radians.
How many hours are in 360 degrees?
How do you write 24 hour clock in words?
The abbreviations AM and PM can be used when writing the time as numerals. Each applies to a different time of day: AM is short for ante meridiem, meaning ‘before noon’….2. AM and PM.
|Time||12-Hour Clock||24-Hour Clock|
|Three in the afternoon||03:00 PM||15:00|
|Half eight in the evening||08:30 PM||20:30|
How do I type a degree symbol?
How to Type the °
- PC. Hold down the Alt key, and on the numeric keypad on the right of the keyboard, type 0176 or Alt+ 248.
- Mac. Press Option Shift 8.
- iOS. From the iOS keyboard on your iPhone or iPad:
- Android. Switch to the numbers and symbols keyboard. The degree symbol should appear on one of the pages.
How many seconds are in an angle of 15?
How do I type a minute symbol?
Either Alt+0176 or Alt+248 can be used to add degree symbol to represent coordinate values in Degrees Minutes Seconds (DMS).
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http://leopand.ru/using-trigonometry-to-find-angle-measures/
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math
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Find the measure of angle, to the nearest degree. BBC – GCSE Bitesize: Finding an angle We have been given the lengths of AC and BC and asked to find angle C. Trigonometry problems – Slope angle – Math Open Reference Given a slope with some know dimensions, how to find the angle of the slope. Solving for an angle in a right triangle using the trigonometric ratios Read and learn for free about the following article: Intro to inverse trig.
Step Find the angle from your calculator, using one of sin- cos-or tan-1. Solving problems using trigonometry – slope angle. Home Algebra Data Geometry Measure Numbers Dictionary Games Puzzles Worksheets.
Find each angle measure to the nearest degree. Using Trig Ratios to Solve Triangles: Angles – Soft Schools Trig ratios can be used not only to find the length of the sides of a right triangle but also to find the measure of the angles. SohCahToa Find an Angle using Inverse Functions – That Quiz Right triangle trigonometry relates the sides of a right triangle to the. But this doesn t help us find the measure of L angle L Langle, L.
Using Trigonometry to Find Angle Measures – Kuta Software Date. We can find an unknown angle in a right-angled triangle, as long as we. Using Right Triangle Trig to find Angle Measures – This video provides a specific example of how to find angle measures using right triangle trigonometry. Inverses of Trigonometric Ratios – Purplemath Explains what the inverse trig buttons on a calculator are, and how to use them. The steps are the same as the ones we. Angle measures of the two acute angles.
Finding an Angle in a Right Angled Triangle – Math is Fun Random Trigonometry Twitter StumbleUpon Facebook Link To Us. Questions involving trigonometry and right-angled triangles will only require you to know. (b) Each open-ended valve or line equipped with a second valve shall be operated in a manner such that the valve on the process fluid end is closed before the. 24hr Day Immersion Heater Timers – TLC Direct Hard Wired Timers Timeswitches – Analogue – Voltage Free Contacts.
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Features Built to Mullard specification by U.S. Figure about 0watts to run essentials like a refrigerator, stove and.
Finally you should learn how connecting the oscilloscope will influence your circuit with regard to. For installing into most walls using the telescopic liners provided.
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Using Trigonometry to Find Angle Measures – Kuta Software
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https://jetestelavirb.com/the-square-of-pi/
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math
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The Square Of Pi. High street apt 3f columbus, oh 43215: And other edible math conundrums.
High street apt 3f columbus, oh 43215: Previous irrational number next irrational number Most people don’t care about finding the square root of pi.
But As You Can See, 22/7 Is Not Exactly Right.
The rule is the same for pi: The number π (/ p aɪ /; The value of pi is 3.1459, and the square root of pi is equal to 1.77.
By Doing This, Instead Of Merely Using The Rounded 3.14, One Will Have An Answer That Is More Accurate.
Contact us about the company profile for pi. The first 10 digits of pi (π) are 3.1415926535. Most people don’t care about finding the square root of pi.
That Clearly Isn't Pi Squared.
Considering this, is pi squared infinite? Using the calculator once more, take the square root of pi. The rhind papyrus (ca.1650 bc) gives us insight into the mathematics of ancient egypt.
Furthermore, What Is The Full Number Of Pi?
Pi r squared pi is used to find area by multiplying the radius squared times pi. And other edible math conundrums. Pi ratio simply squared as g.
The Sqare Root Of Pie Is About 1.7724538509055.
9.8596 degree = 0.172082483 radian. It is denoted as √π. Why not calculate the circumference of a circle using pi here.
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https://www.thomasaquinas.edu/news/dr-carol-day-lining-numbers-place-books-7-9-euclids-elements
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math
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Receive TAC Lectures via Podcast!
by Dr. Carol Day
Thomas Aquinas College
St. Vincent de Paul Lecture and Concert Series
March 19, 2021
When I first taught Euclid’s Elements, I was puzzled about several features of the “Number Books,” Books 7-9. I was not surprised to find that the students were puzzled too. For the most part, we were used to and comfortable with Euclid’s style and method by the time we got through Book 6, but what was he up to in Book 7? The long list of definitions at the beginning showed that he was launching into arithmetic. But why take up numbers at this point? Why not give us more theorems in plane geometry or perhaps move on to solid geometry? What we got instead were propositions about relatively prime numbers and about numerical ratios. I was puzzled, and I am very sure that I was not the only one in the classroom wondering about what Euclid was up to.
There were other puzzling features of Euclid’s presentation. After the usual enunciation in words, he displays numbers in the setting out as lines. Given the mathematical custom in which I was brought up, I would have liked the setting out to be done using algebraic notation, and I noticed that some of the students wanted that too. This was evident from the way they wrote out their demonstrations. I also wondered about the order in which he presented his propositions. Why doesn’t he begin the study of arithmetic from the beginning, as one would expect from his practice in the geometrical books, and then go through theorems about numbers in a systematic way? Why in particular does he begin his study of numbers with relatively prime numbers?
Much later on, I had other questions about the arithmetical part of the Elements. Why are these books placed after the treatment of plane geometry and before the treatment of solid geometry? I also wondered whether we should conceive of Book 10, his treatment of irrational magnitudes, as belonging with Books 7-9 rather than as a book standing on its own or just as a necessary preparation for solid geometry. This last question did not occur to me when I first taught the Elements, but it seemed an obvious thing to wonder about when I came back to Euclid many years later.
My plan is to address all these questions, although I can make no promise to settle them all. Since much of my talk will concern the order of the Elements and the number books within it, it would be reasonable to set out the order in which they will be addressed. I will begin with the representation of numbers by lines. This consideration stands apart from the somewhat entangled issues of the order of propositions and of the books themselves. But I hope to show that an understanding of Euclid’s method of representing numbers provides important clues for understanding the rest.
In the second part of this lecture I will ask about the appropriateness of including arithmetical books in a work of geometry, and in the third and fourth parts I will deal with questions about the order of the propositions in Books 7-9 and with the place of the number books in the overall scheme of the Elements.
Part One: The Representation of Numbers by Lines
Note: when I say line, I will mean straight line, unless I specify otherwise.
I remember many times my much beloved colleague and friend, Molly Gustin, would say that numbers are lines. Despite the fact that we disagreed about this, I can understand why she said it. I think she was influenced both by Euclid’s way of depicting numbers and by Descartes’ extension of arithmetical concepts into geometry. In defense of her notion, remember that it has become a common-place to speak of the Cartesian “number line,” as something comprising all the real numbers. To be fair to Mrs. Gustin, I believe that she was trying to give an account that made sense of calling the real numbers ‘numbers’. But if the whole numbers, those with which Euclid was concerned, are also real numbers, the temptation is there to state in a categorical way that numbers are lines. I think the identification of real numbers with lines is a mistake, but my concern here is not with that but with the interpretation of Euclid. Whatever numbers were for Euclid, they were not lines.
Since Euclid defines number as a multitude of units, one need only look at his definition of unit to see what he understands numbers to be. His definition is broad, to say the least! He says that “An unit is that by virtue of which each of the things that exist is called one.” Thus we can speak of one line, one sphere, one point, one cow, one instance of blue, one thought, and so on. The unit is something common to them all. He does not make clear what this common thing is, probably because he thought it was enough for the mathematician to see that the unit is the principle of number and that it has some existence apart from its concrete or geometrical manifestations. The determining of its exact nature of its existence belongs to a higher science than mathematics.
In my opinion, then, Euclid’s use of lines to represent numerable things does not imply a thesis about the nature of number. What remains, then, is to explain why lines are suitable and in fact the best way available to him for representing numbers.
At least two methods for depicting numbers were available to Euclid. One was the use of numerals. This method was used by Nicomachus in his Introduction to Arithmetic. In his History of Greek Mathematics, Heath compares Nicomachus’ method to Euclid’s, saying that that the method of representing numbers by lines “has the advantage that, as in algebraical notation, we can work with numbers in general without the necessity of giving them specific values; in Nicomachus numbers are no longer denoted by straight lines, so that when different undetermined numbers have to be distinguished, this has to be done by circumlocution, which makes the propositions cumbrous and hard to follow, and it is necessary after each proposition has been stated, to illustrate it by examples in specific numbers. Further, there are no longer any proofs in the proper sense of the word.”
Consider as an example Book 7, Proposition 1. First, here is how Euclid expresses it.
“Two unequal numbers being set out, and the lesser being continually subtracted from the greater, if the number which is left never measures the one before it until the unit is left, the original numbers will be prime to one another.” Following the enunciation comes the “setting out,” as Proclus calls it: “For the less of two unequal numbers AB and CD being continually subtracted from the greater, let the number which is left over never measure the one before it until a unit is left. “ AB and CD refer to a diagram, which looks like this:
__________________ ______________ _____
A H E B C F D G
Here AB and CD are numbers being measured, G is supposed as a common measure, and AH is the unit. It is Euclid’s practice to letter both endpoints of a line, as well as its points of division, assuming that the number it represents needs to be measured. If a number does not need to be measured, he usually names it with a single letter. The proof, then, is carried out using these letters as stand-ins for the numbers and their parts.
If Euclid had recourse only to determinate numbers, the setting out would have to look something like this: “For the lesser of two numbers, for example 5, being continually subtracted from the greater, for example 93, let the number left never measure the one before it until the unit is left, then 5 and 93 are prime to one another.” The supposed proof would be a calculation. 5 x 18 = 90. So with 5 subtracted from 93 eighteen times, we have 3 left. Now 3 subtracted from 5 leaves 2. and 2 subtracted from 3 leaves 1. Since following the subtracting algorithm leads me to the unit before I find a common measure, I want to assert that there is no other common measure. But how do I prove this? I can go through all the numbers up to 5 to see if they also go evenly into 93, but when I see that none of them do what will I have learned? Only something particular to these two numbers. The only alternative is to suppose some indeterminate common measure other than the unit, give it a name such as G, and work out a proof like Euclid’s, in which thinking of the original numbers as particular examples is pointless, in fact distracting.
It’s tempting to simply write off argument by means of examples as unscientific if not impossible. Nonetheless, we ought to think about how it differs from what Euclid does in proving geometrical theorems. Some concrete representation of the thing to be proved needs to be presented to the imagination, and whatever is in the imagination is singular, not universal. To prove a theorem about triangles, Euclid must give us a particular triangle, with determinate sides and angles. How is this unlike using a numerical example?
In a geometrical proof, it is not difficult to look at a concrete individual and attend only to the features that are relevant to the argument. For example, in looking at the drawing of a triangle for the purpose of proving Book 1, 5, that the base angles of an isosceles triangle are equal, we need to imagine that there are two equal and one unequal side and which are the base angles, but we don’t need to attend to the relative lengths of the equal and the unequal sides. It is easy to see that these details do not enter into the argument. We can even see that the proof works if all three sides happen to be equal. The abstraction of the relevant from the irrelevant is often easy to do in geometry. But there is something about the way in which concrete numbers exist in our imagination that gets in the way of performing the necessary mental trick. I think this has to do with the mode in which they must be defined.
To see why the modes of definition are different in arithmetic and in geometry, consider how the infinite exists in each. In magnitude, we have the infinity of infinite divisibility. As such, the infinite has no relevance to the definition of figures, having to do only with their material aspect, that is, with the continuum in which the figures exist. The formal features of figures arise from their shapes. Geometrical figures are defined by their boundaries, and all their properties flow from the nature of these boundaries. Even in theorems having to do with areas and volumes, where the properties that result from their forms are often harder to know, it is by considering the implications of their boundaries that we learn what we can. This is true even in the use of calculus.
It is quite otherwise with numbers. Numbers are infinite by addition, growing ever greater as we count them. Having no position, they also have no boundaries. One might even say that a given number is a boundary. That is, a number terminates a progression radiating outward from the unit. Whatever is formal in the number comes from the nature of this boundary, which gives rise to the distinctive way in which it is a multitude. It follows that unlike magnitudes, which are defined by way of genus and difference, numbers require a different kind of definition.
Let me explain what I mean by that. Suppose I want to define the number four. It is true but not altogether helpful to say that four is four ones, since it begs the question. Rather, four must be defined at the number that comes next after three, as that number in which a unit is added to three. This may sound like a purely nominal definition, but it is more than that. The nature of any number depends on the nature of the number before it, going all the way back to the unit. All the previous numbers are in it as potency to the next number, which is brought to act by the joining of another unit. The act of joining another unit to three makes what was potentially four to become actually four.
What this amounts to is saying that the additional unit plays the role of form or species in the definition of a number, and the number to which it is added plays the role of matter. St. Thomas makes this point in his Commentary on the Metaphysics, Book 8, Lectio 3: “A number is one per se in as much as its final unit gives to the number unity and species; just as in things composed of matter and form a thing is one through its form and takes on its unity and species.”
Let me say in passing that I do not propose to say how the new unit is added, or exactly what it means to add it. However it comes about in the being of the numbers themselves, what the mathematician sees is that three becomes four when another unit is added to it. As a simple example of how this act of joining the last unit determines a new property, just consider how the new unit changes the number from odd to even. But note how this mode of defining reveals very little about the properties of the number. Though it is obvious that the next number after 4 is odd, we cannot see in any easy way that 5 is the only prime number that is the sum and difference of two primes. 5 = 2 + 3, 5 = 7 - 2.
The discovery and proof of theorems like this would be difficult if not impossible without the analytic methods of modern mathematics. Fortunately, this branch of the science, which pursues the characteristic properties of individual species of number, is not what Euclid was concerned with. This is the branch of arithmetic that is as far from geometry as possible.
If then a specific number is the boundary of an act of accumulating units, so that no other kind of definition can be given by us, how do we translate such a definition into something useful for geometry? I think Euclid had a good answer: we reason about numbers by considering them as measuring and as measured. The ultimate measure of a number is the unit, and its multitude is the distinctive way that the unit measures it.
Measuring is an act of dividing. The geometer, therefore, divides numbers and impose order upon them in order to reveal their properties. Now measure is first known to us in extended things, in things we can sense. The first notion of measure is of a magnitude laid out along another magnitude so that it goes into it a certain number of times. The very name of Euclid’s science, Geometry, i.e. earth measurement, refers to this very practical procedure. Although there is something arbitrary in measurement -- one can begin from either end, for example -- there is a comprehensible order of the units from left to right or vice versa. Laying down the unit randomly leads to error and counting the divisions unsystematically leads to confusion. When counting material objects, we tend to imitate this spatial order by systematically ordering the things themselves in space. There is plenty of evidence that in ancient times livestock were counted by associating them one by one with notches in a stick. You may have experienced this in counting pennies by grouping them in groups of five or ten. On the other hand, the units in an abstract number are not laid out alongside each other, nor are they visible in the representation of a number by a numeral. Where are the units in 7? There is no ‘where’ there! And what happens when we subtract one number from another? When we subtract 3 from 7, we don’t think about which of the units in 7 are being taken away! Here we see an advantage of representing numbers by divided lines. By ordering the units in space we give our imagination something to make use of as we go about discovering and proving properties of numbers.
Representing numbers by lines seems to be an obvious choice, but this was not the only choice Euclid could have made. Another technique was available to him, one which had proved useful to his predecessors. Since the unit is indivisible, it would seem logical to represent it by a point. A number, then, would be represented by a set of points, since the unit is as it were the material from which the number is formed. In Metaphysics XIII Chapter 8, Aristotle describes this approach: “They [that is, some of the Pythagoreans] conducted their inquiry at the same time from the standpoint of mathematics and from that of universal formulae, so that from the former standpoint they treated unity, their first principle, as a point.”
This way of depicting numbers has its uses. When the numbers in question have properties analogous to geometrical properties, this way of depicting them can be helpful for the discovery of theorems. Such for example are square, cubic and triangular numbers. For numbers like these, a visual presentation of their nature is possible by drawing an orderly array of dots. Here is an informal demonstration that summing successive odd numbers produces the sequence of square numbers:
Representing these numbers by arrays of dots can indeed serve the imagination well enough, where they are appropriate. Although the diagram is not a formal proof of the theorem, it is in itself quite convincing. This method covers a very small territory in the realm of numbers, however. Symbolizing a number such as 7 by a line of dots does not have any obvious advantage over using a line divided into 7 segments. Euclid’s way seems to have the disadvantage of not representing perfectly the nature of number as discrete quantity, but it is superior in that it does not give the false impression that 7 is nothing more than 7 ones side by side, as if the number had no character and unity of its own.
Let us now look at a distinctive advantage of visually articulating parts of numbers, whether units or other divisors, by the use of divided lines. The lines may always be made of reasonably short length since any arbitrarily small line can be thought of as the unit. As mentioned above, we are able in this way to grasp the number as a whole containing these parts. Because of the abstractness of the representation, it is not hard to disregard the actual number of divisions in the illustration and to focus on what is essential. In other words, there is no reason to pay attention to the actual count of the divisions, as if one were merely calculating.
Lets see how this works by looking at proposition 7, 4, which proves that any number is either a part or parts of any number, the less of the greater.
B E F C
Recall that a number is part of a larger number if it measures it without a remainder, but parts if there is a remainder. Thus 3 is part of 6, but it is parts of 7. In the proof, the larger number is represented by A and the lesser by BC. Although it contains the lesser number, the laying out of BC alongside A isn’t necessary. Everything hangs on whether or not A and BC are prime to one another. If BC measures A, it is a part and all is well. If it does not measure it, we need only take the greatest common measure of A and BC, represented by line D. BC is shown as divided into parts BE, EF, EC equal to D, to show that a part existing in BC is also a part of A. That is what it means to say that BC is parts of A; it is made up of numbers which are themselves parts of A.
The articulation of the lines into parts helps one to understand the reason for the theorem. The fact that BC is shown as divisible into three parts does not get in the way of understanding the proof, for it is not hard to see that the exact number of times D is subtracted does not matter to the argument. The proof rests on the nature of measurement, and measure is illustrated in the lines in a way that does not call to mind vividly the particular results of the measurement. Is this not the key to understanding Euclid’s use of lines? Seeing measurement at work requires an order in space and nothing more.
To sum up, then: By representing a number as a divided line, the teacher exhibits its formal character in a sufficiently detailed way, which he could not do by showing it as a numeral. Showing numbers as lines depicts them as quantities relatable to one another either through one measuring the other or through their having some common measure. In this way Euclid facilitates our grasp of the truths which he wants to prove about them.
Part Two: Why does the Elements contain the Number Books?
Before considering the place of the number books in the Elements, we might ask why they are there at all. Euclid does not tell us why he included them, and I have found nothing in Heath’s history or commentaries to shed light on the matter. Since I can’t answer that question, I can at least point out some advantages of including them. The inclusion of the arithmetical books allows Euclid to show that there is an analogy between the subject matter of geometry and the subject matter of arithmetic by proving comparable properties for numbers and magnitudes, each by means of proper principles. . Examples of this abound, but I will illustrate with one. In 7, 13 Euclid proves “If four numbers be proportional, they will also be proportional alternately.” Here is an example: since 2:4 :: 5: 10, so also 2:5 :: 4:10. This proposition is proved from the definitions in Book 7 of part and parts. In 5, 16 Euclid had proven the comparable theorem in geometry: “If four magnitudes are proportional, they will also be proportional alternately.” This proof rests on the definition of same ratio given at the beginning of Book 5. Euclid’s drawing out of the likeness as well as the difference between geometrical and arithmetic theorems is I think the most important result of including the books on arithmetic, at least from a philosophical point of view. I say this because the relation between number and magnitude was a controversial issue for the Greeks and in fact is still a question of great interest.
We moderns are accustomed to the idea that there is a universal mathematics, one which is most properly expressed in symbols. There have been various ideas about how universal mathematics stands with respect to arithmetic and geometry. For Viete, Descartes’ predecessor in the invention of algebra, the symbols and the rules for their manipulation are the same for both kinds of mathematics, but each requires a distinct process of interpretation and justification. Another opinion is they are unified by a common subject matter, which might be called quantity as such. A common opinion among the moderns is that mathematics is a branch of logic, so that the symbols themselves seem to be its subject matter.
More importantly for our purposes, though, was the pre-Euclidean opinion that all quantity is the same kind of thing because all quantities are commensurable. This Pythagorean understanding would reduce all mathematics to arithmetic. This view could no longer be held after the shocking discovery that the side of a square and its diagonal are have no common measure. Prior to the scandal of the incommensurable, several of the theorems we find in the first four books Elements had flawed proofs based on a purely numerical theory of proportion. Here is how Heath describes the situation:
After the discovery of this one case of irrationality [i.e. of the square root of two] it would be obvious that proportions hitherto proved by means of the numerical theory of proportion, which was inapplicable to incommensurable magnitudes, were only partially proved. Accordingly, pending the discovery of a theory of proportion applicable to incommensurable as well as commensurable magnitudes, there would be an inducement to substitute, where possible, for proofs employing the theory of proportions other proofs independent of that theory. This substitution is carried rather far in Euclid, Books I - IV.
In other words, all of the demonstrations in the first four books of the Elements are valid quite apart from questions about the divisibility of the continuum. Euclid ingeniously shows that many elementary properties of figures do not an any way rest on the difference between the continuous and the discrete. This sets these books apart from those that follow. Once the universally valid theory of proportion has been established, it is possible to treat the rest of mathematics according to the distinctive principles of the continuous and the discrete.
The treatment of proportion in Book 5 of the Elements makes possible a satisfactory treatment of magnitudes both commensurable and incommensurable. By providing the separate but parallel treatment of proportion in number in Book 7, Euclid shows most clearly that geometry and arithmetic must each be developed from its own proper principles, however many theorems they seem to share in common. This, I propose, is one important reason for including the number books.
A second advantage of including the number books is that it makes the Elements is a more complete elementary treatment of mathematics. When we take a look at the contents of these books, we will see evidence that Euclid desired to aim at completeness, sometimes even at the expense of good order. Taken together with Book 10, the number books give an adequate treatment of the ways in which magnitudes can have ratios to one another. All the potentialities of ratio implicit in Book 5, or rather all those appropriate to beginners in mathematics, are revealed to the student.
A third advantage is that numbers show up from time to time in geometrical theorems.
A most noteworthy example of this is in the very last proposition in the Elements, Book 13, Proposition 18: To set out the sides of the five figures [that is, the five regular solids inscribed in the same sphere] and to compare them to one another. Some of these comparisons involve numerical ratios, as that the square on the diameter of the circle is to the square on the side of the inscribed pyramid as 3:2. We learn other truths along the way involving number, some as simple as 1, 41, which says that the parallelogram having the same base as a triangle and is in the same parallels is double the triangle, or as complex as Book 12, Proposition 10, which shows that any cone is a third part of the cylinder which has the same base and the same height. We see that solid geometry, which is the most complete geometry of the physical world, brings together the discrete and the continuous in a profound way. Here we see the most perfect marriage of geometry and arithmetic.
Part III: The Nature of the Number Books and the Order of their Propositions
If we grant, then, that there are some good reasons for including the number books in the Elements, we may still find them to be unsatisfactory in themselves, as being disorderly. One would think that a scientific treatment of arithmetic should begin with definitions and postulates and then proceed to prove the simplest properties of numbers first, followed by more complex ones. Arithmetic pursued in isolation from geometry would look quite different from what we find in the number books.
I have already suggested that Euclid treats number in light of the notion of measuring and being measured. This is demonstrated by the way Book 7 begins. Number is defined as a multitude composed of units, and multitude arises from the unit by way of addition. Addition is a kind of measuring, in the sense of meting out, as when we count out 75 cents for a candy bar. This is measuring as composition. But the more common kind of measurement is a process of resolution, in which we begin with numbers or a magnitudes as given and analyze them into equal parts. To account for this kind of measurement, Euclid next defines part. This use of part is not like that in the axiom which states that the whole is greater than the part. Here part means a part which measures a whole. From these basic ideas underlying measurement Euclid goes on to define the two most fundamental divisions of number into species. Even and odd numbers are distinguished by whether or not they can be measured by the dyad, the number two. The notion of measurement is also required for the definitions of prime and composite numbers. Primes are measured by the unit alone, while composite numbers have other measures as well. Thus we see that measure is at the very root of number and its division into species. Let us look more closely now at some of these divisions.
By defining the even and the odd right after defining part, parts and multiple, and before prime, etc., Euclid seems to acknowledge the primacy of this division. It is certainly the simplest, and the most easily applied to given numbers. Since for every odd there is an even, namely its double, it seems to be the most perfectly symmetrical division of number, and so in some way the most beautiful. The even and odd can themselves be divides into sub-species, and this is what Euclid does next. There are even times even numbers such as 8, even times odd numbers such as 6, and odd times odd numbers such as 9. These subspecies of the odd and even are defined explicitly by measure. For example, an even times even number is one that is measured by an even number an even number of times. Next Euclid gives the other important division of number which comprises them all, namely prime and composite. These two divisions are the only ones given by Euclid which comprehend all numbers. The notions of prime and composite are then extended to relations among numbers. Numbers are prime to one another if they have no common measure and composite to one another if they do. This is not a division of number into species but a description of important properties numbers can have in the category of relation.
It is interesting to note that up to now, Euclid has not defined any of the operations which are taken as fundamental to arithmetic. He assumes both addition and measurement, which is a kind of division, as well-known. Later, subtraction will also be assumed. It is interesting then that he does define multiplication. Perhaps he feels he needs to do this to avoid any confusion with the analogous geometrical operation, the forming of a rectangle. At any rate, rectangles are called to mind in the very next definition, where he defines a plane number as one which has been formed by multiplying one number by another, which in this context are called sides. He similarly defines solid numbers as those produced by the multiplication of three numbers. By defining multiplication in terms proper to arithmetic, he indicates that his use of geometrical terminology in these definitions is only by way of analogy.
The most important examples of geometrical numbers, squares and cubes, are defined next, and then numerical proportion, with a view to defining similar plane and solid numbers. Finally Euclid defines perfect numbers. Recall that these are numbers which are equal to the sum of their measuring parts, including the unit.
It may seem strange that Euclid does not begin with theorems about properties of the odd and even or with the prime and composite numbers. This would be strange if he were interested in pure numbers, in what is now called “Number Theory.” He is concerned instead with numbers in comparison to each other. The principal subject of Book 7 is numerical ratio and proportion. The first proposition gives the criterion by which two numbers are prime to one another, and the second which gives the method for finding the greatest common measure of numbers which not prime to one another. This second proposition is needed for what follows, a series of demonstrations analogous to the propositions about proportional magnitudes in Book 5, up through the sameness of ratio ex aequali. He goes on to present a number of propositions dealing with sameness of ratio that are specific to numbers. Some of these have analogies to geometry. Especially interesting is Proposition 16, which defines cross multiplying. This is comparable to the proposition defining compounding of ratios in Book 6. We see that, right from the beginning, Euclid wants to make us aware of parallels between arithmetic and geometry.
The rest of Book 7 contains more theorems about relatively prime numbers as well as about numbers that are simply prime or composite. Among these are propositions for reducing ratios to their least terms, finding the least common measure, finding the least number measured by two or three numbers, and to find the least number that has given parts. The essence of any numerical ratio is contained most simply in its least terms. This verifies that the subject of this first Book is numerical ratio and proportion and the treatment of them here is the most elementary.
The next two books of arithmetic present many interesting theorems having for the most part some connection with geometry. The principal subject of Book 8 is numbers in continued proportion. These are sequences of numbers in which each one after the first is the geometric mean between the ones prior and posterior to it, for example: 2, 4, 8, 16 ... Starting with Proposition 11, Euclid sets out propositions relating figured numbers (squares, etc.) to continued proportions. The first two of these are particularly important. The first says that between two square numbers there is one mean proportional number, and the square has to the square the duplicate ratio that which the side has to the side, and the second says that between two cube numbers there are two mean proportional numbers, and the cube has to the cube the triplicate ratio of that which the side has to the side. More propositions about figured numbers round out the books.
Book 9 at first sight looks very disorderly, as if it were just a catch-all for other interesting theorems. There may be something to that, but I think we can makes some sense of it. It picks up where Book 8 left off, with more propositions about figured numbers, but the point of view is different than in Book 8. In the first seven propositions, he is interested in figured numbers considered in themselves, not in their relation to other numbers. This theme is carried on in the next sequence of propositions, which deal with continued proportions starting from the unit. Such a sequence builds up a series of numbers, each of which is the prior one multiplied by the second in the series. Here is an example: 1, 3, 9, 27... i.e. 1, 3, 3x3, 3x3x3 ... So even here the individual numbers are of interest, as being a sequence of successive squares or cubes, or numbers arising from squares and cubes. More propositions relating to this theme follow, eventually leading to theorems in which prime numbers play a part in these proportions. These propositions culminate in an investigation of the conditions in which it is possible to find a third proportional to two given numbers, i.e. when, given numbers a and b, is there a number x such that a:b::b:x.
What happens next, leading up to the end of the number books, is puzzling. Prop. 20 shows that there is no end to the generation of prime numbers. This complicated and very important proposition could have been proved in Book 7. The only rationale I can see for including it here is that Book 9 has been more closely focused on the properties of given numbers taken in themselves than were the first two books. Proposition 20 is followed some others (21-30) which are elementary and even trivial, having to do with odd and even numbers. It is hard to see how these are not out of place, and I am inclined to doubt that Euclid put them there. But if I had to speculate: One possible way to relate these propositions to the ones that come before in Book 9 is to note that most of them relate to the unending production of numbers from other numbers. All the kinds of numbers he has dealt with so far have been showed to be indefinitely many. This is shown explicitly for primes and implicitly for the rest. The continued proportions produce endless series of squares, cubes, and similar plane and solid numbers. Similarly but more obviously, addition produces as many even and odd numbers as we want. Multiplication gives us even times even, even times odd, and odd times odd numbers. Propositions 32 -34 deal explicitly with these kinds of composite numbers.
This brings us to the final propositions, 35 and 36. Proposition 36, which requires 35, gives us a way to make perfect numbers. Recall that perfect numbers are those whose factors when added together make up the number. The number 6 is the first of these, since 6 = 1 + 2 + 3. Is it interesting that Euclid ends the number books with this difficult construction of perfect numbers, just as he ends the work as a whole with the construction of the prefect solids. The number of perfect solids is finite. It is still not known whether or not there are infinitely many perfect numbers.
To sum up my account of the order within the number books:
1. First we have the fundamentals of how numbers relate to one another as prime or composite and how they relate to one another in ratio and proportion.
3. Next we have continued proportions and how they relate to figured numbers. The view shifts from division, that is, measurement, to multiplication.
4. Next we have truths about the figured numbers themselves, their simple production by multiplication and their special production in continued proportions beginning from the unit.
5. Next we have the production of numbers of various other kinds, culminating in perfect numbers.
Part Four: The Ordering of Books in The Elements
To what extent may the order of the Elements be attributed to Euclid? Heath gives this answer: Euclid’s own works “show no signs of any claim to be original; in the Elements, for instance, although it is clear that he made great changes, altering the arrangement of whole Books, redistributing propositions between them, and inventing new proofs where the new order made the earlier proofs inapplicable, it is safe to say that he made no more alterations than his own acumen and the latest special investigations...showed to be imperative in order to make the exposition of the whole subject more scientific than the earlier efforts of writers of elements.” If Heath is right, we must take seriously not only the inclusion of the number books in the Elements, but also their place in the work as a whole. We ought to be able to find a rationale according to which Euclid’s order makes sense. As we look into this, it is important to keep in mind that the order appropriate to arithmetic considered within the framework of geometry is not the same as the best order for teaching arithmetic as an art of calculation.
We must begin by considering how Euclid structures his treatment of geometry. The subject of geometry is magnitude. Magnitude is divided into extension in one dimension (straight lines), in two dimensions (plane figures) and in three dimensions (solid figures). This division gives structure to Euclid’s work, but not in a simple way. It is not possible to begin with lines and work up to solids or to begin with solids and work down to lines. Euclid does of course begin with lines in one sense. Straight lines and circles are postulated, but they appear in Book 1 only as boundaries or as auxiliary lines within figures. This is not the same thing as a study the one dimensional as such. He does makes such a study but it is difficult and has to be deferred. Solid geometry cannot be studied before plane geometry, since the properties of solids can’t be known without knowing about their boundaries. Solids are the figures most difficult to understand and perhaps also the most beautiful, so it is fitting as well as necessary that they come last in the work. Plane geometry must therefore be treated first.
Plane geometry is developed at length in Books 1-4, and this section ends with the inscribing and circumscribing of regular polygons in and about circles. In Book 4, we join together the most perfect plane figures in constructions that are beautiful both to the mind and to the eye. This book brings to completion a distinct part of Euclid’s subject, but the treatment of plane figures is far from being completed. Book 6 deals with the important subject of ratio and proportion in two dimensional figures. This study demands knowledge of ratio and proportion in a more universal way, so the development of plane geometry is necessarily interrupted by Book 5. Book 6 brings to completion the elements of plane geometry.
Book 10 is the only book which deals expressly with lines. It is the science of the one dimensional carried on as far as Euclid’s method allows. I have already said that Euclid could not begin with the science of the one dimensional, and now I must explain why not. Extension, whether in one, two or three directions, serves as the material component of geometry. A science first of all considers formal properties of its subject. Since the material causes of a thing are as such unintelligible, they must be made intelligible through form. This is true at every level. Wood, the material of furniture, is known through the formal properties of wood. Elementary particles are known through their forms, and the obscurity we find when we try to understand them comes from the elusiveness of their forms. Prime matter is known only insofar as it is demanded by generation and corruption. In geometry too the forms, which are the shapes, must be understood before we can know the areas and volumes contained by them.
Now consider how lines can be known. First we can see that there is a difference between the straight and the curved, and that while there is only one way of being straight, there are infinitely many ways of being curved. Some kinds of curvature are intelligible and some are not, and the geometer is interested in those that are. Euclid deals with curved lines only as boundaries of figures, but Apollonius and other ancient geometers begin to study curved lines as such. But is there a possibility of studying lines as material, that is, in the way in which we study area and volume? Yes. Euclid begins this study in Book 10 and is able to carry it quite far. That the subject of Book 10 is straight lines in particular and not magnitude in general, as in Book 5, is made clear by the words he uses in enunciating the theorems. He even goes so far as to posit a common standard by which all such lines can be classified as either rational or irrational. He comes ever so close to Descartes’ idea of introducing a unit into geometry.
It remains to be seen why the study of lines is not a good place to begin. Every species of magnitude is divided by the species below it. In plane geometry, a portions of the plane is delimited by lines, straight or curved, producing triangles, circles and so forth. In solid geometry, the three dimensional continuum is delimited by plane figures and curved surfaces to bring forth cubes, pyramids, spheres etc. These figures are often very beautiful, and in that they approach more closely to the reality of the world, they seem especially worthy of contemplation. The student of the line, however, has as it were a very limited resource. The only way to divide a one dimensional object is to mark off a point or points, to count the divisions and to look at the ratios of the parts, and perhaps their ratios to other lines that have been set out. That sounds pretty boring, on the face of it! The amazing thing is that, far from being barren of interest, there are such riches to be found in the division of the line that we are far from having discovered them all.
Although the line is the simplest geometrical object, there are good reasons not to treat it first. Pedagogically it makes sense to treat the more knowable before the less knowable. And whereas commensurable, that is numerable, lines do seem more knowable than figures, the same cannot be said of incommensurable lines. Books 5 and 10 make the greatest demands on the student’s powers of abstraction. The fact that incommensurables were not known to the earliest geometers points to their obscurity. Perhaps also the fact that the imagination is less vividly engaged when studying lines makes the propositions about them more difficult to learn and remember.
Although the reasons just given have some force, the more essential reason is mathematical. To divide or measure lines, it is necessary to carry out constructions in two dimensions. Euclid bisects a straight line in Book 1, 10 and in Book 6, 9 he cuts off a prescribed part from a given straight line. In the latter proposition, he shows that any straight line may be measured by any number. He even anticipates irrational divisions of lines in Book 6, 13, where he constructs a mean proportional between any two lines. These illustrate that, in order to measure a line or to show that it cannot be measured by some other line, it is necessary to carry out constructions in the plane. Finally, it is worth mentioning that Book 10 includes some applications of proportion to squares and thus implicitly to other rectilinear figures. This is a hint that the distinction between rational and irrational is applicable to all kinds of extension. For all these reasons, it is necessary for Euclid to put Book 10 after Book 6. But are there also good reasons not to defer the treatment of straight lines until after solid geometry, to the very end of the book?
That we should not put Book 10 last can be seen in at least two ways. First, the treatment of incommensurables underlies the argument by approach to a limit and the powerful method of proof by double reductio. Using the latter, Euclid is able to establish the important theorems that circles are in the duplicate ratios of their diameters and spheres are in the triplicate ratio of the same. Thus the treatment of the irrational as well as of the rational are made to serve the purposes of solid geometry. Second, the perfect solids are clearly meant to be the climax of the whole book of the Elements. That there are only five of these is a source of great wonder. The plane figures which bound these figures involve both simple numerical ratios (as that the diameter of the hexagon is twice its side) and irrational ratios, such as that found in the triangle upon which the regular pentagon is built. This could now be known without Book 10. For these reasons alone, it is right for Book 10 to come before Book 11, the first book on solids.
To sum up the order I have justified so far: plane geometry in Books 1-4, proportion in magnitude generally and then in plane figures in Books 5-6, rational and irrational lines in Book 10, solid geometry in Books 11-13. All that is missing from this picture are the number books. Where do they fit in?
First, we can see the number books as belonging to the study of ratio and proportion, since this is implied in the understanding of number through measurement. Since arithmetic is easier than geometry and prior to it, one might wonder why Euclid does not put these books right before Book 5, so that ratio and proportion are treated first in number and then in magnitude. A simple answer might be that this would unnecessarily interrupt his treatment of plane figures. Another possibility, which would avoid this problem, would have been to begin the entire work with the books on number. After all, the theorems in this part are independent of the geometrical theorems, and starting with arithmetic would have some advantages. Numbers are better known and more accessible to the student than magnitudes. Also, separating off the treatment of multitude from that of magnitude would reinforce the idea that arithmetic is not simply reducible to geometry but is a science in its own right.
Despite the fact that arithmetic is an independent science, the number books do not stand alone in the Elements as pure arithmetic. I think they must be seen as integral to Euclid’s approach to geometry. I have spoken at length about how Euclid considers number by means of the idea of measurement. This is not the only possible way to conceive them. For instance, Richard Dedekind writes: “I regard the whole of arithmetic as a necessary, or at least natural, consequence of the simplest arithmetic act, that of counting, and counting itself as nothing else than the successive creation of the infinite series of positive integers in which each individual is defined by the one immediately preceding.” Starting with addition rather than with measurement could form the basis of a work on arithmetic and no doubt is the best way to go for treating the art of calculation. Euclid is not interested in calculation, and Dedekind’s way of developing a science of arithmetic departs from the path of the ancients. Euclid seems also not to have been very much interested in the kind of arithmetic one finds in Nicomachus and other ancient writers on the subject. For Euclid, the path to a scientific treatment of arithmetic passes through geometry.
Seeing the number books in the context of geometry allows us to understand the placement of the number books. The reason for placing them between 6 and 10 cannot be necessity, since they are independent of the rest. If necessity is not the reason, he must have seen it as appropriate to place them where he does, right before Book 10.
This idea is supported by the character of the first few propositions in Book 10. A careful look reveals some parallels between how Books 7 and 10 begin. Proposition 10, 1 has no equivalent in the number books, but Proposition 2 parallels Book 7, Proposition 1. Here is 7, 1: “Two unequal numbers being set out, and the less being continually subtracted in turn from the greater, if the number which is left never measures the one before it until an unit is left, the numbers will be prime to one another.” Compare this to 10, 2: “If, when the less of two unequal magnitudes is continually subtracted in turn from the greater, that which is left never measures the one before it, the magnitudes will be incommensurable.” This proposition reveals the distinctive character of magnitude, as opposed to multitude. But Euclid goes on to make explicit how multitude can exist in magnitude. Propositions 3 and 4 exactly parallel 7 2 and 3 by finding common measures of two and three commensurable magnitudes respectively. Propositions 5 - 8 nail down the difference between commensurable magnitudes and numbers. He shows that commensurable magnitudes have the ratio of a number to a number and conversely, and that incommensurable magnitudes do not have the ratio of a number to a number, and conversely.
From these considerations, we may infer that Euclid wanted us to think about number and magnitude in contrast and comparison to one another. The number books should not be thought of as standing on their own as an independent treatment of arithmetic randomly inserted into a book of geometry. By looking first at number as manifest in lines, and then at lines where number fails to cover all its possibilities, Euclid manifests the necessity to go beyond the flawed geometry of his predecessors to a true and more complete science of magnitude and figure.
Here, then, is my account of the order of the Books of the Elements. The first four books contain the elementary propositions about figures that can be known without having to invoke a theory of proportion. Of these, Book 1, which deals with rectilinear figures is the foundation of all the rest. This book ends with the important and beautiful Pythagorean theorem and its converse. Book 2 gives analytical tools for the books to follow. Book 3 deals with properties of circles, the simplest figure after the straight line and next in the order of learning after the basic rectilinear figures. It presupposes book 1. The last three propositions of the book reveal the power of theorems in Book 2 to reveal complicated properties of simple figures. These only hint at what the geometer can figure out with the second book in his tool-kit. Book 4 beautifully brings together the regular polygons, of which the square and the equilateral triangle are the most perfect, with the circle, by inscribing and circumscribing. Book 5 teaches the fundamental theorems about ratio and proportion in magnitude, and this doctrine is applied in Book 6 to reveal many important and beautiful theorems about plane figures. Books 7-9 treat of numbers, while Book 10 deals comprehensively (as much as was possible for Euclid) with lines both rational, which correspond to numbers, and irrational, which do not. Book 11 presents the most fundamental theorems about constructions in three dimensions and with solids formed by planes. Book 12 deals with solids based upon the circle, and with ratios of volume found in various kinds of solids. Finally, Book 13 constructs the five regular solids within a sphere and considers the ratios of their sides to one another. Some of these ratios can be expressed in numbers and some cannot. Euclid shows that the regular solids draw together the rational and the irrational, number and that which cannot be numbered. In this way he brings the elementary study of geometry to a beautiful and fitting conclusion.
Elements, Book VII, definition 1.
See Aristotle, Metaphysics Book XIII, for an extensive discussion of various ideas about the nature of the unit, of number and of other mathematical objects.
Sir Thomas Heath, A History of Greek Mathematics, Vol. 1, p.98, Dover Publications (New York, 1981).
To describe this in a neo-Platonic way, one might say that numbers are emanations from the One.
Russell’s definition of two as the set of all twos seems to me to have the same problem.
St. Thomas Aquinas, Commentary on Metaphysics Books 7-12, 1725 (Augustine Institute, Green Bay, Wisconsin, 2020), my translation: “Est enim per se unum numerus, inquantum ultima unitas dat numero speciem et unitatem,; sicut etiam in rebus compositus ex materia et forma, per formam est aliquid unum, et unitatem et speciem sortitur.”
Joe Roberts, Lure of the Integers, The Mathematical Association of America (1992), p. 52.
Other measures are of course possible. For example, two, what the Greeks call the dyad, measures all even numbers.
In Middle English these sticks were called tallies or tally sticks.
1084b 24-26. In this passage, Aristotle is criticizing their confusion of mathematical conceptions with metaphysical ones.
A proposition purporting to show how to know whether 3 numbers have a fourth proportional exists in the Greek, but the text is corrupt. See the note in Densmore’s edition, p. 26.
Without high speed computers, it is not possible to find many of these, since we are required to sum up the continued proportion starting from one and based on 2 until the sum becomes prime.
A History of Greek Mathematics, Vol. 2, p.357.
In Book 10, Euclid treats thoroughly of algebraic irrationals of the second degree, and of a few of degree four. He does not treat of those of the third degree, and he gives no indication of awareness of the transcendental irrationals.
“Continuity and Irrational Numbers,” in Essays on the Theory of Numbers, Dover Publications (New York, 1963), p. 4.
“Two unequal magnitudes being set out, if from the greater there be subtracted a magnitude greater than its half, and from that which is left a magnitude greater than its half, and if this procedure be repeated continually, there will be left some magnitude which will be less than the lesser magnitude set out.” The porism extends the theorem to the subtraction of halves.
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| 55,510 | 102 |
https://oncotherm.com/ranks-of-the-journals-which-contain-oncothermia-articles/
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math
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“The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index that reflects the yearly average number of citations that recent articles published in a given journal received. It is frequently used as a proxy for the relative importance of a journal within its field; journals with higher impact factors are often deemed to be more important than those with lower ones.”
Oncothermia related articles were published in several journals with high impact factor. The total impact factor of our articles is 455,712.
There is an other way to rank a journal. “Quartile rankings are therefore derived for each journal in each of its subject categories according to which quartile of the IF distribution the journal occupies for that subject category. Q1 denotes the top 25% of the IF distribution, Q2 for middle-high position (between top 50% and top 25%), Q3 middle-low position (top 75% to top 50%), and Q4 the lowest position (bottom 25% of the IF distribution).”
For more please visit the following site: https://researchassessment.fbk.eu/quartile_score
Via the following link you should see the Q and the D ranking journals: https://www.scimagojr.com/journalrank.php
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| 1,212 | 5 |
http://www.matstud.org.ua/ojs/index.php/matstud/article/view/210
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math
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Factorisation of orthogonal projectors
We study the problem of a special factorisation of an orthogonal projector~$P$ acting in the Hilbert space $L_2(\mathbb R)$ with $\dim\ker P<\infty$. In particular, we prove that the orthogonal projector~$P$ admits a special factorisation in the form
$P=VV^*$, where $V$ is an isometric upper-triangular operator in the Banach algebra of all linear continuous operators in $L_2(\mathbb R)$. Moreover, we
give an explicit formula for the operator $V$.
I. Gohberg, M. Krein, Theory of Volterra operators in Hilbert space and its applications, Nauka Publ., Moscow, 1967 (in Russian); Engl. transl.: Amer. Math. Soc. Transl. Math. Monographs, V.24, Amer. Math. Soc., Providence, RI, 1970.
S. Albeverio, R. Hryniv, Ya. Mykytyuk, Factorisation of non-negative Fredholm operators and inverse spectral problems for Bessel operators, Integr. equ. oper. theory, 64 (2009), 301–323.
D.R. Larson, Nest algebras and similarity transformations, Ann of Math. (2), 121 (1985), №2, 409–427.
Copyright (c) 2021 N. S. Sushchyk, V. M. Degnerys
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Matematychni Studii is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) license.
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| 1,324 | 10 |
http://brittgow.global2.vic.edu.au/2008/09/02/how-many-chocolate-buds-in-choc-chip-cookies/
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math
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Students enjoyed a Maths300 activity during Literacy and Numeracy Week, estimating the number of chocolate chips a manufacturer would need to add to a batch of ten cookies to try to ensure that each biscuit had a minimum of 7 chocolate buds. Initially some students believed that just a few more than 70 should suffice, while others decided the more the better and thought a few hundred should be added – just to make sure! After coming up with some ways to use random number generators to model the problem (10-sided dice, cards, throwing stones on a 2 x 5 grid) we used the Maths300 software to generate a stem and leaf plot for 100 trials. Following the activity, students estimated that between 110 and 150 chocolate buds were sufficient to have confidence that each cookie contained 7 choc buds. And now they want to make cookies…..
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| 841 | 1 |
https://yk-game.com/games/1001
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math
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We've created a game with beautiful graphics and easy gameplay, that you'll instantly love. Play more than 100. 000 different puzzles categorized into thousands of puzzle collections. You'll never run out of puzzles to solve! Jigsaw puzzle comes crammed with features, so laying puzzles have never been so enjoyable. Shuffle the pieces, show a preview, toggle borders, toggle the sound, hide the time, and much more under settings. How to start a game: Click a collection from the main screen and then choose a puzzle to play. Set the number of pieces you want in that puzzle and then click "Start Puzzle". That will begin the puzzle. Laying the puzzle: Click and drag to move the pieces and right-click a piece to rotate it. If two pieces fit together, they will "click" together and make a little sound. Once all the pieces are together and you've solved the puzzle and congratulations screen will be shown.
Aladdin game is adventure fun game Help Aladdin in his journey
Aladdin Adventure game is fun auto runing game Help our hero to in his arabian journey in the quest of gold How to play Game features: -5 Beautiful World: -Many many villian -final boss fight -Nice graphics and good Concepts
Take aim with magic gemstone bubbles in this Middle-Eastern-themed bubble shooter. But make sure you break out your best moves, because you have a limited number you can make in each level!
The Arabian Desert is full of mysterious treasures that are yours for the taking.
Play 1001 Arabian Nights 2 - Aladdin and The Magic Lamp Game
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Return to ancient Arabia for another puzzling adventure. This time, Sinbad's along for the ride. . .
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Brain 100 is a little game that puts your memory to the ultimate test. Can you memorize all the tiles with the cute cat on a 3x3 board? Too easy? How about a 4x4, 5x5 or 6x6 board? Well, maybe it's not as easy as it looks. Seriously, this is an addictive game that will keep its player entertained for hours.
Hidden Object Game based on original book of Arabian Nights - Brings the Arabian Nights to interactive game. - Lush Persian influenced art - Become the Sultan in Arabian Nights and listen to Scheherazade as she tells of Aladdin, Sinbad, Ali Baba and more. - Find hidden genies to unlock exciting and exotic bonus stories and levels. - Contains complete stories with bookmarks to match game plot progression so the player can read along. - Over 10 varieties of Hidden Object gameplay keep things fun, fresh, and exciting. - Over 1,200 items included to allow for endless replayability. Pick proper item on story screen regarding to object names listed on GUI.
Best Genie Matching Game live aladdin story and save the sultan palace from the very arrogant Jafar. Your journey will be plenty of discovery and new missions. Use mouse to match genies and follow tutorials to learn all movements
1 Player Games 10 Games Airplane Games Animal Games Basketball Games Bus Games Bus Driving Games Car Driving Games Cat Games Chicken Games Defense Games Dog Games Exit Games Food Games Fun Games Gold Games Gold Miner Games Ice Games Key Games Love Games Mahjong Games Matching Games Maze Games Pacman Games Parking Games Phone Games Racing Games Robots Games Rocket Games Sad Monkey Games Ship Games Smartphone Games Snow Games Sonic Games Sports Games Tablet Games Tank Games Tower Games War Games Water Games
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| 3,613 | 15 |
http://ir.lib.uth.gr/handle/11615/15/discover?rpp=10&filtertype_0=dateIssued&filtertype_1=dateIssued&filter_0=1999&filter_relational_operator_1=equals&filter_1=%5B1991+TO+1999%5D&filter_relational_operator_0=equals&filtertype=subject&filter_relational_operator=equals&filter=Problem+solving
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math
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Now showing items 1-5 of 5
Position control for constrained Robots
The problem of position control, for robot manipulators constrained to carry a load, is studied. Using a nonlinear P-D feedback law the design requirements of command matching and command following are proved to be always ...
Robust disturbance decoupling with simultaneous exact model matching via static measurement output feedback
The problem of robust exact model matching with simultaneous robust disturbance decoupling for linear systems with nonlinear uncertain structure (NLUS) and with measurable and non measurable disturbances is solved via an ...
Disturbance decoupling of singular systems via P-D feedback
The problem of disturbance decoupling of singular systems via proportional plus derivative (P-D) feedback is solved. The necessary and sufficient condition for the problem to be solvable is established as a rank condition ...
Robust input-output decoupling via static measurement output feedback
In this paper the problem of robust input-output decoupling for linear systems with nonlinear uncertain structure (NLUS), via an independent from the uncertainties static measurement output feedback law, is studied. The ...
Pitch and flight path control with simultaneous forward gust rejection
The problem of rejecting atmospheric disturbances with simultaneous input-output decoupling of the pitch angle and the flight path angle of an aircraft, is studied. The problem is proven to be solvable for almost all flight ...
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https://max.book118.com/html/2019/0326/5023014131002022.shtm
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math
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( ) 1. —_____________ she quit?
—No, she isn’t. She is very strict.
A. Is B. Am C. Are
( )2._____________your music teacher?
A. Who’s B. What’s C. Who
( )3. ______________you know Mr Li?
A. Does B. Do C. Did
( )4. —____________________________
—Yes, she is.
A. Is she young? B. Is he young? C. Are she young?
( ) 5. —Is your English teacher strict?
—No, she isn’t. She is very ___________________ .
A. quiet B. kind C. old
( ) 7. —What is ___________like?
A. him B. she C. he
( )8. —Do you have new teachers?
A. Yes, she is. B. Yes, I do. C. No, I do.
( ) 9. —What’s she like?
A. She is our new music teacher.
B. She is Amy.
C. She is very polite.
( )10. —Who’s that young lady?
A. She is very hard-working.
B. She is my sister.
C. He is our new English teacher.
( ) 12. —Who’s your head teacher?
A. He’s kind.
B. Yes, she is.
C. Miss White.
( ) 13. She is polite______________ clever.
A. and B. but
( ) 14. Who ________________that young lady?
A. are B. is
( )15. She_______________quiet.
A. is B. are
( )16. She is______________head teacher.
A. us B. our
1. my new teacher
2. I don’t know.
3. tall and young
4. My mother is kind.
5. I like funny teachers.
6. a strict man
1. ( ) 2. ( ) 3. ( ) 4. ( ) 5. ( ) 6. ( )
( ) 1. 当你要询问别人的中文老师是谁时，你会说________________________
A. What’s your Chinese teacher?
B. Who your Chinese teacher?
C. Who your art teacher?
( ) 2. 当别人问你知道琼斯吗？他会说：_______________________________
A. Do you know Mr Jones?
B. Where’s Mr Jones?
C. Is he Mr Jones?
( ) 3.你想了解他是否和蔼，你会说：__________________________________
A. Is he kind?
B. He is kind.
C. Is he kind?
( ) 4.当你想说布莱克女士是我们的新英语老师时，你会说：_____________
A. Miss Black will be
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| 1,825 | 58 |
http://ams.org/mathimagery/displayimage.php?album=32&pid=424
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math
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The connection between mathematics and art goes back thousands of years. Mathematics has been used in the design of Gothic cathedrals, Rose windows, oriental rugs, mosaics and tilings. Geometric forms were fundamental to the cubists and many abstract expressionists, and award-winning sculptors have used topology as the basis for their pieces. Dutch artist M.C. Escher represented infinity, Möbius bands, tessellations, deformations, reflections, Platonic solids, spirals, symmetry, and the hyperbolic plane in his works.
Mathematicians and artists continue to create stunning works in all media and to explore the visualization of mathematics--origami, computer-generated landscapes, tesselations, fractals, anamorphic art, and more.
"Butterflies 6-4," by Doug Dunham (University of Minnesota Duluth, MN)
11" x 11", Color printer, 2009
This is a hyperbolic pattern of butterflies, six of which meet at left front wing tips and four of which meet at their right rear wings. The pattern is inspired by M.C. Escher's Euclidean image Regular Division Drawing Number 70, and is colored similarly. Disregarding color, the symmetry group of this pattern is generated by 6-fold and 4-fold rotations about the respective meeting points of the wings, and is 642 in orbifold notation (or [4,6]+ in Coxeter notation). This pattern exhibits perfect color symmetry and its color group is S3, the symmetric group on three objects. --- Doug Dunham (University of Minnesota Duluth, MN, http://www.d.umn.edu/~ddunham/)
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| 1,503 | 5 |
https://writtencasey.blog/2019/06/21/attempt-recap-of-godel-formal-systems/
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math
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Trying to learn mathematics. Comments and corrections welcome. Piece of a work in progress.
All consistent axiomatic formulations of number theory include undecideable propositions.
The single, circular ‘loop’ of the statement above is the assertion that, although the statement is true, it cannot be proven to be true. This parallels the way Principia Mathematica contained mathematical statements of truth that could not be proven through the text itself.
Gödel showed that probability is a weaker notion than truth. His sentence G showed that no fixed system could adequately represent the complexity of whole numbers-no matter how complicated or elegant. No connective set of principles could explain ‘a whole’. ‘A whole’ is a sum greater than its constituent parts.
See Paul’s first letter to the Corinthians which makes the point that although sun, water, and soil are required and can explain growth, they are not growth itself. Growth results in death (sic. cell senescence) which returns as birth/reproduction.
The main paradox in math is trying to enliven our intuitive realizations with formalized, axiomatic explanations?
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https://www.doubtnut.com/question-answer-physics/a-horizontal-platform-with-an-object-placed-on-it-is-executing-shm-in-the-vertical-direction-the-amp-643189286
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math
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Updated On: 20-06-2022
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weather Churu given to be equal to explore and we can say this experiment can be written as cake spot is equal to empty and when the information in this finding maximum acceleration so we can say this particle has maximum acceleration at the Eastern portion always directed towards evergreen chal so we can say here at the maximum spacing in the woods lives we can say to take into to export at a word in a pseudo force into a at downloads and the same situation questions we can senior engineer at the upward position into a max and we can say no
sex and the spring is produced writing so we can say among the maximum compression and maximum stretching we have maximum acceleration at the maximum compression so this is the situation if the block does not get detached from the maximum compression and not even that detects and the maximum setting which implies that anything to come out equal to m2go MM cancels out comes out to be equal to in speaker se emacs maximum acceleration square into 2 cube is equal to which is put into 10 power minus 3 and corresponding period so we can say you comes out as or more than the buy it now
the time period comes out as 25 route finder we can say we can see that this comes out at 2.4 into 10 power minus 3 is so we can say here this comes out Apple t is equal to 1 to 10 power minus 4 square minus 4 by 4 wire can be written as that simple 25 so this interaction with its frequency of value of this comes out as a sequel to 5 result
Click here to get PDF DOWNLOAD for all questions and answers of this chapter - DC PANDEY ENGLISH Class 11 SIMPLE HARMONIC MOTION
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http://threadspodcast.com/mean-square/mean-square-error-calculation-in-matlab.html
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math
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Mean Square Error Calculation In Matlab
Browse other questions tagged matlab mean-square-error or ask your own question. Are non-English speakers better protected from (international) phishing? How can I call the hiring manager when I don't have his number? MATLAB KFUPM 435.532 προβολές 46:38 U01V03 RMSE - Διάρκεια: 3:59. check over here
You can also add an author to your watch list by going to a thread that the author has posted to and clicking on the "Add this author to my watch Equalizing unequal grounds with batteries Where are sudo's insults stored? First, convert them to doubles in case they are uint8 images, as is common. Tagging Messages can be tagged with a relevant label by any signed-in user.
How To Calculate Root Mean Square Error In Matlab
Learn more MATLAB and Simulink resources for Arduino, LEGO, and Raspberry Pi test Learn more Discover what MATLAB ® can do for your career. workspace; % Make sure the workspace panel is showing. squaredErrorImage = (double(grayImage) - double(noisyImage)) .^ 2; % Display the squared error image. Mean Square Error Formula In Image Processing Play games and win prizes!
Why does Luke ignore Yoda's advice? Matlab Code For Mean Square Error Of Two Images Join the conversation Toggle Main Navigation Log In Products Solutions Academia Support Community Events Contact Us How To Buy Contact Us How To Buy Log In Products Solutions Academia Support Community Author To add an author to your watch list, go to the author's profile page and click on the "Add this author to my watch list" link at the top of Were students "forced to recite 'Allah is the only God'" in Tennessee public schools?
Click on the "Add this search to my watch list" link on the search results page. Mean Square Error Matlab Neural Network Close × Select Your Country Choose your country to get translated content where available and see local events and offers. Then just doMSE = mean((desired - mean).^2); 5 Comments Show 2 older comments Maria Maria (view profile) 18 questions 2 answers 0 accepted answers Reputation: 2 on 20 Apr 2014 Direct Other ways to access the newsgroups Use a newsreader through your school, employer, or internet service provider Pay for newsgroup access from a commercial provider Use Google Groups Mathforum.org provides a
Matlab Code For Mean Square Error Of Two Images
How to create a company culture that cares about information security? set(gcf, 'units','normalized','outerposition',[0 0 1 1]); Maria Maria (view profile) 18 questions 2 answers 0 accepted answers Reputation: 2 on 21 Apr 2014 Direct link to this comment: https://www.mathworks.com/matlabcentral/answers/126373#comment_209202 Dear Mr Image How To Calculate Root Mean Square Error In Matlab You can add tags, authors, threads, and even search results to your watch list. Mean Square Error Formula John Saunders 39.311 προβολές 5:00 Matlab Demo 2 VR - Διάρκεια: 17:04.
Darryl Morrell 98.627 προβολές 12:23 U1 - Postlab - RMSE and Correlation notes - Διάρκεια: 6:13. http://threadspodcast.com/mean-square/mean-square-error-calculation-in-excel.html Learn more You're viewing YouTube in Greek. Discover... David Dorran 91.909 προβολές 18:04 how to calculate Mean Square Error in Digital Image Processing - Διάρκεια: 2:37. Immse Matlab
jensi asir (view profile) 0 questions 1 answer 0 accepted answers Reputation: 0 Vote0 Link Direct link to this answer: https://www.mathworks.com/matlabcentral/answers/81048#answer_121267 Answer by jensi asir jensi asir (view profile) 0 questions You might also look to PSNR and SSIM (see wikipedia) to compare two matrices. Why planet is not crushed by gravity? http://threadspodcast.com/mean-square/mean-square-error-example-calculation.html subplot(1,2,2); plot(t, y, 'b-', 'LineWidth', 3); grid on; ylim([0, yCenter+radius]); title('Height of a point as it revolves around', 'FontSize', fontSize); xlabel('time', 'FontSize', fontSize); ylabel('Y, or Azimuth', 'FontSize', fontSize); % Enlarge figure
mse = sum(sum(squaredErrorImage)) / (rows * columns); % Calculate PSNR (Peak Signal to Noise Ratio) from the MSE according to the formula. How To Calculate Mean Square Error Example Abbasi Nasser M. If X is a matrix of shape NxMxP, sum(X,2) forms a sum over the columns of X, i.e., the SECOND dimension of X, producing a result that has shape Nx1xP. –user85109
Predicted = [1 3 1 4]; How do you evaluate how close Predicted values are to the Actual values?
Abbasi (view profile) 2331 posts Date: 15 Mar, 2011 09:15:47 Message: 3 of 5 Reply to this message Add author to My Watch List View original format Flag as spam On Not the answer you're looking for? Vincent Rouillard 519 προβολές 17:04 Signal Analysis using Matlab - A Heart Rate example - Διάρκεια: 18:04. Mse Matlab Source Code Islam mohaisen 29.770 προβολές 22:17 Matlab Essentials - Sect 12 - Adjusting the Display Precision for Calculations - Διάρκεια: 11:49.
Join the conversation Toggle Main Navigation Log In Products Solutions Academia Support Community Events Contact Us How To Buy Contact Us How To Buy Log In Products Solutions Academia Support Community See Alsomean | median | psnr | ssim | sum | var Introduced in R2014b × MATLAB Command You clicked a link that corresponds to this MATLAB command: Run the command DGSPhysics400 866 προβολές 6:13 Root-mean-square deviation - Διάρκεια: 5:11. If the third number is 3 then either you changed my demo to use a color image (most likely) or else somehow your cameraman.tif image is not the original one.
Apply Today MATLAB Academy New to MATLAB? Related Content 1 Answer Wayne King (view profile) 0 questions 2,674 answers 1,085 accepted answers Reputation: 5,360 Vote1 Link Direct link to this answer: https://www.mathworks.com/matlabcentral/answers/69397#answer_80629 Answer by Wayne King Wayne King Discover... Close Was this topic helpful? × Select Your Country Choose your country to get translated content where available and see local events and offers.
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https://stanford.library.sydney.edu.au/archives/fall2019/entries/nominalism-metaphysics/notes.html
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Notes to Nominalism in Metaphysics
1. There is a third conception of Nominalism, championed by Nelson Goodman, on which it is the doctrine that there is ‘no distinction of entities without distinction of content’, which comes to be the idea that no two distinct entities can be broken down into exactly the same atoms (1972, 159–60). This is different from the two senses of Nominalism distinguished in the main text, since it does not reject universals or abstract objects per se. Clearly some abstract objects and universals must be rejected by Goodmanian Nominalism: sets or classes, structured propositions, structural universals; but the problem with these is not that they are abstract or universal but that they violate Goodman's principle that no two distinct entities can be composed of the same atoms. Though the motivation for Goodman's Nominalism is one of the motivations for the other two kinds of Nominalism distinguished above, namely the ‘aversion to unwonted multiplication of entities’ (Goodman 1972, 159), Goodman's Nominalism is very different from the other two kinds of Nominalism since rather than rejecting a kind of entity what it rejects is a ‘means of construction’ (Goodman 1986, 160) or composition. Why does Goodman call it ‘Nominalism’? He sometimes states his view as the view that the world is a world of individuals (1972, 155) and this sounds nominalist in the sense of rejecting universals. However, for Goodman an individual is simply the value of a variable of the lowest type in a certain system and so a universal could count as an individual for him. Since Goodman´s conception of Nominalism is not widespread I shall not discuss it in this entry.
2. Thus so-called Trope Theory counts as a kind of Nominalism. In Rodriguez-Pereyra 2002 the word ‘Nominalism’ is given a sense according to which it means the rejection of universals and tropes (2002, 3). Although the word is sometimes used in that more restricted sense, it is more correct and more in line with older tradition to use ‘Nominalism’ (in one of its senses) to mean rejection of universals.
3. Lowe's view is not that this is the only proper characterisation of abstract objects, but simply that this is one of them.
4. This is true, for instance, of the Nominalism of Goodman and Quine in their joint 1947 paper, at least as far as non-spatiotemporality is concerned (Goodman and Quine 1947, 105).
5. The main sceptic about such a distinction was F. P. Ramsey (1925).
6. The way I have drawn the distinction between particulars and universals is by no means unproblematic. Firstly, there are problems with the instantiation relation. It is not clear whether it is indeed prior to the distinction between particulars and universals or even exactly what it consists in. Secondly, the distinction entails that although roundness and squareness are universals, (round and square)-ness is not, since given that nothing can be round and square, (round and square)-ness can have no instances. But, if roundness and squareness are universals and (round and square)-ness exists, it is plausible that (round and square)-ness is a universal. Thirdly, the distinction entails that properties that can have only one instance, like the property of being the tallest man ever, count as particulars, but it is not clear that, if there are universals, this property should not be classified as a universal. I do not mean to suggest that these problems are not solvable, nor do I mean to suggest that they are.
7. Another option, exemplified in Armstrong (1997, 118–19), is to accept that a relation of instantiation must be postulated, but to argue that only one is needed, because all the steps of the regress supervene upon the first and supervenience brings no ontological addition. The idea that supervenience brings no ontological addition is controversial.
8. Although close to it, this need not amount to the same as Goodman's principle that no two entities can be broken down into the same entities, for it can be held, as in Lewis 1986b, that composition is the combining of many things into one, and that sets are sums of singletons. In that case the principle that no two things can be composed by exactly the same parts does not rule out singleton sets, since the singleton is not generated through the combining of many things. But Goodman's principle is supposed to rule out singleton sets.
9. Campbell calls tropes ‘abstract’ because he takes as abstract those entities that do not ordinarily exist apart from other instances of qualities, not because he thinks of them as non-spatiotemporal (Campbell 1990, 2–3).
10. Alternatively one might say that properties are predicates or that properties are concepts. But these views seem to have very little appeal, and are subject to the same difficulties as Predicate Nominalism and Concept Nominalism as presented in the main text of this entry.
11. Except for ‘Trope Theory’, all the names of the other nominalist theories in this subsection derive from Armstrong 1978, vol. I, 12–16.
12. By the aggregate of scarlet things it is meant the aggregate of wholly scarlet things. The wholly scarlet parts of partially scarlet things count as wholly scarlet things.
13. No distinction between classes and sets is intended in this entry.
14. In the case of n-place relations, the theory identifies them with classes of ordered n-tuples.
15. It is assumed here that particulars are world-bound, i.e. that none are parts of more than one world, as is the case in Lewis' theory.
16. This does not mean that necessarily every one who believes that sets of spatiotemporally located members are spatiotemporally located is committed to the idea that such sets are concrete, for they might draw the abstract/concrete distinction in a different way than I have done here. But it does mean that they take sets of spatiotemporally located members to be concrete in the sense of this entry.
17. Why ‘particulars and/or properties and/or relations’? Because propositions may have only properties or relations as constituents. An example might be the proposition that scarlet resembles vermillion. But properties and relations, as we saw in a previous section, may be reducible to particulars, in which case every proposition must have particulars as constituents.
18. Note that Quine thought that the relativity of eternal sentences to languages turned them problematic in a way similar to propositions, for Quine thought that the notion of language has no clear and intelligible conditions of identity, and this is what he found problematic about propositions (Quine 1969, 142).
19. As presented in Balaguer 1998, semantic fictionalism is inspired by and similar, but not exactly analogous, to the kind of fictionalism defended by Hartry Field in the Philosophy of Mathematics (1980). In particular, unlike Field's mathematical fitcionalism, Balaguer's semantic fictionalism does not require that reference to abstract objects is dispensable (1998, 811). Balaguer does not assert that semantic fictionalism is true (1998, 810).
20. But sometimes the word ‘Nominalism’ is used in connection to a stance with respect to possible worlds, e.g. in Loux 1998, 176. But Loux uses it in a sense different from the one adopted in this entry. For Loux the ‘possible worlds nominalist’ must believe that other worlds exist and contain only concrete particulars and that by means of such possible worlds and the concrete particulars that populate them is possible to carry out the nominalistic project of providing a reductive account of talk about properties, propositions, and the like (1998, 176). The nominalist about possible worlds, as I shall understand the position here, is committed neither to the claim that such reductive account is possible nor to the claim that possible worlds exist.
21. Note that sometimes Plantinga doesn't use a biconditional but instead says only that a states of affairs S includes (precludes) a states of affairs S* if … (1974: 45, 2003a: 107). But it is quite clear that he is providing definitions (1974: 44), which is why the biconditional is more appropriate, and indeed he uses the biconditional in his 2003b: 194 when introducing the notion of inclusion.
22. Stalnaker takes possible worlds to be properties. But are his possible worlds universals? If it is essential of universals that they can have more than one instance then Stalnaker's possible worlds seem not to be universals, since they can have only one instance.
23. As it is clear from his 1986b, Forrest takes these uninstantiated properties to be universals.
24. Note that here every subset of a world is a world itself, something that does not happen in Adams' account, since on his account the sets of propositions that constitute possible worlds are maximal.
25. Lewis explored four different ways of drawing the abstract/concrete distinction (the Way of Example, the Way of Conflation, the Negative Way, and the Way of Abstraction) and the consequences that these ways had with respect to the concreteness of possible worlds as he took them to be. He concluded that, ‘by and large, and with some doubts in connection with the Way of Example and the Negative Way’, he should say of worlds as he took them to be that they are concrete (1986a, 86).
26. Rodriguez-Pereyra 2004 proposes an alternative modal realist conception of possible worlds as sums or collections of, among other things, pure sets. If this is what possible worlds are it seems that they are not concrete, or at least not purely concrete.
27. These are first order atomic states of affairs. Higher order states of affairs can bring together more than one universal. Armstrong admits higher order states of affairs.
28. But there is an exception to Armstrong's combinatorialism. Strictly speaking not all the possible states of affairs are combinations of the elements of the actual world. Some of them involve alien particulars, that is particulars that do not exist in the actual world (1989, 58). Armstrong rejects, though, alien universals (1989, 55). Thus no possible state of affairs can involve universals not present in the actual world.
29. With a couple of further conditions: that the conjunction in question be a totality of atomic states of affairs and that for every particular figuring in a conjunction of states of affairs that is a possible world there must be at least one state of affairs in that conjunction in which the particular is combined with a monadic universal. See Armstrong (1989, 47–8).
30. That the prefix is called a ‘story prefix’ does not mean that what is mentioned within the prefix must be a work of fiction: it can be any representation whatsoever, whether true or false (Rosen 1990, 331). So it can be a philosophical theory postulating the existence of possible worlds.
31. Clearly modal fictionalism is an option not only for those who believe that possible worlds do not exist, but also for those who simply do not believe that they exist.
32. But the modal fictionalist need not be a nominalist about abstract objects in general, in which case he need not worry about whether theories are abstract or concrete.
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https://www.hackmath.net/en/examples/unit-conversion?page_num=23
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Unit conversion - examples - page 23
- Temperature conversion
The normal human body temperature is 98.6 degrees Fahrenheit. What is the temperature in degrees Celcius?
- Customary length
Convert length 65yd 2 ft to ft
- Hr to min
Sue biked to school in 5/12 of an hour. How many minutes did it take her to ride to school?
- Car crash
On the road, with a maximum permitted speed of 60 km/h, there was a car crash. From the length of the vehicle's braking distance, which was 40 m, the police investigated whether the driver did not exceed that speed. What is the conclusion of the police, as
- Reservoir 3
How many cubic feet of water is stored in the reservoir that has a length of 200 feet, a width of 100 feet, an overflow depth of 32 feet, and a current water level of 24 feet?
- Ping time
Calculate theoretical ping time between Orlando and Shenzhen which is 14102 km distant. Ping time measures the round-trip time for small messages sent from the origin to a destination that is echoed back to the source. The name comes from active sonar term
Trevor wishes to tile the floor of his bathroom. The bathroom is rectangular and is 4.2m long and 3.3m wide. The tiles are 30cm by 30cm. Calculate the cost to tile the floor if each tile costs 72 cents.
- Phone plan
Victoria's cell phone plan costs $30.00 a month. If she used 12.5 hours in May, how much did Victoria pay per minute?
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https://learnesy.com/4-ways-to-use-correlation-in-excel-for-a-business-controller2/
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math
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Correlation indicates in statistics the strength and direction of a relationship between two or more variables. The correlation is often stated with a correlation coefficient. One method for determining the correlation between two variables is bivariate analysis. The correlation coefficient has a value between 1 and -1, where 0 indicates no relationship, 1 indicates the maximum positive relationship and -1 indicates the maximum negative relationship.
Read the post in Swedish here
What is correlation?
In short, it can be said that correlation is about, whether or not, a couple of variables fluctuate or not. However, it should be remembered that correlation does not have to mean causation. Just because two things react similarly does not mean that one causes what happens to the other. In the economy, we can often see clear connections between, for example, the number of visitors and revenue or between market costs and revenue. See below illustration where the costs are on axis number 2 and have a positive value:
The correlation above is as much as 0.9 for cost 1 and only 0.1 for cost 2. COGS or direct manufacturing costs are an example of costs that usually have a high correlation with revenue as the sales price is usually set in relation to direct and indirect manufacturing costs and the margin you want. Promotional costs are another example of a cost that usually follows the revenue curve.
What do I use correlation for?
I usually use the correlation function; CORREL to the following work:
- Financial statements reconciliation
- Implementation driver-based forecast
- Campaign Analysis
Scenario analysis is another area where you may need to understand correlations in a company. There are certainly a lot you can use the function for, but it is mainly for the above work I use the function in Excel.
The function in Excel
The function is very simple in Excel, start typing CORREL or KORREL (if you have a Swedish setting) and Excel will find the function. Select the first factor you want to compare and click “;” before selecting the comparison factor. Note that an equal amount of observations are not needed for the formula to work, but as many columns in the formula.
Financial statements reconciliation
Certain costs such as travel costs, car costs and market costs often correlate strongly with sales. You can with advantage use CORREL to help verify which costs are linked to, for example, sales in a company.
In the example above, we see that cost C has a correlation of almost -1, which is the highest possible correlation. This says that cost C and income A are highly linked and that June’s value in the financial statements should be around 112 if it is assumed that C normally accounts for 10% of A. To work with correlations in financial statements and when doing cost analysis and revenue analysis is very valuable. Spending time understanding what correlates with what in a company can provide great benefits and is something I usually start with as a consultant if I want to understand what affects what in a company.
If you have done your correlation analysis and found a number of costs such as COGS, car costs, market costs, etc. that are related to sales, you can with advantage calculate an index for how to apply the costs in a budget or in a forecast. What can complicate things is that the accounting department may “not always keep up” and CORREL gives a lower correlation than it should. What I mean here is that if the finance department has not received an invoice for a cost that should correlate with sales, and fails to reserve the cost, the correlation will be lower than it should be. You may need to harmonise the cost picture before calculating the correlation.
Above you see an example of how you can quickly give a budget proposal for 2021 based on having analysed the correlation and calculated an index or ratio for costs in 2020. The company management here assumes a revenue increase of 10% and it is up to the controlling department to calculate a proposal for remaining costs.
What I usually do when I work with the development of budget or forecasting processes is that I look at the correlation and which costs are easy to predict based on, for example, sales or number of employees.
Drivers are the most important efforts and activities that drive a business’s operational and financial results. Common examples are number of sellers, number of stores, website traffic, marketing campaigns, production units.
Other large costs that do not correlate with anything, I usually distinguish and later break down into activities and forecast separately.
When I worked at Apoteksgruppen, I did a lot of campaign analysis, which was incredibly fun. Trying to discern patterns and understand the impact of campaigns is not always easy. What I analysed was not just how the campaign and sales were connected, but also how long the campaign effect lasted after the campaign was over and whether they jumped up a notch regarding normal sales.
The 2 examples below show that different offers work differently and affect sales differently. Test if you can figure out which offer affects total sales the most in the 2 cases and if you can discern an improvement in total sales thanks to the campaign?
Product A shows that the 25% discount correlates to 1.0 with total sales and only 0.2 with the offer 3 for 2. The regular sales increase significantly during the campaigns and it is not only the discounted sales that contribute to increased total sales. However, the trend is steady and not rising or falling. The conclusion is that if you do not run a campaign, sales would not be so high, however, it can affect profitability with extensive campaigns.
In Product B’s case, it is the reverse where “3 for 2” correlates well with sales, which has a rising trend and peaks during the campaign. One can assume here that campaign can be important in the event of a gradual increase in trend, which is what one wants to achieve.
In this post, I have shown that the CORREL function is great for reconciliations and forecasting, but that it can also be used for other analysis. Check out one of my other posts, where I show how to easily make a professional doughnut chart and when I usually use it.
Carl Stiller in collaboration with Learnesy
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https://www.physicsforums.com/threads/differential-geometry.390141/
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How important is to learn differential geometry to do Physics?
Applications here have been found in relativity and spacetime theories.
Gravity is curvature of spacetime, but for the electromagnetic, electroweak, and strong forces, gauge fields and field strengths are connections and curvatures of abstract internal spaces.
When not to use forms
It is time to correct the impression I may have given that differential forms are the solution to all mathematical problems………..The formalism of differential forms and the exterior calculus is a highly structured language. This structure is both a strength and a limitation. In this language there are things we cannot say……………I must admit that in several places in this book I first had to work things out in “old tensor”.
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https://www.geeksforgeeks.org/geometry-and-co-ordinates/
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Polygons are planes figures formed by a closed series of rectilinear segments. Ex– Triangle, Rectangle etc.
1. Sum of all the angles of a polygon with n sides = (n-2)π
2. Sum of all exterior angles = 360°
3. No. of sides = 360°/exterior angle
Classification of polygons –
A triangle is a polygon having three sides.
1. Area = 1/2 x base x height
2. Area = √s(s-a)(s-b)(s-c) where s = a+b+c/2
3. Area = rs (where r is in-radius)
4. Area = 1/2 x product of two sides x sine of angle
5. Area = abc/4R where R = circumradius
Congruency of Triangles:
1. SAS congruency: If two sides and an included angle of one triangle are equal to two sides and an included angle of another, the two triangles are congruent.
2. ASA congruency: If two angles and the included side of one triangle is equal to two angles and the included side of another, the triangles are congruent.
3. AAS congruency: If two angles and side opposite to one of the angles is equal to the corresponding angles and sides of another triangle, the triangles are congruent.
4. SSS congruency: If three sides of one triangle are equal to three sides of another triangle, the two triangles are congruent.
5. SSA congruency: If two sides and the angle opposite the greater side of one triangle are equal to the two sides and the angle opposite to the greater side of another triangle, then triangle are congruent.
Similarity of Triangles:
1. AAA similarity: If in two triangles, corresponding angles are equal, then the triangles are similar.
2. SSS similarity: If the corresponding sides of two triangles are proportional then they are similar.
3. SAS similarity: If in two triangles, one pair of corresponding sides are proportional and the included angles are equal then the two triangles are similar.
1. Height = a√3/2
2. Area = √3a2/4
3. R(circum radius) = 2h/3 = a/√3
4. r(in radius) = h/3 = a/2√3
5. In equilateral triangle orthocenter, in-centre, circumcenter and centroid coincide.
Area = b/4√(4a2 – b2)
where b=base and a=equal sides
1. Median: A line joining the mid-point of a side of a triangle to the opposite vertex is called a radian.
- A median divides a triangle in two parts of equal area.
- The point where three medians meet is called centroid of the triangle.
- The centroid of a triangle divides each median in ratio 2:1.
2. Altitude: A perpendicular drawn from any vertex to the opposite side is called the altitude.
- The point where all altitudes meet at a point is called the orthocenter of triangle.
3. Perpendicular bisector: A line that is a perpendicular to a side and bisects it is the perpendicular bisector of the side.
- The point at which perpendicular bisectors of the sides meet is called the circumcenter.
- The circumcenter is the centre of the circle that circumscribes the triangle.
- The lines bisecting the interior angles of a triangle are the angle bisectors of that triangle.
- The angle bisectors meet at a point called the incentre.
- The angle formed by any side at the incentre is always 90° more than the half of angle opposite to the side.
1. Length of direct common tangents is
= √[(Distance between their centres)2-(r1 – r2)2]
= √[(O1O2)2 – (r1 – r2)2]
2. Length of traverse common tangents is
= √[(Distance between their centres)2-(r1 + r2)2]
= √[(O1O2)2 – (r1 + r2)2]
Question 1: If each interior angle of a regular polygon is 108°. The number of sides of the polygon is
Solution : Interior angle = 108°
Exterior angle = 180 – 108 = 72
Number of sides of polygon = 360° /exterior angle
= 360° /72
Questions 2: The ratio of angles of triangle is 2:3:5. Find the smallest angle of the triangle.
Solution : Ratio of angles 2:3:5
then 2x + 3x + 5x = 180
10x = 180
x = 18
Hence, the smallest angle = 18×2 = 36°
Question 3: Two medians AD and BE of ∆ABC intersect O at right angle. If AD = 9cm and BE = 6cm, then the length of BD is
O is the centroid which divides the median in 2:1.
So, AO:OD = 2:1
AD = 3 units -> 9 cm
1 unit -> 3 cm
So, OD = 3 cm
BE = 3 units -> 6cm
So, BO = 4 cm
∆BOD is a right angled triangle.
BD2 = BO2 + OD2
BD2 = (4)2 + (3)2
BD2 = 16 + 9 = 25
BD = 5 cm
Question 4: The side AB of a parallelogram ABCD is produced to E in such a way that BE = AB, DE intersects BC at Q. The point Q divides BC in the ratio
Solution : Acc. to question
AD || BC and AB || DC
∠1 = ∠2 (Corresponding alternate angle)
∠3 = ∠4 (Corresponding alternate angle)
and ∠BEQ is common
By AAA property both are similar ∆EQB ∼ ∆EDA
So, EB/EA = EQ/ED = QB/AD
AD=BC & EA = 2EB
then 1/2 = QB/BC
=> BQ = QC
Hence, Q divides BC in ratio 1:1.
Question 5: In a ∆ABC, AB=AC and BA is produced to D such that AC=AD. Then the ∠BCD is
Solution :Acc. to question
ABC is an isosceles triangle.
=> ∠C = ∠B = θ
=> ∠CAD = ∠C + ∠B = 2θ (An exterior angle of a triangle is equal to the sum of the opposite interior angles.)
AC=AD So, ∆ADC is also an isosceles triangle.
In ∆ADC, ∠A + ∠C + ∠D = 180°
2∠C = 180° – 2θ (∠C = ∠D)
∠C = 90° – θ
∠BCD = θ + 90° – θ
∠BCD = 90°
Question 6: If O is the circumcenter of ∆PQR, and ∠QOR = 110°, ∠OPR= 25°, then the angle ∠PRQ is
If O is the circumcenter then OP=OR=OQ.
∠OPR = 25°
then ∠PRO = 25°
∠OQR + ∠ORQ + ∠QOR = 180°
2∠ORQ = 180° – 110°
∠ORQ = 35°
So, ∠PRQ = ∠PRO + ∠ORQ
= 25° + 35°
Question 7: In ∆ABC, DE || AC, D and E are two points on AB and CB respectively. If AB=20 cm and AD = 8 cm, then BE : CE is
AB = 20 cm and AD = 8 cm
DE || AC
then, ∠A = ∠D and ∠C = ∠E
∠B is common
By AAA property, ∆ABC ∼ ∆DBE
therefore BD/AD = BE/CE
BE/CE = 12/8
BE/CE = 3/2
Hence, BE : CE = 3:2
Question 8: Angle between the internal bisectors of two angles of a triangle ∠B and ∠C is 110°, then ∠A is
Internal bisectors of angles intersect each other at Incentre.
∠BIC = 110°
The angle formed by any side at the incentre is always 90° more than the half of angle opposite to the side.So,
∠BIC = 90° + 1/2∠A
1/2∠A = 110° – 90°
∠A = 20×2 = 40°
Question 9: The distance between two parallel chords of length 8 cm and each in a circle of diameter 10cm is
AB = CD = 8 cm
radius = D/2 = 10/2 = 5 cm
OB2=OM2 + MB2
52 = OM2 + 42
OM2 = 25 – 16
OM = 3 cm
MN = 2 x OM = 2 x 3 = 6 cm
Question 10: The radius of two concentric circles are 12cm and 13cm. If the chord of the greater circle be a tangent to the smaller circle, then the length of that chord is:
Solution : Acc. to Question
AO = 13 cm and OD = 12 cm
AO2= DO2 + AD2
132 = 122 + AD2
AD2 = 169 – 144
AD = 5cm
AB = 2xAD = 10 cm
Questions 11: Two tangents are drawn at the extremities of diameter AB of a circle with centre O. If a tangent to the circle at the point C intersects the other two tangents at Q and R, then the measure of the ∠QOR is
Solution : Acc. to question
In ∆OCR and ∆RBO
OC = OB (radius)
RC = RB (tangent from same point)
PR is common
By SSS property both are congruent ∆OCR ≅ ∆RBO
Similarly they are also congruent ∆OCQ ≅ ∆QAO
Then ∠COR = ∠ROB = x
and ∠AOQ = ∠COQ = y
2x + 2y = 180°
x + y = 90°
∠QOR = 90°
Question 12: Two equal circles whose centres are O and O’ intersect each other at the point A and B, OO’= 24 cm and AB = 10 cm then the radius of the circle is
AB = 10 cm
AC = BC = 5 cm
OC = CO’ = 12 cm
In right angled triangle ∆ACO
OA2 = OC2 + AC2
OA2 = 122 + 52
OA2 = 144 + 25
OA = 13 cm
Question 13: The distance between the centers of two circles of radii 6 cm and 3 cm is 15 cm. The length of the traverse common tangent to the circles is:
Solution : Length of traverse common tangent = √[(Distance between their centres)2-(r1 + r2)2]
=√[(15)2-(6 + 3)2]
=√(225 – 81)
= 12 cm
Question 14: If the distance between two points (0, -5) and (x, 0) is 13 units, then the value of x is:
Solution :We know that
(Distance)2 =[(x2-x1)2 + (y2 – y1)2]
(13)2 = [(x2-0)2 + (0 – (-5) )2]
169 = x2 + 25
x = 12 units
Whether you're preparing for your first job interview or aiming to upskill in this ever-evolving tech landscape, GeeksforGeeks Courses
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100309.57/warc/CC-MAIN-20231202010506-20231202040506-00275.warc.gz
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CC-MAIN-2023-50
| 8,339 | 170 |
http://mathhelpforum.com/algebra/26773-train-travel-word-problem.html
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math
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Hate to do this, but I'm having trouble setting up the following word problem:
A train leaves Union Station for Central Station, 216 km away, at 9 a.m. One hour later, a train leaves Central Station for Union Station. They meet at noon. If the second train had started at 9 a.m. and the first train at 10:30 a.m. they would still have met at noon. Find the speed of each train.
Now I've tried to set it up as
Problem is that; a) I've already set myself up for messing up this problem (because the mph varies too much) b) it gives the trains time up to noon and that makes the 216 km invalid(?).
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917119642.3/warc/CC-MAIN-20170423031159-00435-ip-10-145-167-34.ec2.internal.warc.gz
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CC-MAIN-2017-17
| 594 | 4 |
https://math.answers.com/questions/Will_repeating_decimals_always_or_never_be_rational_numbers
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math
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Repeating decimals are ALWAYS rational numbers.
Yes, they will.
Repeating decimals are always rational.
Yes, terminating decimals are always rational numbers.
Yes. All numbers are rational numbers except repeating decimals like 1.3(repeating). * * * * * Repeating decimals are also rationals. However, the quotient is not defined if the second number is the integer zero!
There are are three types of decimals: terminating, repeating and non-terminating/non-repeating. The first two are rational, the third is not.
They are always rational numbers.
they always are.
If you consider terminating decimals as ones that end in repeating 0s, then the answer is "always".
Yes, that's what "repeating" refers to.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662587158.57/warc/CC-MAIN-20220525120449-20220525150449-00511.warc.gz
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CC-MAIN-2022-21
| 705 | 10 |
https://ti.inf.ethz.ch/ew/mise/mittagssem.html?action=show&what=abstract&id=2878e198922eaa28b27d724421bc3e1bba340f6a
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math
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Prof. Emo Welzl and Prof. Bernd Gärtner
|Mittagsseminar Talk Information|
Date and Time: Thursday, February 03, 2005, 12:15 pm
Duration: This information is not available in the database
Location: This information is not available in the database
Speaker: Penny Haxell (Univ. of Waterloo)
The Ramsey number for a graph H is defined to be the smallest N such that every colouring of the edges of KN with two colours contains a monochromatic copy of H (i.e. one in which all edges have the same colour). A classical result from graph Ramsey theory states that (for n >= 5) the Ramsey number for the cycle with n vertices is 2n-1 if n is odd, and 3n/2-1 if n is even. Here we consider the same problem for 3-uniform hypergraph cycles, and obtain asymptotically best possible results.
Automatic MiSe System Software Version 1.4803M | admin login
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679103810.88/warc/CC-MAIN-20231211080606-20231211110606-00530.warc.gz
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CC-MAIN-2023-50
| 842 | 8 |
https://app.memrise.com/course/700001/learn-mathematics/639/?action=prev
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math
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Level 638 Level 640
24 words 0 ignored
Ready to learn Ready to review
Check the boxes below to ignore/unignore words, then click save at the bottom. Ignored words will never appear in any learning session.
x=f(t), y=f(t), a<t<b
has the "initial point" (f(a), g(a)) and the terminal point (f(b), g(b)).
If dx/dt does not equal zero, we can solve for dy/dx.
The parametric curve will have a horizontal tangent when dy/dt = 0
The parametric curve will have a vertical tangent when dx/dt =0 (provided that dy/dt do not equal zero at this point). No 0/0's.
To find d^2y/dx^2 go back to dy/dx = (dy/dt)/(dx/dt) and replace y with dy/dx.
Determine concavity of a parametric curve
To do this, calculate the second derivative.
=the integral of g(t)f'(t)dt from alpha to beta
In parametric terms we modify this:
(-r, theta) =
r=2 produces a circle centered at O.
or more generally: F(r, theta)=0, consists of all points P that have at least one polar representation (r, theta), whose coordinates satisfy the equation.
x=r*cos(theta)=f(theta)cos(theta) , y =r*sin(theta) = f(theta)sin(theta)
To find a tangent line to a polar curve r=f(theta), we regard theta as a parameter and write its parametric equation as:
We locate the vertical tangents setting dx/dtheta equal to zero.
We locate the horizontal tangents by finding the points where dy/dtheta = 0, provided that dx/dtheta do not equal zero.
Arc Length Polar
if we interchange x and y we obtain
An equation of the parabola with focus (0,p) and directrix y=-p is x^2=4py
The point located halfway between the focus and the directrix lies on the parabola; it is called the vertex.
A parabola is the set of points in a plane that are equidistant from a fixed point F (called the focus) and a fixed line (called the directrix).
We get an equivalent equation by squaring and simplifying.
An equation of the parabola with the focus (0,p) and the directrix y=-p is...
It opens upward if p>0 and downward if p<0.
a=(1)/(4p), then the standard equation of a parabola becomes y=ax^2
What is a sequence?
A sequence can be thought of as a list of numbers written in a definite order:
Notice that for every positive integer N there is a corresponding number aN, and so...
a sequence can be defined as a function whose domain is the set of positive integers. But we typically write aN instead of f(n) (or f(x)) for the value of the function of the number n.
If limN->infinity aN exists, we say the sequence converges (or is convergent).
if we can make the terms aN as close to L as we like by taking N sufficiently large.
if n>N then the absolute value (aN-L)< epsilon.
if for every epsilon >0 there is a corresponding integer N such that:
then lim n-> infinity aN=L.
If lim x-> infin f(x)=L and f(n) = aN when N is an integer:
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s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400198652.6/warc/CC-MAIN-20200920192131-20200920222131-00012.warc.gz
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CC-MAIN-2020-40
| 2,758 | 40 |
https://www.weedinprovincetown.com/provincetown-marijuana-news/www-weedinprovincetown-com-provincetown-marijuana-news
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math
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Here's a question to ponder: should people use the word "cannabis" or "marijuana" when referring to the psychoactive plant?
Our friends at Ask Ars beg the question and it's an interesting one. We evolved....so should the name as well?
I've also been told by some younger friends that "pot" is very old school and shows my age. What?
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s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320301063.81/warc/CC-MAIN-20220118213028-20220119003028-00129.warc.gz
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CC-MAIN-2022-05
| 332 | 3 |
https://www.deseretnews.com/article/700227395/Drive-smarter-save-money.html
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math
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WASHINGTON Want to know the exact savings that your car can score from various energy-saving strategies?
Take the Drive $marter Challenge that the Alliance to Save Energy is launching today.
Enter your car's model and year at www.drivesmarterchallenge.org, and the site will tell you the total you can save from the six easiest energy-saving moves. A lot depends on the vehicle.
For example, the driver of a 2008 Volkswagen Passat Wagon one of the most fuel-efficient midsize station wagons can save $444 a year, assuming an average gas price of $3.79 a gallon
On the other hand, a driver with a 2008 Mercedes-Benz E63 AMG wagon one of the least fuel-efficient midsize wagons can save $761 a year.
In rank order, and with the maximum savings in parentheses, these are the simplest steps for the average car:
• Speed costs. Gas mileage decreases rapidly above 60 mph. Stay under that limit and ...
• Avoid jackrabbit starts and rapid braking. (Together they'll save up to $255 a year.)
• Reduce your miles traveled by 5 percent ($100 a year)
• Keep tires properly inflated ($65 a year.)
• Ditch the junk in the trunk ($40 a year for each 100 pounds.)
• Select the right oil ($40 per year)
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s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376824448.53/warc/CC-MAIN-20181213032335-20181213053835-00532.warc.gz
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CC-MAIN-2018-51
| 1,199 | 12 |
https://www.spiedigitallibrary.org/conference-proceedings-of-spie/2774/0000/Application-of-group-indices-of-refraction-to-achromatic-lens-design/10.1117/12.246720.short?SSO=1
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math
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An approach to color correction is described in which the ratio of the group velocity to the speed of light in vacuum (the group index of refraction) in glass is used, in conjunction with the more familiar phase index of refraction, to control longitudinal color in a system of thin lenses in contract. It is shown that at the wavelength of a turning point where the phase power of a lens is locally independent of wavelength, the phase power is equal to the group power. It is further shown that in a lens consisting of three or more elements, if the phase and group powers are equal and the group power has a turning point at the same wavelength, the second derivative of phase power with respect to wavelength is zero at that wavelength (the lens is confocal and achromatic in both phase and group power and the secondary spectrum is locally zero). The group index of refraction and the concept of group aberrations can equally by applied to exact raytracing for thick lens systems. In using easily calculated derivatives of the phase index of refraction the approach affords a computational simplicity that is well suited to computer-aided lens design.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583509996.54/warc/CC-MAIN-20181016030831-20181016052331-00428.warc.gz
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CC-MAIN-2018-43
| 1,156 | 1 |
https://www.syllablecount.com/syllables/mathematics
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math
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How many syllables are in mathematics? 4 syllables
Divide mathematics into syllables: math-e-mat-ics
How to pronounce mathematics:
US English Accent and Pronunciation:
British English Accent and Pronunciation:
Definition of: Mathematics (New window will open)
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Mathematics Poems: (See poems with this word. New window will open)
Synonyms and Words Related to Mathematics
mathematic (4 syllables),
math (1 Syllables), maths (1 Syllables)
algorithm (4 syllables), math (1 syllables), maths (1 syllables), numbers (2 syllables),
Two syllable words that rhyme with Mathematics
Three syllable words that rhyme with Mathematics
Four syllable words that rhyme with Mathematics
acrobatics, aerobatics, automatics, charismatics, democratic's, democratics, informatics, mathematics, numismatics, systematics, telematics
What do you think of our answer to how many syllables are in mathematics? Are the syllable count, pronunciation, words that rhyme, and syllable divisions for mathematics correct? There are numerous syllabic anomalies found within the U.S. English language. Can mathematics be pronounced differently? Did we divide the syllables correctly? Do regional variations in the pronunciation of mathematics effect the syllable count? Has language changed? Provide your comments or thoughts on the syllable count for mathematics below.
Comment on the syllables in Mathematics
A comprehensive resource for finding syllables in mathematics, how many syllables are in mathematics, words that rhyme with mathematics, how to divide mathematics into syllables, how to pronounce mathematics in US and British English, how to break mathematics into syllables.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224654606.93/warc/CC-MAIN-20230608071820-20230608101820-00038.warc.gz
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CC-MAIN-2023-23
| 1,832 | 20 |
https://repository.bilkent.edu.tr/items/3917a79e-676f-48bf-80eb-a5e6f8e2d453
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math
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Analysis of the elliptic-profile cylindrical reflector with a non-uniform resistivity using the complex source and dual-series approach: H-polarization case
An elliptic-profile reflector with varying resistivity is analyzed under the illumination by an H-polarized beam generated by a complex-source-point (CSP) feed. The emphasis is done on the focusing ability that is potentially important in the applications in the optical range related to the partially transparent mirrors. We formulate the corresponding electromagnetic boundary-value problem and derive a singular integral equation from the resistive-surface boundary conditions. This equation is treated with the aid of the regularization technique called Riemann Hilbert Problem approach, which inverts the stronger singular part analytically, and converted to an infinite-matrix equation of the Fredholm 2nd kind. The resulting numerical algorithm has guaranteed convergence. This type of solution provides more accurate and faster results compared to the known method of moments. In the computations, a CSP feed is placed into a more distant geometrical focus of the elliptic reflector, and the near-field values at the closer focus are plotted and discussed. Various far-field radiation patterns including those for the non-uniform resistive variation on the reflector are also presented.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947473401.5/warc/CC-MAIN-20240221070402-20240221100402-00749.warc.gz
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CC-MAIN-2024-10
| 1,351 | 2 |
http://scitation.aip.org/content/aip/journal/apl/99/13/10.1063/1.3640213
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math
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Full text loading...
(Color online) M(H) isothermal magnetization of: (a) Tb5Si2Ge2 in the temperature range of 77–300 K and (b) Gd5Si2Ge2 in the temperature range of 77–340 K, for applied fields H up to 31 T. Arrott plots for: (c) Tb5Si2Ge2 (Inset: T = 124 K) and (d) Gd5Si2Ge2 (Inset: T = 314 K).
(Color online) (a) Temperature dependence of the spontaneous magnetization (blue dots) and reciprocal susceptibility (red triangle) curves of Tb5Si2Ge2 obtained from Arrot representation. The dashed lines (dash lines) are the spontaneous magnetization Brillouin curves assuming and . (b) Temperature dependence of the HC (T). (c) Magnetic and crystallographic phases diagram of Tb5(Si x Ge1− x )4 taken from Ref. 8 including the determined value of (star). The square represents the temperature of the order-disorder transition (for x > 0.45: PM →FM and for x < 0.45 from PM to AFM state). The circle symbols represent the order-order transition also called spin reorientation transition.
(Color online) Change in the magnetic free energy as a function of temperature of both structures (M and O(I)) for Tb5Si2Ge2 using Eq. (1).
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s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394010672371/warc/CC-MAIN-20140305091112-00065-ip-10-183-142-35.ec2.internal.warc.gz
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CC-MAIN-2014-10
| 1,162 | 5 |
https://scholarship.claremont.edu/hmc_fac_pub/1046/
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math
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In the game Knock ’m Down, tokens are placed in N bins. At each step of the game, a bin is chosen at random according to a fixed probability distribution. If a token remains in that bin, it is removed. When all the tokens have been removed, the player is done. In the solitaire version of this game, the goal is to minimize the expected number of moves needed to remove all the tokens. Here we present necessary conditions on the number of tokens needed for each bin in an optimal solution, leading to an asymptotic solution. MR Subject Classifications: primary: 91A60
© 2001 The Electronic Journal of Combinatorics
A. Benjamin, M. T. Fluet, M. L. Huber, Optimal Token Allocations in Solitaire Knock 'm Down, The Electronic Journal of Combinatorics, Vol. 8, No. 2, 1-8, #R2, 2001.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510603.89/warc/CC-MAIN-20230930050118-20230930080118-00308.warc.gz
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CC-MAIN-2023-40
| 785 | 3 |
http://www.maths.manchester.ac.uk/~tv/Seminar/2008-2009/cheltsov.html
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math
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Ivan Cheltsov (University of Edinburgh)
A method of Kobayashi constructs an Einstein metric with positive Ricci curvature on a circle bundle over a complex Fano manifold that admits a Kähler-Einstein metric. Boyer and Galicki generalized the method of Kobayashi to a Seifert bundle over a Fano orbifold that admits an orbifold Kähler-Einstein metric. But the existence of Kähler-Einstein metrics on Fano orbifolds is a subtle problem that is still unsolved (even for Fano manifolds). For smooth two-dimensional Fano manifolds (del Pezzo surfaces), this problem has been completely solved by Gang Tian in 1990.
For Fano orbifolds, we know many obstructions to the existence of a Kähler-Einstein metric, which are due to Matsushima, Futaki, Tian, Yau, Sparks, Donaldson and Thomas. For a Fano orbifold V, it has been conjectured by Yau that V admits a Kähler-Einstein metric if and only if V is stable in a certain sense. Proving this conjecture is currently a major research programme in geometry (the talk of Simon Donaldson on Miles60 conference in London (July, 2008) is exactly about this conjecture). See http://arxiv.org/abs/0801.4179 and http://arxiv.org/abs/0803.0985. But even for smooth three-dimensional Fano manifolds, we know little about the existence of a Kähler-Einstein metric. The only known sufficient condition for the existence of a Kähler-Einstein metric on a Fano orbifold is due to Tian, Siu, Nadel, Kollar and Demailly. This condition can be formulated in terms of the so-called alpha-invariant of Tian (or so-called global log canonical threshold for Fano orbifolds). This holomorphic invariant plays important role in Kähler geometry (existence of a Kähler-Einstein metric, convergence of the Kähler-Ricci flow, etc). Surprisingly, this invariant also plays important role in birational geometry and singularity theory. We describe this invariant and its application in geometry.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267865995.86/warc/CC-MAIN-20180624005242-20180624025242-00445.warc.gz
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CC-MAIN-2018-26
| 1,915 | 3 |
https://www.worksheetkey.com/simplifying-square-roots-worksheet/
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math
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Simplifying Square Roots Worksheet. Plot of quadratic equation root, patterns and algebra take a look at, free 5th grade test questions, online prentice hall pre- algebra, trig intermediate examination solutions. A) sq. roots of complete numbers and monomial algebraic expressions; … Simplifying Square Roots of Whole Numbers exercise sheet. Boolean algebra calculator, the means to enter dice root into ti eighty three calculator, interactive sq. root games, trigonometry problem fixing with solutions, algebra questions sheets.
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Part of the Fertile Crescent, the word in Greek means… 25 scaffolded questions that begin out relatively easy and end with some precise challenges. Displaying all worksheets related to – Simplifying Square And Cube Roots. Displaying all worksheets associated to – Simplifying Square Root Expressions. A really great exercise for permitting college students to understand the concept of Simplifying Roots.
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Answers for math worksheets, quiz, homework, and lessons. Optimize your follow of converting non-perfect sq. numbers to good squares, with these exclusive exercises. Decipher the least number that should be divided or multiplied with the given numbers. If you want the reply to be a complete number, choose “good squares,” which makes the radicand to be a perfect sq. (1, 4, 9, 16, 25, and so forth.). If you select to permit non-perfect squares, the reply is typically an endless decimal that’s rounded to a certain number of digits. Each worksheet is randomly generated and thus unique.
Simplifying Square Roots Valentines Day Worksheet & Coloring Exercise
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https://www.math.uic.edu/seminars/view_seminar?id=4454
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math
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The Cube Problem for Linear Orders
Abstract: Does there exist a linear order that isomorphic to its lexicographically ordered cube but not to its square? Sierpinski posed this problem in his 1958 textbook on set theory Cardinal and Ordinal Numbers. The corresponding question has been answered positively for many other classes of structures, including groups, rings, topological spaces, Boolean algebras, and graphs. However, the answer to Sierpinski’s question turns out to be negative: every linear order isomorphic to its cube is already isomorphic to its square. In this talk, we outline a proof of this result, and connect it with several other problems about linear orders.
Tuesday November 15, 2016 at 4:00 PM in SEO 427
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https://www.assignmentexpert.com/homework-answers/mathematics/trigonometry/question-30726
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math
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Answer to Question #30726 in Trigonometry for Kristen Woods
A. 13,200 ft^2
B. 122,000 ft^2
C. 26,400 ft^2
D. 24,600 ft^2
Area=0.5*first leg*second leg
So in our case Area=0.5*120*220=13200 ft^2, answer A.
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http://www.chegg.com/homework-help/questions-and-answers/objects-near-surface-earth-fall-downward-acceleration-g-98-m-s2-absence-air-resistance-add-q1352291
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math
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Objects near the surface of the earth fall downward with an acceleration of g=9.8 m/s2 in the absence of air resistance. In addition, a glider on a frictionless air track has a constant acceleration parallel to the air track. Let the air track make a ?=10o angle with the horizontal.
A) Draw the free body diagram of the glider including the weight and normal force. Draw the y axis perpendicular to the air track and the x axis parallel to the air track.
B) If the glider weighs 0.5 kg, what is the magnitude of the weight?
C) Find the component of the weight that acts perpendicular to the air track
D) Find the component of the weight that acts parallel to the air track.
E) Find the acceleration of the glider parallel to the air track. Compare your answer to the value of g sin?.
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s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738660342.42/warc/CC-MAIN-20160924173740-00237-ip-10-143-35-109.ec2.internal.warc.gz
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http://www.trigonometry101.com/Trapezoid
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math
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Trapezoid - Wikipedia
An acute trapezoid has two adjacent acute angles on its longer base edge, while an obtuse trapezoid has one acute and one obtuse angle on each base.
Trapezoid - Math is Fun
has a pair of parallel sides: is an Isosceles trapezoid when both angles coming from a parallel side are equal, and the sides that aren't parallel are equal in length.
Trapezoid | Definition of Trapezoid by Merriam-Webster
Define trapezoid: a quadrilateral having only two sides parallel; trapezium; a bone in the wrist at the base of the metacarpal of the index finger
Trapezoid -- from Wolfram MathWorld
A trapezoid is a quadrilateral with two sides parallel. The trapezoid is equivalent to the British definition of trapezium (Bronshtein and Semendyayev 1977, p. 174).
Trapezoid | Define Trapezoid at Dictionary.com
Trapezoid definition, a quadrilateral plane figure having two parallel and two nonparallel sides. See more.
Quadrilaterals - Square, Rectangle, Rhombus, Trapezoid ...
An Isosceles trapezoid, as shown above, has left and right sides of equal length that join to the base at equal angles.. The Kite. Hey, it looks like a kite (usually).. It has two pairs of sides:
Trapezoid - definition of trapezoid by The Free Dictionary
Define trapezoid. trapezoid synonyms, trapezoid pronunciation, trapezoid translation, English dictionary definition of trapezoid. trapezoid n. 1. Mathematics a. A quadrilateral having two parallel sides.
Trapezoid - Mathwarehouse.com
The midsegment of a trapezoid is the segment that joins the midpoints of the nonparallel sides of a trapezoid. In the trapezoid below, ...
Trapezoid - K-6 Geometric Shapes
The Trapezoid Explained: Everything a K-6 student needs to know about this shape.
Area of a Trapezoid | Math Goodies
The area of a polygon is the number of square units inside that polygon. Area is 2-dimensional like a carpet or an area rug.
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CC-MAIN-2018-17
| 1,883 | 20 |
https://firstlegaldocs.com/23090-rancho.jnt
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math
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A Lesson Progression Using Ray Tracing Diagrams Analyzing Shadow Images. Couple of fairly simple geometry problems applying the law of reflection. 9 Figure 26-14 Principal Rays Used in Ray Tracing for a Concave Mirror. Optics CONVEX MIRRORS Extra Practice Worksheet a Draw a ray diagram for. Question Mirrors And Lenses Ray Tracing Worksheet The Object Is Given For. Resolving power and MTF trigonometric ray tracing and chromatic and. Light and Geometric Optics CONVEX MIRRORS Extra Practice Worksheet a Draw.
Home Lab Week 7 Refraction Ray Tracing and Snell s Law Home Lab 7. Physics Worksheet 14 Chapter 24 Geometric Optics Converging Lenses. For mirrors and lenses we can use simple rules to trace the paths. Can produce this image ray tracing for mirrors PowerPoint the thin-lens. Instruments resolving power and MTF trigonometric ray tracing and. Trace around the glass block with your pencil to mark its position. Chief Ray The vertex 17 Ray Tracing Applications Concave mirror object. Please post to the Chapter 25 worksheets discussion forum on the Physics.
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CC-MAIN-2022-40
| 1,066 | 2 |
http://wow.joystiq.com/profile/2348790/
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math
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Mar 25th 2009 9:25AM More of a mistake in BC, but arena ruined pvp for me.
The old vanilla wow system of rankings/server only BG's
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s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422122086301.64/warc/CC-MAIN-20150124175446-00088-ip-10-180-212-252.ec2.internal.warc.gz
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https://archive.org/details/NASA_NTRS_Archive_20110016575
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math
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An accelerated-testing methodology has been developed for measuring the slow-crack-growth (SCG) behavior of brittle materials. Like the prior methodology, the accelerated-testing methodology involves dynamic fatigue ( constant stress-rate) testing, in which a load or a displacement is applied to a specimen at a constant rate. SCG parameters or life prediction parameters needed for designing components made of the same material as that of the specimen are calculated from the relationship between (1) the strength of the material as measured in the test and (2) the applied stress rate used in the test. Despite its simplicity and convenience, dynamic fatigue testing as practiced heretofore has one major drawback: it is extremely time-consuming, especially at low stress rates. The present accelerated methodology reduces the time needed to test a specimen at a given rate of applied load, stress, or displacement. Instead of starting the test from zero applied load or displacement as in the prior methodology, one preloads the specimen and increases the applied load at the specified rate (see Figure 1). One might expect the preload to alter the results of the test and indeed it does, but fortunately, it is possible to account for the effect of the preload in interpreting the results. The accounting is done by calculating the normalized strength (defined as the strength in the presence of preload the strength in the absence of preload) as a function of (1) the preloading factor (defined as the preload stress the strength in the absence of preload) and (2) a SCG parameter, denoted n, that is used in a power-law crack-speed formulation. Figure 2 presents numerical results from this theoretical calculation.
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https://encyclopediaofmath.org/wiki/Fermat_great_theorem
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math
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Fermat great theorem
Fermat's famous theorem, Fermat's big theorem, Fermat's last theorem
The assertion that for any natural number the equation (the Fermat equation) has no solution in non-zero integers . It was stated by P. Fermat in about 1630 in the margins of his copy of the book Aritmetika by Diophantus as follows: "It is impossible to partition a cube into two cubes, or a biquadrate into two biquadrates, and in general any power greater than the second into two powers with the same exponent" . And he then added: "I have discovered a truly marvellous proof of this, which this margin is too narrow to contain" . A proof of the theorem for was found in Fermat's papers. No general proof has so far been obtained (1984), despite the efforts of many mathematicians (both professional and amateur). An unhealthy interest in proving this theorem was stimulated at one time by a large international prize, which was abolished at the end of the First World War.
It has been conjectured that there is no proof of Fermat's last theorem at all.
For the theorem was proved by L. Euler (1770), for by P.G.L. Dirichlet and A. Legendre (1825), and for by G. Lamé (1839) (see ). It is sufficient to prove the theorem for and for every prime exponent , that is, it is enough to prove that the equation
has no solutions in non-zero relatively-prime integers . One can also assume that and are relatively prime to . For a proof of Fermat's theorem one considers two cases: case 1 when , and case 2 when . The proof of the second case is more difficult and is usually carried out by the method of infinite descent. An important contribution to proving Fermat's last theorem was made by E. Kummer, who invented a fundamentally new method based on his development of the arithmetic theory of a cyclotomic field. It makes use of the fact that in the field , , the left-hand side of equation (1) splits into linear factors , which are -th powers of ideal numbers (cf. Ideal number) in in case 1 and differ from -th powers by a factor , , in case 2. If divides the numerators of the Bernoulli numbers (), then by the regularity criterion does not divide the class number of and these ideal numbers are principal. Kummer
proved Fermat's theorem in this case. It is not known whether the number of regular numbers is infinite or finite (by Jensen's theorem the number of irregular prime numbers is infinite ). Kummer proved the theorem for some irregular prime numbers and also established its validity for all . In case 1 he showed that (1) implies the congruences
which are valid for any permutation of . Hence he obtained that if equation (1) has a solution in case 1, then for ,
In case 2 Kummer proved Fermat's theorem under the following conditions: 1) , , where is the first factor of the class number of (this is equivalent to the requirement that only one of the numerators of the numbers , where , is divisible by ); 2) (); and 3) there is an ideal modulo which the unit
is not congruent to the -th power of an integer in , where is a primitive root modulo and
Kummer's method has been widely developed in several articles on Fermat's last theorem (see , ). It has been established that (2) holds if (1) does in case 1 for , 9, 11, 13, 15, 17, 19. Under the same conditions M. Krasner showed that there is a number such that for (2) is true for all numbers , where .
H. Brückner showed that the amount of numbers , , with numerators divisible by is greater than . Suppose that , . P. Remorov showed that there are constants and , , such that for all , , case 1 of the Fermat theorem is true. M. Eichler established that case 1 is true for , where is the index of irregularity of , . H. Vandiver proved case 1 for , where is the second factor of the class number of . He obtained interesting results on case 2 in and . For example, he showed that the Fermat theorem is true under the following conditions: 1) ; and 2) (), . The following theorem is most important: Let be an irregular prime number and let be the indices of the Bernoulli numbers among with numerators divisible by ; if none of the units () is congruent to the -th power of an integer in modulo , where is the prime ideal dividing a prime number with (), then Fermat's theorem is true. From this Vandiver obtained an effectively-verifiable criterion for irregular prime numbers by means of which the Fermat theorem has been proved on a computer for all (see ).
There are various results on case 1 of Fermat's last theorem. As early as 1823 Legendre published a result of S. Germain: If there is a prime number such that the congruence () has no integer solutions not divisible by , and is not a -th power residue modulo , then case 1 of the Fermat theorem holds (see ). Hence he showed that if at least one of the numbers , (), , is prime, then case 1 holds. This proposition has been extended to all . A. Wieferich discovered the following criterion: If , where is the Fermat quotient, then case 1 is true. D. Mirimanoff proved this for . Subsequently, case 1 was established by a number of other authors for all for which , where is any prime number . From this the first case of Fermat's theorem follows for , where contain only prime numbers in their prime factorizations. Calculations on a computer showed that among the numbers only two: and satisfy the condition , but for these . This proves case 1 for all . P. Furtwängler gave fairly simple new proofs of the results of Wieferich and Mirimanoff based on Eisenstein's reciprocity law. He also proved that if is a solution of (1) and , then , where but , or but , or but .
A great variety of other criteria are known for case 1 of the Fermat theorem. They are connected with the solvability of certain congruences or with the existence of prime numbers of a certain form. The equation is not valid if divides neither nor (see ). It is impossible in practice to produce a counterexample to Fermat's last theorem. K. Inkeri showed that if the integers , , satisfy (1), then , and in case 1: .
Fermat's last theorem can be stated as follows: For every natural number there are no rational points on the Fermat curve except the trivial ones, and . Rational points on the Fermat curve have been studied by methods of algebraic geometry. By these methods it has been proved (1983) that the number of rational points on the Fermat curve is finite in every case. This follows from the Mordell conjecture, which was proved by G. Faltings . D.R. Heath-Brown has shown, using the Mordell conjecture, that Fermat's last theorem holds for almost-all primes , cf. . Also, by methods of analytic number theory, L.M. Adleman, Foury and Heath-Brown have shown that case 1 holds for infinitely many primes , cf. .
One can look at Fermat's equation in algebraic integers, entire functions, matrices, etc. There is a generalization of Fermat's theorem for equations of the form .
|||Diophantus of Alexandria, "Aritmetika and the book on polygonal numbers" , Moscow (1974) (In Russian; translated from Greek)|
|||H.M. Edwards, "Fermat's last theorem. A genetic introduction to algebraic number theory" , Springer (1977)|
|[3a]||E. Kummer, "Bestimmung der Anzahl nicht äquivalenter Classen für die aus ten Wurzeln der Einheit gebildeten complexen Zahlen" J. Reine Angew. Math. , 40 (1850) pp. 93–116|
|[3b]||E. Kummer, "Zwei besondere Untersuchungen über die Classen-Anzahl und über die Einheiten der aus ten Wurzeln der Einheit gebildeten complexen Zahlen" J. Reine Angew. Math. , 40 (1850) pp. 117–129|
|[3c]||E. Kummer, "Allgemeiner Beweis des Fermatschen Satzes, dass die Gleichung $x^\lambda+y^\lambda=z^\lambda$ durch ganze Zahlen unlösbar ist, für alle diejenigen Potenz-Exponenten $\lambda$, welche ungerade Primzahlen sind und in den Zählern der ersten $\frac12(\lambda-3)$ Bernoullischen Zahlen als Factoren nicht vorkommen" J. Reine Angew. Math. , 40 (1950) pp. 130–138|
|||Z.I. Borevich, I.R. Shafarevich, "Number theory" , Acad. Press (1966) (Translated from Russian) (German translation: Birkhäuser, 1966) MR0195803 Zbl 0145.04902|
|||E. Kummer, "Einige Sätze über die aus den Wurzeln der Gleichung gebildeten complexen Zahlen, für den Fall, dass die Klassenanzahl durch teilbar ist, nebst Anwendung derselben auf einen weiteren Beweis des letzten Fermat'schen Lehrsatzes" Abh. Akad. Wiss. Berlin, Math. Kl. (1857) pp. 41–74|
|||H. Vandiver, "Fermat's last theorem" Amer. Math. Monthly , 53 (1946) pp. 555–578 Zbl 52.0161.13|
|||P. Ribenboim, "Thirteen lectures on Fermat's last theorem" , Springer (1979)|
|||M. Krasner, "Sur le premier cas du théorème de Fermat" C.R. Acad. Sci. Paris , 199 (1934) pp. 256–258 Zbl 0010.00702 Zbl 60.0129.01|
|||H. Brückner, "Zum Beweis des ersten Falles der Fermatschen Vermutung für pseudoreguläre Primzahlen $l$" J. Reine Angew. Math. , 253 (1972) pp. 15–18|
|||P.N. Remorov, "On Kummer's theorem" Uchen. Zap. Leningrad. Gosudarstv. Univ. Ser. Mat. Nauk , 144 : 23 (1952) pp. 26–34 (In Russian) MR81310|
|||M. Eichler, "Eine Bemerkung zur Fermatschen Vermutung" Acta Arith. , 11 (1965) pp. 129–131 MR0182607 Zbl 0135.09401|
|||H. Vandiver, "Fermat's last theorem and the second factor in the cyclotomic class number" Bull. Amer. Math. Soc. , 40 (1934) pp. 118–126 MR1562807|
|||H. Vandiver, "On Fermat's last theorem" Trans. Amer. Math. Soc. , 31 (1929) pp. 613–642 MR1501503|
|||H.S. Vandiver, "Examination of methods of attack on the second case of Fermat's last theorem" Proc. Nat. Acad. Sci. USA , 40 : 8 (1954) pp. 732–735 MR62758|
|||S. Wagstaff, "The irregular primes to 125.000" Math. Comp. , 32 (1978) pp. 583–591 MR491465|
|||A. Wieferich, "Zum letzten Fermatschen Theorem" J. Reine Angew. Math. , 136 (1909) pp. 293–302|
|||D. Mirimanoff, "Zum letzten Fermatschen Theorem" J. Reine Angew. Math. , 139 (1911) pp. 309–324|
|||D.H. Lehmer, "On Fermat's quotient, base 2" Math. Comp. , 36 (1981) pp. 289–290 MR595064|
|||P. Furtwängler, "Letzter Fermat'scher Satz und Eisenstein'sches Reziprozitätsprinzip" Sitzungsber. Akad. Wiss. Wien Math.-Naturwiss. Kl. IIa , 121 (1912) pp. 589–592|
|||G. Terjanian, "Sur l'equation " C.R. Acad. Sci. Paris , A285-B285 : 16 (1977) pp. 973A-975A (English abstract) MR0498370|
|||K. Inkeri, "Abschätzungen für eventuelle Lösungen der Gleichung im Fermatschen Problem" Ann. Univ. Turku Ser. A , 16 : 1 (1953) pp. 3–9 MR0058629 Zbl 0051.28003|
|||M.M. Postnikov, "An introduction to algebraic number theory" , Moscow (1982) (In Russian)|
|||G. Faltings, "Endlichkeitssätze für abelsche Varietäten über Zahlkörpern" Invent. Math. , 73 (1983) pp. 349–366|
|||D.R. Heath-Brown, "Fermat's last theorem for "almost all" exponents" Bull. London Math. Soc. , 17 (1985) pp. 15–16|
|||L.M. Adleman, D.R. Heath-Brown, "The first case of Fermat's last theorem" Invent. Math. , 79 (1985) pp. 409–416 MR778135|
In fact, Heath-Brown and, independently, A. Granville, cf. [a1], have proved that the density of the exponents for which Fermat's last theorem holds is one.
It is now (1988) known that Fermat's last theorem holds for all $n < 150000$, and that case 1 holds for all primes up to , cf. [a2].
Recently (1987), K. Ribet, using ideas of G. Frey and J.-P. Serre, showed that Fermat's last theorem is implied by the Weil–Taniyama conjecture in the theory of elliptic curves (cf. Elliptic curve).
|[a1]||S. Wagon, "Fermat's last theorem" Math. Intelligencer , 8 : 1 (1986) pp. 59–61 MR823221|
|[a2]||P. Ribenboim, "Recent results about Fermat's last theorem" Cand. Math. Bull. , 20 (1977) pp. 229–242 MR463088|
Fermat great theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Fermat_great_theorem&oldid=53456
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| 11,715 | 49 |
https://app-wiringdiagram.herokuapp.com/post/geometry-standardized-test
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math
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GEOMETRY STANDARDIZED TEST
Congruent Figures - anderson
4-1 Standardized Test Prep Congruent Figures Multiple Choice For Exercises 1–6, choose the correct letter. Prentice Hall Geometry • Teaching Resources Reserved. 57 Name Class Date 4-6 Standardized Test Prep Congruence in Right Triangles Multiple Choice For Exercises 1–4, choose the correct letter. 1. Which additional piece of
Standardized Test Practice, Mathematics: Applications
Standardized Test Practice. Standardized Test Practice randomly selects a total of 20 questions from lessons for Chapter 1 through the chapter that you indicate. Choose your chapter from the list below. Chapter 1 - Number Patterns and AlgebraGlencoe/McGraw-Hill · Mathematics
Glencoe Mathematics - Online Study Tools
Standardized Test Practice randomly selects a total of 20 questions from lessons for Chapter 1 through the chapter that you indicate. Choose your chapter from the list below.
Geometry: Standardized Test Practice Workbook, Teachers
Geometry: Standardized Test Practice Workbook, Teachers Edition [MCDOUGAL LITTEL] on Amazon. *FREE* shipping on qualifying offers. McDougal Littell STANDARDIZED TEST PRACTICE WORKBOOK Teacher's Edition Workbook.Reviews: 7Format: PaperbackAuthor: MCDOUGAL LITTEL
Solutions to Geometry (9780076639298) :: Free Homework
Shed the societal and cultural narratives holding you back and let free step-by-step Geometry textbook solutions reorient your old paradigms. NOW is the time to make today the first day of the rest of your life.
Videos of geometry standardized test
Click to view on YouTube3:18Geometry Test chapter 11 viewsYouTube · 1/6/2012Click to view on YouTube1:22Standardized Testing : ACT Math Tutoring4 viewsYouTube · Click to view on YouTube3:47Geometry: Lesson One Angles15K viewsYouTube · 3/27/2009See more videos of geometry standardized test[PDF]
Georgia Standardized Test Practice Workbook
Georgia Geometry Standardized Test Practice Workbook The Standardized Test Practice Workbook provides practice exercises for every lesson in a standardized test format. Included are multiple-choice, quantitative-comparison, and multi-step problems. The Standardized Test Practice for every lesson is correlated to the Georgia
Solutions to Geometry (9780130625601) :: Free Homework
Free step-by-step solutions to Geometry (9780130625601) - Slader[PDF]
NAME DATE PERIOD 6 Standardized Test Practice
Standardized Test Practice (continued) C06-38A-873963 4x - 4 16 Chapter 6 64Glencoe Geometry 6 15. A polygon has six congruent sides. Lines containing two of its sides contain points in its interior. Name the polygon by its number of sides, and then classify it as convex or concave and[PDF]
CHAPTER Standardized Test A 5 For use after Chapter 5
Geometry Chapter 5 Assessment Book 99 Standardized Test B continued For use after Chapter 5 10. Which is a possible value of x? A 2 8 5 x B 4 C 14 D 17 11. Using the Hinge Theorem and the diagram, you can conclude: 60° 120° L M S K P A m∠ KLM < m∠ QSP B QS 5 LM C PS > LM D none of these 12. Based on the diagram, which is a true statement[PDF]
Mr. Q’s Honors Geometry Christmas Break 2012 Homework!
Mr. Q’s Honors Geometry Christmas Break 2012 Homework! To keep you fit during the off-season and ready for the New Year! All of the questions are multiple choice.
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https://app.seesaw.me/activities/q4985y/how-the-world-works-provocation
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math
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1. Choose 1 material - Take a photo of it. 2. Think about how you used it in different stations. 3. What did you notice about this material? 4. Label the material with key words: (a) What is it? (b) What is it like? (c) What does it do? (d) Can it change? Explain.
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