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Some rational numbers, such as 1/10, need a finite number of digits after the decimal point to write them in decimal form. The number one tenth is written in decimal form as 0.1. Numbers written with a finite decimal form are rational. Some rational numbers, such as 1/11, need an infinite number of digits after the decimal point to write them in decimal form. There is a repeating pattern to the digits following the decimal point. The number one eleventh is written in decimal form as 0.0909090909 ... .
A percentage could be called a rational number, because a percentage like 7% can be written as the fraction 7/100. It can also be written as the decimal 0.07. Sometimes, a ratio is considered as a rational number.
Irrational numbers are numbers which cannot be written as a fraction, but do not have imaginary parts (explained later).
Irrational numbers often occur in geometry. For example, if we have a square which has sides of 1 meter, the distance between opposite corners is the square root of two, which equals 1.414213 ... . This is an irrational number. Mathematicians have proved that the square root of every natural number is either an integer or an irrational number.
One well-known irrational number is pi. This is the circumference (distance around) of a circle divided by its diameter (distance across). This number is the same for every circle. The number pi is approximately 3.1415926535 ... .
An irrational number cannot be fully written down in decimal form. It would have an infinite number of digits after the decimal point, and unlike 0.333333 ..., these digits would not repeat forever.
Real numbers is a name for all the sets of numbers listed above:
The real numbers form the real line. This is all the numbers that do not involve imaginary numbers.
Imaginary numbers are formed by real numbers multiplied by the number i. This number is the square root of minus one (−1).
There is no number in the real numbers which when squared, makes the number −1. Therefore, mathematicians invented a number. They called this number i, or the imaginary unit.
Imaginary numbers operate under the same rules as real numbers:
Imaginary numbers were called "imaginary" because when they were first found, many mathematicians did not think they existed. The person who "discovered" imaginary numbers was Gerolamo Cardano in the 1500s. The first to use the words "imaginary number" was René Descartes. The first people to use these numbers were Leonard Euler and Carl Friedrich Gauss. Both lived in the 18th century.
Complex numbers are numbers which have two parts; a "real" part and an "imaginary" part. Every type of number written above is also a complex number.
Complex numbers are a more general form of numbers. The complex numbers can be drawn on a number plane. This is composed of a real number line, and an imaginary number line.
All of normal mathematics can be done with complex numbers:
To multiply two complex numbers is more complicated. It is easiest to describe in general terms, with two complex numbers a + bi and c + di.
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For example, (4 + 5i) × (3 + 2i) = (4 × 3 − 5 × 2) + (4 × 2 + 5 × 3)i = (12 − 10) + (8 + 15)i = 2 + 23i.
A real or complex number is called a "transcendental number" if it can not be obtained as a result of an algebraic equation with integer coefficients.
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Proving that a certain number is transcendental can be extremely difficult. Each transcendental number is also an irrational number. The first people to see that there were transcendental numbers were Gottfried Wilhelm Leibniz and Leonhard Euler. The first to actually prove there were transcendental numbers was Joseph Liouville. He did this in 1844.
Some well-known transcendental numbers include:
November
November (Nov.) is the eleventh and penultimate (second-last) month of the year in the Gregorian calendar, coming between October and December. It has 30 days. Its name is from the Latin word "novem", which meant "nine". It was the ninth month of the year before January and February were added to the Roman Calendar.
November always begins on the same day of the week as March, and additionally, February in common years. November always ends on the same day of the week as August.
November is the eleventh month of the year in the Gregorian calendar, after October and before December, which is the last month. November has 30 days. It was the ninth month in the old Roman calendar, which is where its name comes from. It kept its name when January and February were added to the beginning of the year, despite becoming the eleventh month. The ninth month is now September.
November begins on the same day of the week as February in common years and March every year, as each other's first days are exactly 39 weeks (273 days) and 35 weeks (245 days) apart respectively. November ends on the same day of the week as August every year, as each other's last days are exactly 13 weeks (91 days) apart.
In common years, November starts on the same day of the week as June of the previous year, and in leap years, September and December of the previous year. In common years, November finishes on the same day of the week as March and June of the previous year, and in leap years, September of the previous year.
In years immediately before common years, November starts on the same day of the week as August of the following year, and in years immediately before leap years, May of the following year. In years immediately before common years, November finishes on the same day of the week as May of the following year, and in years immediately before leap years, February and October of the following year.
In the Northern Hemisphere, November is an Autumn (Fall) month, and the further north in the hemisphere, the more likely it is to get colder as December approaches. In the Southern Hemisphere it is a Spring month. In each hemisphere, it is the seasonal equivalent of May in the other.
Several observances around the beginning of the month are believed to be related, linked to the old Celtic celebration of Samhain on November 1. These events include Halloween (October 31), Day of the Dead in Mexico (October 31 to November 2), All Saints Day (November 1) and All Souls Day (November 2).
In several mainly Christian countries, it is month in which people who died in war are commonly remembered, mainly related to the end of World War I on November 11, 1918. Near the end of the month Advent, the period leading up to Christmas, begins.
National anthem
A national anthem is a country's official national song that the people of a country use to remember and respect their country.
Some countries, like Spain, have a national anthem which has no lyrics (words of a song)
Name
A name is a word (or a set of words) given to things and people.
For example, "cat" is the name of a kind of animal. "Ryan" is a name of a person, usually a male. "Julia" is a common female name.
The word 'name' can also be used as a verb. To name something is to give it a name.
In many cultures, there are rules and customs about how to give a person a name.
Some of the rules are defined by laws, and others are defined by traditions (doing things in the way they have been done for a long time).
There are rules about different aspects of the names and naming, including the following:
1. Number of parts of a name
In some cultures, a person has a one-part name, such as "ShiningWater."
In other cultures, a person has a two-part name, such as "John Smith."
In some cultures, a person can have any number of name parts. In the United States, for example, some people have three: first name, middle name, and last name. Other people have only two: a first and last name.
In Chinese cultures, it is typical for a person to have three-part name, such as "Cheah Ching San," where "Cheah" is the surname. Written in English format a comma is introduced making it "Ching San, Cheah."
2. Relations with names of parents and other relatives
In some cultures, people have the same "family name" (or surname) as their parents. For example, the father of John Smith may be Mike Smith. And Mike Smith's father may be James Smith. The "Smith" part is the same for all the family.
In other cultures, a person has the same name as his or her father, but the name is in a different place. For example, Shafiq Hanif's son may be Hanif Kamal. Hanif is in both the father's and son's name.
3. Name changes
In some cultures, a name changes when people marry, divorce, go through some religious ceremony, etc. For example, in some Spanish-speaking countries, people use two last names: their mother's father's name and their father's name. If Elena Rodriguez Gomez and Jose Sanchez Soria marry, she may change her name to Elena Rodriguez de Sanchez, and their child could be named Pilar Sanchez Rodriguez, taking the names of both of her grandfathers.
4. Name origins
In some cultures, personal names come from history. In most European countries, some first names are taken from the Bible. In some cultures, names are taken from a relative. In other cultures, a name shows what the parents hope their child will be like. A baby may be given a name Wisdom because parents hope the baby will be a wise girl or boy.
Some cultures avoid giving people a name of an animal. For example, there is no name like dog, cat, snake, owl, or fish in Japanese people's first names. But in some cultures animal names may be good.
5. Lengths, pronunciations, spelling, etc.
In some languages and cultures, you can tell if a word is a person's name or not by just looking at the spelling or listening to its pronunciation. There are some other linguistic patterns. For example, many Chinese names are made up of three syllables.
6. Use of names, titles, nicknames, etc.
In some cultures, people use names when they call each other. In other cultures, people use their nicknames. In some other cultures, people use their titles ("father," "professor," etc.) when they call each other.
7. Spelling of names, titles, nicknames, etc.
8. Name awareness
Taking note of names is taken a step farther by those who elect to celebrate a name (e.g., "Celebrate Your Name Week") whether their own name, someone else's name, or names in general, complete ownership of one's name might very well include celebrating it.
9. Middle names
While some people might choose to "hide" a middle name for any number of reasons (i.e., they consider the middle name they were given to be an "embarrassment"), others have taken to celebrating their middle name (e.g., "Middle Name Pride Day").
In the English language, names exclusively are usually pronounced in correlation with the spelling, however can be pronounced as desired, e.g. John is (jon) but can also be (ned). However, not probable, is held true in the English rules of grammar.
Examples of names
Sarah, Lucy, Ellen, Claire, Ben.
Names can be shortened e.g. Isabelle can become Izzy or Belle.
Here are some things that are often found in Japanese names today. In the past, people went by different rules.
1. Number of parts of a name
Japanese names have two parts. One is the family name and the other is the given name.
"Suzuki Ichiro" is a name of a Japanese person. Suzuki is the family name, and Ichiro is the first name. In the Japanese language, the family name comes first, and the given name comes second. (It is like writing Smith John, instead of John Smith.)
Only some members of the royal family do not have a family name.
2. Relations with names of parents and other relatives
A newborn baby gets a family name from their parents. The parents have the same family name. So, a son of Ono Yoko (female) and Ono Ken (male) is Ono something.
The family name Ono is mostly shared by the paternal (male) part of the family. So Ono Ken's parents have the family name Ono, but Ono Yoko's parents probably do not.
3. Name changes
Names of people change when they marry and divorce. It is a custom in many parts of the world that women change their family name to that of their new husband when they marry. However, in Europe and North America especially, many women no longer do this even though their mothers and grandmothers may have. Sometimes, the man will take the woman's family name.
4. Name origins
5. Lengths, pronunciations, spelling, etc.
6. Use of names, titles, nicknames, etc.
Niihau
Niihau (or Niʻihau) is the smallest of the inhabited islands of Hawaii, in the United States. It has a land area of 70 sq. miles (184 km). It is the oldest of the eight main islands.
The whole island is owned by the Robinson family. They bought it from the Kingdom of Hawaii for $10,000. It was said that the buyer, Elizabeth Sinclair (later Sinclair-Robinson), liked the island better than other places such as Waikiki, Pearl Harbor, and the island of Lanai. There is a small US Navy base where a handful of Navy people work.
The island has a few hundred permanent inhabitants. Almost all of them are native Hawaiians. They support themselves largely with small family farms. Many work for the ranch owned by the Robinsons. The native Hawaiians lead a rural, low-tech life. They speak the Hawaiian language and keep traditions alive. This is because Ms. Sinclair promised to help preserve Hawaiian culture and tradition when she bought the island. Niihau is the only one of the Hawaiian islands where the Hawaiian language is the main language.
Niihau is also known as the "Forbidden Island". This is due to the fact that until recently, the island was off-limits to all but family members, US Navy personnel, government officials and expressly invited guests. Now, tourists can go on one of a limited number of supervised tours or hunting safaris.
On the beaches of the island are found shells which are the only shells to be classified as gems. Niihau shells and the jewelry made from them are very popular. Many, especially those with darker and richer color, are collectors items. The sale of shells and shell jewelry brings extra money for the local people.
Nēnē
The Nēnē, or Hawaiian goose ("Branta sandvicensis") is a species of goose. It is found today on only three Hawaiian islands. It gets its name from its soft call.
This is an unmistakable species, with its generally brown plumage (feathers) and darker head. Its strong toes have much reduced webbing (skin between the toes), an adjustment to the lava flows on which it breeds. The Nēnē goes about on land much more than other water birds. When moulting (dropping old feathers and growing new ones), the Nēnē cannot fly, as do other geese, a factor which made it vulnerable to hunting.
The Nēnē was once among the most threatened waterfowl species around the world. Once common, hunting and predators brought to the islands such as mongooses, pigs and cats reduced the population to only 30 birds in the 1950s. However, this species breeds well in captivity (zoos and bird parks), and has been successfully re-introduced. There are also good numbers in wild bird collections.
The Nēnē is the state bird of Hawaii.
Network
A communication network is a group of things that are connected or linked together. They may be used for talking or other communication to transfer information, data, signal and things as in a transport network. The pattern by which things are connected is called a network topology. A television network, for example, connects television stations. Computer networks are numerous.
Fishing net
A fishing net is a woven trap usually used to catch fish. They are usually made out of rope. A net is a kind of tool.
Internet slang
Internet slang is slang words which are used on the internet. Most of these words are new, such as Wiki and blog, which were not used before the internet became popular.
Some old words were given new meanings, such as mail (which now means email). This makes many metaphors on the Internet, such as boot (which otherwise mean a shoe) and link (which otherwise means a joint in a metal chain). Some existing acronyms, such as "AFK" (To mean "Away from keyboard") and "IRL" (To mean "In real life") were used on bulletin board systems before the internet became popular. These are now used on the internet, such as in chat rooms and on instant messenger software.
People have also created some verbs and adjectives to describe things that only happen on the internet: