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statement_describes/test.jsonl

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-{"question": "The statement of Pitot theorem describes", "references": ["tangential quadrilateral", "circumscribed quadrilateral", "tangent quadrilateral"]}
-{"question": "The statement of Anne's theorem describes", "references": ["quadrilateral", "tetragon", "4-gon", "cuadril\u00e1tero", "quadrangle", "quadrangular"]}
-{"question": "The statement of Mostow rigidity theorem describes", "references": ["hyperbolic manifold"]}
-{"question": "The statement of spin-statistics theorem describes", "references": ["spin", "spin angular momentum"]}
-{"question": "The statement of Kodaira embedding theorem describes", "references": ["K\u00e4hler manifold"]}
-{"question": "The statement of law of cosines describes", "references": ["triangle", "3-gon", "2-simplex", "\u2206"]}
-{"question": "The statement of Clifford's theorem on special divisors describes", "references": ["algebraic curve"]}
-{"question": "The statement of Hurwitz's automorphisms theorem describes", "references": ["algebraic curve"]}
-{"question": "The statement of Berger's inequality for Einstein manifolds describes", "references": ["Einstein manifold"]}
-{"question": "The statement of Tarski\u2013Seidenberg theorem describes", "references": ["semialgebraic set"]}
-{"question": "The statement of Chevalley's structure theorem describes", "references": ["algebraic group", "group variety"]}
-{"question": "The statement of Finsler\u2013Hadwiger theorem describes", "references": ["square", "2-orthoplex", "bicross", "2-cube", "2-cross-polytope", "regular quadrilateral"]}
-{"question": "The statement of Parikh's theorem describes", "references": ["context-free language"]}
-{"question": "The statement of theorem of the cube describes", "references": ["complete variety", "complete algebraic variety", "scheme", "invertible sheaf"]}
-{"question": "The statement of Six circles theorem describes", "references": ["circle", "\u2b55", "\u26aa", "triangle", "3-gon", "2-simplex", "\u2206"]}
-{"question": "The statement of Riemann\u2013Roch theorem describes", "references": ["compact Riemann surface"]}
-{"question": "The statement of Gauss's law for magnetism describes", "references": ["magnetic flux", "\u03a6", "magnetic flux density", "B-field", "magnetic induction"]}
-{"question": "The statement of Pappus's hexagon theorem describes", "references": ["hexagon", "6-gon", "Hexagonal"]}
-{"question": "The statement of Japanese theorem for cyclic quadrilaterals describes", "references": ["cyclic quadrilateral", "inscribed quadrilateral"]}
-{"question": "The statement of Law of tangents describes", "references": ["triangle", "3-gon", "2-simplex", "\u2206"]}
-{"question": "The statement of implicit function theorem describes", "references": ["implicit function"]}
-{"question": "The statement of Pedoe's inequality describes", "references": ["triangle", "3-gon", "2-simplex", "\u2206"]}
-{"question": "The statement of Kodaira vanishing theorem describes", "references": ["K\u00e4hler manifold"]}
-{"question": "The statement of four color theorem describes", "references": ["planar graph", "graph coloring", "Graph Coloring Problem"]}
-{"question": "The statement of Weber's theorem describes", "references": ["algebraic curve"]}
-{"question": "The statement of trillium theorem describes", "references": ["triangle", "3-gon", "2-simplex", "\u2206"]}
-{"question": "The statement of De Franchis theorem describes", "references": ["algebraic curve"]}
-{"question": "The statement of Pascal's theorem describes", "references": ["conic section", "conic curve", "hexagon", "6-gon", "Hexagonal"]}
-{"question": "The statement of Cauchy's theorem describes", "references": ["convex polytope"]}
-{"question": "The statement of Weitzenb\u00f6ck's inequality describes", "references": ["triangle", "3-gon", "2-simplex", "\u2206"]}
-{"question": "The statement of Harcourt's theorem describes", "references": ["triangle", "3-gon", "2-simplex", "\u2206"]}
-{"question": "The statement of Lefschetz hyperplane theorem describes", "references": ["algebraic variety", "variety"]}
-{"question": "The statement of Bretschneider's formula describes", "references": ["quadrilateral", "tetragon", "4-gon", "cuadril\u00e1tero", "quadrangle", "quadrangular"]}
-{"question": "The statement of Ceva's theorem describes", "references": ["triangle", "3-gon", "2-simplex", "\u2206"]}
-{"question": "The statement of Legendre's theorem on spherical triangles describes", "references": ["spherical triangle", "spherical triangles"]}
-{"question": "The statement of Steiner\u2013Lehmus theorem describes", "references": ["triangle", "3-gon", "2-simplex", "\u2206"]}
-{"question": "The statement of Pappus' area theorem describes", "references": ["triangle", "3-gon", "2-simplex", "\u2206", "parallelogram"]}
-{"question": "The statement of Minkowski's first inequality for convex bodies describes", "references": ["convex body"]}
-{"question": "The statement of Noether's theorem on rationality for surfaces describes", "references": ["algebraic surface"]}
-{"question": "The statement of Ptolemy's theorem describes", "references": ["cyclic quadrilateral", "inscribed quadrilateral"]}
-{"question": "The statement of Levi decomposition theorem describes", "references": ["Lie algebra"]}
-{"question": "The statement of Harnack's curve theorem describes", "references": ["algebraic curve"]}
-{"question": "The statement of B\u00e9zout's theorem describes", "references": ["algebraic curve"]}
-{"question": "The statement of Menelaus' theorem describes", "references": ["triangle", "3-gon", "2-simplex", "\u2206"]}
-{"question": "The statement of five points determine a conic describes", "references": ["conic section", "conic curve"]}
-{"question": "The statement of pizza theorem describes", "references": ["disk", "disc", "circle"]}
-{"question": "The statement of Faltings' theorem describes", "references": ["algebraic curve"]}
-{"question": "The statement of triangle inequality describes", "references": ["triangle", "3-gon", "2-simplex", "\u2206"]}
-{"question": "The statement of Luttinger's theorem describes", "references": ["Fermi liquid", "Landau-Fermi liquid theory", "Fermi liquid theory", "Fermi surface"]}
-{"question": "The statement of Robertson\u2013Seymour theorem describes", "references": ["undirected graph", "minor graph", "graph minor", "minor"]}
-{"question": "The statement of van Aubel's theorem describes", "references": ["quadrilateral", "tetragon", "4-gon", "cuadril\u00e1tero", "quadrangle", "quadrangular"]}
-{"question": "The statement of Casey\u2019s theorem describes", "references": ["circle", "\u2b55", "\u26aa"]}
-{"question": "The statement of Bochner\u2013Yano theorem describes", "references": ["Riemannian manifold", "Riemann space", "Riemann manifold", "Riemannian space"]}
-{"question": "The statement of Lester's theorem describes", "references": ["triangle", "3-gon", "2-simplex", "\u2206"]}
-{"question": "The statement of Eilenberg's inequality describes", "references": ["Lipschitz function", "Lipschitz continuous function", "Lipschitz map"]}
-{"question": "The statement of Barbier's theorem describes", "references": ["curve of constant width"]}
-{"question": "The statement of Musselman's theorem describes", "references": ["triangle", "3-gon", "2-simplex", "\u2206"]}
-{"question": "The statement of Beckman\u2013Quarles theorem describes", "references": ["Euclidean space", "Euclidean vector space", "finite-dimensional real vector space"]}
-{"question": "The statement of Dinostratus' theorem describes", "references": ["quadratrix of Hippias"]}
-{"question": "The statement of Pompeiu's theorem describes", "references": ["equilateral triangle", "regular triangle", "equiangular triangle"]}
-{"question": "The statement of Castelnuovo\u2013de Franchis theorem describes", "references": ["algebraic curve", "algebraic surface"]}
-{"question": "The statement of Weil reciprocity law describes", "references": ["algebraic curve"]}
-{"question": "The statement of Napoleon's theorem describes", "references": ["triangle", "3-gon", "2-simplex", "\u2206"]}
-{"question": "The statement of Descartes' theorem describes", "references": ["circle", "\u2b55", "\u26aa"]}
-{"question": "The statement of Belyi's theorem describes", "references": ["algebraic curve"]}
-{"question": "The statement of Ending lamination theorem describes", "references": ["hyperbolic 3-manifold"]}
-{"question": "The statement of De Gua's theorem describes", "references": ["tetrahedron", "3-simplex", "triangular pyramid"]}
-{"question": "The statement of Tameness theorem describes", "references": ["hyperbolic 3-manifold"]}
-{"question": "The statement of Hellin's law describes", "references": ["multiple birth"]}
-{"question": "The statement of quadratic formula describes", "references": ["zero of a function", "zero", "root", "x-intercept", "root of a function"]}
-{"question": "The statement of edict of government doctrine describes", "references": ["legislation", "legislative act"]}
-{"question": "The statement of Cayley\u2013Bacharach theorem describes", "references": ["cubic plane curve"]}
-{"question": "The statement of Orr\u2013Sommerfeld equation describes", "references": ["hydrodynamic stability", "hydrodynamic instability", "Hagen\u2013Poiseuille equation", "Hagen-Poiseuille flow", "Poiseuille's law", "Poiseuille flow"]}
-{"question": "The statement of Euler's theorem in geometry describes", "references": ["triangle", "3-gon", "2-simplex", "\u2206", "inscribed circle", "incircle"]}
-{"question": "The statement of Marden's theorem describes", "references": ["cubic function", "triangle", "3-gon", "2-simplex", "\u2206"]}
-{"question": "The statement of Crofton formula describes", "references": ["curve", "curved line"]}
-{"question": "The statement of exterior angle theorem describes", "references": ["triangle", "3-gon", "2-simplex", "\u2206"]}
-{"question": "The statement of Fagnano's problem describes", "references": ["triangle", "3-gon", "2-simplex", "\u2206"]}
-{"question": "The statement of Kuratowski's theorem describes", "references": ["planar graph"]}
-{"question": "The statement of Five circles theorem describes", "references": ["circle", "\u2b55", "\u26aa"]}
-{"question": "The statement of Riemann\u2013Roch theorem for surfaces describes", "references": ["algebraic surface"]}
-{"question": "The statement of Hadwiger\u2013Finsler inequality describes", "references": ["triangle", "3-gon", "2-simplex", "\u2206"]}
-{"question": "The statement of Hinge theorem describes", "references": ["triangle", "3-gon", "2-simplex", "\u2206"]}
-{"question": "The statement of law of cotangents describes", "references": ["triangle", "3-gon", "2-simplex", "\u2206"]}
-{"question": "The statement of Theorem on friends and strangers describes", "references": ["friendship graph"]}
-{"question": "The statement of geometric mean theorem describes", "references": ["right triangle", "right-angled triangle"]}
-{"question": "The statement of Ado's theorem describes", "references": ["Lie algebra"]}
-{"question": "The statement of Droz-Farny line theorem describes", "references": ["triangle", "3-gon", "2-simplex", "\u2206"]}
-{"question": "The statement of abc conjecture describes", "references": ["natural number", "n (natural number)", "n", "natural number (ambiguously including zero)", "natural numbers (individually)", "\u2208\u2115", "\u2115"]}
-{"question": "The statement of Miquel's theorem describes", "references": ["triangle", "3-gon", "2-simplex", "\u2206"]}
-{"question": "The statement of Carnot's theorem describes", "references": ["triangle", "3-gon", "2-simplex", "\u2206"]}
-{"question": "The statement of Murakami\u2013Yano formula describes", "references": ["tetrahedron", "3-simplex", "triangular pyramid"]}
-{"question": "The statement of Angle bisector theorem describes", "references": ["triangle", "3-gon", "2-simplex", "\u2206"]}
-{"question": "The statement of fixed-point theorem describes", "references": ["fixed point", "fixpoint", "invariant point", "equilibrium point"]}
-{"question": "The statement of Hodge index theorem describes", "references": ["algebraic surface"]}
-{"question": "The statement of Ono's inequality describes", "references": ["right triangle", "right-angled triangle"]}
-{"question": "The statement of Spherical law of cosines describes", "references": ["spherical triangle", "spherical triangles"]}
-{"question": "The statement of Stewart's theorem describes", "references": ["triangle", "3-gon", "2-simplex", "\u2206"]}
-{"question": "The statement of Erd\u0151s\u2013Mordell inequality describes", "references": ["triangle", "3-gon", "2-simplex", "\u2206"]}
-{"question": "The statement of meaning\u2013text theory describes", "references": ["meaning", "text"]}
-{"question": "The statement of Seven circles theorem describes", "references": ["circle", "\u2b55", "\u26aa"]}