non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies...
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Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements...
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century stimulated the development of non-Euclidean geometry generally, including hyperbolic geometry. Elliptic geometry has a variety of properties that differ...
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hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry...
56 KB (7,019 words) - 21:44, 8 August 2024
The geometry that underlies general relativity is a famous application of non-Euclidean geometry. Since the late 19th century, the scope of geometry has...
100 KB (9,874 words) - 21:49, 13 August 2024
19th-century formulation of non-Euclidean geometry. The definition of the Euclidean norm and Euclidean distance for geometries of more than three dimensions...
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Absolute geometry is a geometry based on an axiom system for Euclidean geometry without the parallel postulate or any of its alternatives. Traditionally...
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non-Euclidean geometries, the old postulates were re-formalized to define Euclidean spaces through axiomatic theory. Another definition of Euclidean spaces...
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affine geometries and Euclidean geometry is a special instance of this type of geometry. In some other geometries, such as hyperbolic geometry, lines...
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higher dimensional generalizations Euclidean geometry, the study of the properties of Euclidean spaces Non-Euclidean geometry, systems of points, lines, and...
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geodesy, spherical geometry and the metrical tools of spherical trigonometry are in many respects analogous to Euclidean plane geometry and trigonometry...
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Taxicab geometry or Manhattan geometry is geometry where the familiar Euclidean distance is ignored, and the distance between two points is instead defined...
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geometry is the study of geometries as axiomatic systems. There are several sets of axioms which give rise to Euclidean geometry or to non-Euclidean geometries...
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three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and...
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In mathematics, affine geometry is what remains of Euclidean geometry when ignoring (mathematicians often say "forgetting") the metric notions of distance...
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transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, projective space, and a selective...
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the end of the 19th century, such as non-Euclidean, projective, and affine geometry. In the Greek deductive geometry of Euclid's Elements, a general line...
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800 BC) – Euclidean geometry Manava (c. 750 BC–690 BC) – Euclidean geometry Thales of Miletus (c. 624 BC – c. 546 BC) – Euclidean geometry Pythagoras...
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Information geometry Integral geometry Inversive geometry Inversive ring geometry Klein geometry Lie sphere geometry Non-Euclidean geometry Noncommutative...
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dimensions Timeline of geometry – Notable events in the history of geometry History of Euclidean geometry History of non-Euclidean geometry History of mathematics...
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Space (category Geometry)
mathematicians began to examine geometries that are non-Euclidean, in which space is conceived as curved, rather than flat, as in the Euclidean space. According to...
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Parallel postulate (category Non-Euclidean geometry)
albeit different geometries. A geometry where the parallel postulate does not hold is known as a non-Euclidean geometry. Geometry that is independent...
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differential geometry and mathematical physics. His work was noted especially for clarity of exposition. He was the first to prove consistency of non-Euclidean geometry...
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(ISBN 0-486-63830-8), including the subtitle Circle Geometry, Moebius Transformation, Non-Euclidean Geometry. The Basic Library List Committee of the Mathematical...
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properties vary from point to point, including the standard types of non-Euclidean geometry. Every smooth manifold admits a Riemannian metric, which often helps...
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two thousand years, until the simultaneous discoveries of the non-Euclidean geometries by Gauss, Bolyai, Lobachevsky and Riemann in the 19th century led...
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Hyperplane (redirect from Hyperplane (geometry))
reflections. A convex polytope is the intersection of half-spaces. In non-Euclidean geometry, the ambient space might be the n-dimensional sphere or hyperbolic...
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Triangle (redirect from Euclidean triangle)
generally, four points in three-dimensional Euclidean space determine a tetrahedron. In non-Euclidean geometries, three "straight" segments (having zero curvature)...
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Square (redirect from Square (geometry))
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four sides of equal length and four equal angles (90-degree angles...
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philosopher, and mathematician. He is considered the forerunner of non-Euclidean geometry. The son of a lawyer, Saccheri was born in Sanremo, Genoa (now Italy)...
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