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Summary Of: Non-Euclidean geometry

The essential difference between Euclidean and non-Euclidean geometry is the nature of... Non-Euclidean geometry systems differ from Euclidean geometry in that they modify Euclid... these early attempts made at trying to formulate non-Euclidean geometry however provided flawed proofs of the parallel postulate... While Lobachevsky created a non-Euclidean geometry by negating the parallel postulate... and through this work the ideas of the non-Euclidean geometry came step by step to the mathematical community... manuscripts only the very starting points of the non-Euclidean geometry can be found... written evidence that Gauss had worked out the non-Euclidean geometry to an extent comparable to the works of Bolyai and Lobachevsky... Non-Euclidean geometry often makes appearances in works of... portraying non-Euclidean geometry as a stark...

Encyclodia Page On: Non-Euclidean geometry

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Behavior of lines with a common perpendicular in each of the three types of geometry | | hyperbolic | elliptic geometry | Euclidean geometry | parallel | Euclid's 5th postulate | Playfair's Postulate | infinitely | hyperbolic geometry | elliptic geometry | perpendicular | distance | parallel postulate | hyperbolic geometry | elliptic geometry | elliptic geometry | spacetime | Mobius strip | Klein bottle | Euclidean geometry | Greek | mathematician | Euclid | Elements | propositions | parallel postulate | parallel postulate | equivalent | geometers | proof by contradiction | Arabian mathematician | Ibn al-Haytham | Persian | Omar Khayyám | Nasīr al-Dīn al-Tūsī | Italian | Giovanni Girolamo Saccheri | quadrilaterals | Lambert quadrilateral | Saccheri quadrilateral | hyperbolic | elliptic geometries | Playfair's axiom | Witelo | Levi ben Gerson | Alfonso | John Wallis | Saccheri | Hungarian | János Bolyai | Russian | Nikolai Ivanovich Lobachevsky | Carl Friedrich Gauss | János Bolyai | Bernhard Riemann | Riemannian geometry | manifolds | Riemannian metric | curvature | Euclidean space | elliptic geometry | On a sphere, the sum of the angles of a triangle is not equal to 180°. The surface of a sphere is not a Euclidean space, but locally the laws of the Euclidean geometry are good approximations. In a small triangle on the face of the earth, the sum of the angles is very nearly 180°. | | Models of non-Euclidean geometry | modelled | plane | elliptic geometry | great circles | equator | meridians | globe | hyperbolic geometry | hyperbolic geometry | Eugenio Beltrami | pseudosphere | curvature | hyperbolic space | Klein model | Poincaré disk model | Poincaré half-plane model | equiconsistent | logically consistent | horosphere | infinitely | Dehn plane | surreal numbers | speed of light | hyperbolic geometry | synthetic geometry | Einstein | general relativity | Hubble constant | Riemannian geometry | science fiction | fantasy | horror fiction | H. P. Lovecraft | time dilation | Affine geometry | Projective geometry | Spherical geometry | Taxicab geometry | Hyperbolic geometry | Hyperbolic space | Elliptic geometry | Absolute geometry | Ordered geometry | Riemannian geometry | Parallel postulate | Schopenhauer's criticism of the proofs of the Parallel Postulate | Encyclopedia of the History of Arabic Science | Routledge | Witelo | Ibn al-Haytham | Book of Optics | Levi ben Gerson | Saccheri | ISBN 0716799480 | Stewart, Ian | Flatterland | ISBN 0-7382-0675-X | PlanetMath | Categories | Geometry | Non-Euclidean geometry | Hyperbolic geometry |
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