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The essential difference between Euclidean geometry and these two non-Euclidean geometries is the nature of parallel lines: In Euclidean geometry, given a point and a line, there is exactly one line through the point that is in the same plane as the given line and never intersects it.
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www.cs.unm.edu/~joel/NonEuclid/noneuclidean.html
www.cs.unm.edu/~joel/NonEuclid/noneuclidean.html
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The two commonly mentioned non-Euclidean geometries are hyperbolic geometry and ellptic geometry. If one takes "non-Euclidean geometry" to mean a geometry satisfying all of Euclid's postulates but the parallel postulate, these are...
http://wiki.answers.com/Q/What_are_the_names_of_Non-Euc...
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The 2 types of non-Euclidean geometries are hyperbolic geometry and ellptic geometry.
http://wiki.answers.com/Q/What_are_two_types_of_Non-Euc...
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As a followup to my earlier question on non-Euclidean geometries, I would like to know how many types ... Mathematically, any function which assigns a non-negative number to each pair of points determines a geometry: you just consider the distance between two points P and Q to be the whatever the function value f(P,Q) is.
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www.math.toronto.edu/mathnet/questionCorner/noneucgeom....
www.math.toronto.edu/mathnet/questionCorner/noneucgeom.html
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In Reply to: Re: Names of two Non-Euclidean Geometries posted by Nicholas on October 19, 1998 at 22:19:50: ... I need the names of two non-Euclidean geometries please! Thanks! ... Re: Names of two Non-Euclidean Geometries Bryan 18:20:39 2/28/104 (2)
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mobydicks.com/lecture/Euclidhall/messages/192.html
mobydicks.com/lecture/Euclidhall/messages/192.html
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what are the names of two non euclidean geometries? - raven 12:14:46 10/19/100 ... Re: Names of two Non-Euclidean Geometries - Nicholas 22:19:50 10/19/98 ... Re: Names of two Non-Euclidean Geometries - carolina bustamante 16:50:04 9/06/104...
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mobydicks.com/lecture/Euclidhall/wwwboard23.html
mobydicks.com/lecture/Euclidhall/wwwboard23.html
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non-Euclidean geometry, branch of geometry in which the fifth postulate of Euclidean geometry, which allows one and only one line parallel to a given line through a given external point, is replaced by one of two alternative postulates.
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www.factmonster.com/ce6/sci/A0835830.html
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Riemann himself did not fully work out the applications of this new Geometry, but his successors did, especially Cayley (1821-1895) and Klein (1849-1925). It was the latter who invented the names by which the two different non-Euclidean Geometries are now usually known;
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www.reciprocalsystem.com/euclid/callahan/callah3.htm
www.reciprocalsystem.com/euclid/callahan/callah3.htm
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Euclidean geometry, elementary geometry of two and three dimensions (plane and solid geometry), ... The modern period in geometry begins with the formulations of projective geometry by J. V. Poncelet (1822) and of non-Euclidean geometry by N. I. Lobachevsky (1826) and János Bolyai ... Parallel bundles in planar map geometries.
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www.infoplease.com/ce6/sci/A0858360.html
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