View source for Models of non-Euclidean geometry

'''Models of non-Euclidean geometry''' are [[Mathematical model|mathematical model]]s of geometries which are [[Non-Euclidean geometry|non-Euclidean]] in the sense that it is not the case that exactly one line can be drawn parallel to a given line ''l'' through a point that is not on ''l''.   In hyperbolic geometric models, by contrast, there are [[Infinity|infinitely]] many lines through ''A'' parallel to ''l'', and in elliptic geometric models, parallel lines do not exist. (See the entries on [[Hyperbolic geometry|hyperbolic geometry]] and [[Elliptic geometry|elliptic geometry]] for more information.)
Euclidean geometry is modelled by our notion of a "flat [[Plane (mathematics)|plane]]." 
The simplest model for elliptic geometry is a sphere, where lines are "[[Great circle|great circle]]s" (such as the [[Astronomy:Equator|equator]] or the meridians on a [[Globe|globe]]), and points opposite each other are identified (considered to be the same). 
The [[Pseudosphere|pseudosphere]] has the appropriate [[Curvature|curvature]] to model hyperbolic geometry. 

==See also==
*[[Projective geometry]]
*[[Spherical geometry]]
*[[Taxicab geometry]]
*[[Riemannian geometry]]

==References==
* Ian Stewart. ''Flatterland''. Perseus Publishing; {{ISBN|0-7382-0675-X}} (softcover, 2001)
* Marvin Jay Greenberg. ''Euclidean and non-Euclidean geometries: Development and history''.  Publisher: W H Freeman 1993. {{ISBN|0-7167-2446-4}}.

==External links==
*[http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Non-Euclidean_geometry.html MacTutor Archive article on non-Euclidean geometry]

[[Category:Classical geometry]]

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