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Topic: Euclidean, Hyperbolic and Elliptic Geometry
Replies: 4   Last Post: Mar 12, 2009 9:24 PM

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Brian

Posts: 1
Registered: 2/26/09
Re: Euclidean, Hyperbolic and Elliptic Geometry
Posted: Feb 26, 2009 10:00 PM
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Being the Brian that he is talking about, I did not ask that. However your questions are still valid. There is no universal rules that apply because there are no universal postulates that must be included a geometry. The main difference between Euclidean geometry and Hyperbolic and Elliptic Geometry is with parallel lines. In Euclidean geometry there is an axiom which states that if you take a line A and a point B not on that line you can draw one and only one line through B that does not intersect line A. In hyperbolic geometry you can draw an infinite amount of lines through point B that do not intersect line A. In elliptic geometry there is no such line though point B that does not intersect line A. Euclidean geometry is generally used on medium sized scales like for example our planet. On extremely large or small scales it get more and more inaccurate. This is all off the top of my head so please correct me if I am wrong.

Here is a Wikipedia URL which has information about Hyperbolic functions. http://en.wikipedia.org/wiki/Hyperbolic_function



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