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Math Forum » Discussions » Math Topics » geometry.pre-college.independent

Topic: Euclids postulates and non-Euclidean geometry
Replies: 7   Last Post: Aug 23, 2007 5:04 PM

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Joshua Zucker

Posts: 1,450
Registered: 1/30/05
Re: Euclids postulates and non-Euclidean geometry
Posted: Mar 8, 2006 3:07 PM
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Hi there,
I think the other reason to focus on negations of the fifth postulate,
instead of the first, is that without the first postulate we wouldn't
call what we're doing "geometry" any more.

Even WILDLY different geometries, like finite geometries, discrete
geometries, projective geometries, or what have you, all maintain that
through any two points there is a (not necessarily unique?) line.

--Joshua Zucker

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