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alexb
Charter Member
2212 posts 
Mar2908, 11:38 AM (EST) 

1. "RE: Projective Geometry"
In response to message #0

Absolutely! Projective geometry in which any two lines intersect is nonEuclidean. Hyperbolic and Elliptic geometries came from different interpretations of the Fifth Postulate and this is why the are commonly labeled nonEuclidean. Projective geometry was an independent development but is as much nonEuclidean as the other two. In addition, any nondiscrete geometry is also nonEuclidean. So geometries may be nonEuclidean but for different reasons. Quite often the Taxicab geometry is presented as one of the variety. I believe it's a misnomer. In fact, I do not think it's a geometry at all. It's a metric space, yes, but not a geometry. It violates the most common requirement of having a single line through any two points. 

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