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Jun25-11, 02:06 PM
P: 408
What is a line in hyperbolic geometry?

Ok, thanks. I was just confused because I didn't see him write anywhere that we consider a line to be the shortest distance between two points, which is what I assumed it would be. Can we replace the parallel postulate in Euclidean geometry with the postulate that the figures take place on flat planes, and get the same familiar Euclidean geometry? Or does that not make sense for some reason?...I don't see why you can't prove that parallel lines are at a constant distance from each other that way, or am I misunderstanding something?