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Hyperbolic geometry 
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#1
Jan2609, 09:36 AM

P: 196

I like to learn some basic hyperbolic geometry!
Starting with the hyperbolic plane, the upper half plane with the hyperbolic lines being all halflines perpendicular to the xaxis, together with all semicircles with center on the xaxis. Why and how are there always infinitely many hyperbolic lines parallel to a given hyperbolic line L and passing through a given point p not lying on L? Does parallel in hyperbolic geometry just mean two lines do not cut each other? Second problem. My book says the boundary of the hyperbolic plane can be thought of as real line [tex]\cup[/tex] infinity, which is supposed to be a circle. I can't see this to be a circle. What does the author mean? thank you 


#2
Jan2609, 02:14 PM

P: 626

Have you read this at all: http://en.wikipedia.org/wiki/Hyperbolic_geometry?



#3
Feb409, 07:21 PM

P: 707

For the upper half plane, it is good to map it onto the disc conformally and take the induced metric. 


#4
Feb409, 07:28 PM

P: 707

Hyperbolic geometry



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