I like to learn some basic hyperbolic geometry!(adsbygoogle = window.adsbygoogle || []).push({});

Starting with the hyperbolic plane, the upper half plane with the hyperbolic lines being all half-lines perpendicular to the x-axis, together with all semi-circles with center on the x-axis.

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

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# Hyperbolic geometry

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