Can anyone help me on some hyperbolic geometry proofs?

[Kratzer]

I'm taking a class on Euclidean/non-Euclidean geometry. We just got to hyperbolic geometry and i'm having some trouble with these proofs:

These proofs use the Klein model (which is a circle 'w' in the Euclidean plane. O is the center of w and OR is the radius. The "interior" of w consists of all points X such that OX<OR . In Klein's model the interior points of w represent the points of the hyperbolic plane)

*Deduce that in hyperbolic geometry the altitudes of an acute triangle are concurrent and the lines containing the altitudes of an obtuse triangle are concurrent in a point which may be ordinary, ideal, or ultra ideal.

*Prove that the medians of a triangle are concurrent (in hyperbolic geometry). (the hint in the book says this theorem holds in hyperbolic geometry by a special position argument in the Klein model)

[Triumph36]

Damn, these are tough. I studied Non-Euclidian geometry last year - which 'Klein' is the Klein model named after, do you know? We used something called the Hjelmslev image to reflect the non-Euclidian plane - it appears to be the same principle.

The only way I can think to proceed on the first one is by reductio proof - I can't see how you'd ever prove that in an acute triangle, a theoretical point A is the place where they'd meet. I can only see assuming that they're not concurrent and somehow proving that that causes an absurdity (given that it's hyperbolic geometry and all you've got three angle measures, probably something about a triangle of >180 degrees).

Sorry I couldn't be of more assistance; you probably already considered that. Hyperbolic geometry is fun though.

[AlphaWice]

H-Triangle stuff. (http://www.maths.gla.ac.uk/~wws/cabripages/hyperbolic/hyperbolic0.html)

Let me know if you need more help. But basically, copy it straight out. If it refers to a theorem, copy that straight out, etc.