- #1
murmillo
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Homework Statement
I have to show that the Poincare disk satisfies the incidence axiom that any line contains at least two points.
Homework Equations
There are two kinds of lines on the Poincare disk. I've found 2 points for the first kind, which are straight lines going through the origin. The second kind are lines
L a,b = {(x,y) | (x-a)2 + (y-b)2 = a2 + b2 - 1, with x2 + y2 < 1}
The Attempt at a Solution
Given a and b, I need to find (x, y) and (x',y') that lie on the line.
I've shown that x^2+y^2+1 = 2ax+2by, but I don't know if I'm headed in the right direction.