The synthetic geometry of hyperbolic space (cont'd)

This continuation of last week's talk will establish more basic facts about the geometry of hyperbolic space.  In this talk I will describe the isometry group (spoiler: in the ball model, it is the group of Mobius transformations that preserve the Euclidean unit ball) and use this to complete the classification of hyperbolic geodesics and spheres.  Time permitting, I will establish the "Gauss-Bonnet formula" for hyperbolic triangle area.