AlgTop20: The geometry of surfaces

This lecture relates the two dimensional surfaces we have just classified with the three classical geometries- Euclidean, spherical and hyperbolic. Our approach to these geometries is non-standard (the usual formulations are in fact deeply flawed) and we concentrate on isometries, avoiding distance and angle formulations. In particular we introduce hyperbolic geometry via inversions in circles---the Beltrami Poincare disk model.

This is the 20th lecture in this beginner's course on Algebraic Topology, given by N J Wildberger at UNSW.