An introduction to spherical, Euclidean and hyperbolic geometry in two and three dimensions, with an emphasis on the similarities and differences between these flavors of geometry. The most important tool in analyzing these geometries will be a study of their symmetries; you will see how this leads naturally to basic notions in group theory and topology. Topics to be covered include classical tessellations, the Gauss-Bonnet theorem, scissors congruence, orbifolds, and fibered geometries. |