By Andrew Kreihn
Abstract: The recognition of hyperbolic geometry as a valid geometry was a pivotal step in launching the study of geometry to its modern form. Yet for being both historically significant as well as closer to Euclidean geometry than every other geometry, it is often not taught. We’ll try to get an overview of the basic theorems of hyperbolic geometry, to develop a bit of intuition for what it might be like to live in hyperbolic space, and to discover some of the beautiful relationships between hyperbolic, Euclidean, and spherical geometry. No prerequisite knowledge is necessary, except perhaps some loose knowledge of what lines, circles, and triangles are, but a good imagination will be useful.