Geometry

The purpose of this course is to explore various systems of geometry, as well as different approaches to these systems. A brief review of high-school geometry (including an exposition of logical objections to it) will be the starting point for branching out into other areas. Problem solving will play a central role in the development and exposition of much of the material in the course. Topics may be chosen from analytic, neutral, non-Euclidean (Lobechevskian and Riemannian), and incidence geometries.