MTH 210 Euclidean and Non-Euclidean Geometry
Begins with a close study of portions of Euclid's Elements, including complete coverage of the first book. The historical impact of his axiomatic approach and its ultimate refinement in Hilbert's axioms will be explored. This course will cover some of the history of the attempts to prove the Parallel Postulate, leading up to the discovery of non-Euclidian geometries in the 19th century. The two main models of non-Euclidean geometries (elliptic and hyperbolic) will be described and some of their properties investigated. Finally, the history of geometry since the discovery of non-Euclidean geometries (e.g. Kline's Erlanger Program) will be briefly covered.
Prerequisite
One year of high school geometry or MTH 134