MAT 360 Euclidean & Non-Euclidean Geometry

This course begins by showing how the proofs of familiar geometric results contained in Euclid’s Elements can be made more rigorous by the introduction of Hilbert’s axioms. The course also explores neutral geometry (omitting the Parallel Postulate), non-Euclidean geometries (replacing the Parallel Postulate with alternative assumptions), and hyperbolic trigonometry. The historical developments, ruler and compass constructions, and discussion of the axiomatic method and philosophical implications should be of particular use to future secondary education mathematics instructors. Typically offered only in the spring semester of odd years. Prerequisite(s): MAT 290 or permission of instructor. 3 hour(s).