Euclidean and non-Euclidean Geometries

Catalog description

This course begins with a thorough and rigorous treatment of Euclidean plane geometry, including classical proofs, straightedge and compass constructions, trigonometry, the dot product and the Euclidean Parallel Postulate. The course continues with a study of Elliptical geometry, in which the curvature is positive, and there are no parallel lines, and the angle sum of any triangle is bigger than 180 degrees and Hyperbolic geometry, where there is negative curvature, and there are infinitely many parallel lines through a given point not on a given line. Other examples considered include crochet, tessellations and the art work of the famous artist M.C. Escher, the film Flatland and Professor Thomas Banchoff's film on the Hyper- Cube. The course concludes with a discussion of possible implications and generalizations including the geometry of other kinds of surfaces such as the torus. Prerequisite(s): MS 181 .