MATH 4520 - Classical Geometries

(MQR-AS)

Fall (offered every 2-3 years). 4 credits. Student option grading.

Prerequisite: MATH 2210, MATH 2230, MATH 2310, or MATH 2940, or permission of instructor. Students will be expected to be comfortable with proofs.

Staff.

Introduction to hyperbolic and projective geometry - the classical geometries that developed as Euclidean geometry was better understood. For example, the historical problem of the independence of Euclid’s fifth postulate is understood when the existence of the hyperbolic plane is realized. Straightedge (and compass) constructions and stereographic projection in Euclidean geometry can be understood within the structure of projective geometry. Topics in hyperbolic geometry include models of the hyperbolic plane and relations to spherical geometry. Topics in projective geometry include homogeneous coordinates and the classical theorems about conics and configurations of points and lines. Optional topics include principles of perspective drawing, finite projective planes, orthogonal Latin squares, and the cross ratio.