The Story of Geometry

The field of geometry is thousands of years old and over time has undergone a number of revolutionary changes. In this seminar we will study geometry through a historical lens. Beginning with the axiomatic geometry of Euclid, we will trace the development of the subject, learning how the realization in the mid-19th century that one of Euclid’s axioms could be dropped led to the exciting discovery of hyperbolic and spherical geometries. We will learn how these geometries relate to the modern notions of manifolds and curvature, concluding with a discussion of Perelman’s breakthrough proof of the century-old Poincaré Conjecture. 3 hrs. sem.