We start by exploring a beautiful observation about the sum of exterior angles of polygons in the plane. We then discuss two kinds of geometries-that on the sphere and that on the hyperbolic plane-and how we can use our observation about polygons to detect the curvature of these spaces.

This talk should be accessible to those of all mathematical backgrounds, though some familiarity with calculus will be helpful.

The PDF and video files of this lecture will later appear on Alex Iosevich’s CoronaVirus Lecture Series web page.