Date: 8 February 2019 Location: Hempfield High School, Room 213 Speaker: Vince Coll, Lehigh University Title: Why curves curve: finding the geodesics on a donut Abstract: Based on an intuitively appealing way of defining what is meant by a geodesic on a two-dimensional surface in three-dimensional Euclidean space, we describe the general behavior of the geodesics on a surfaces of revolution and give a simple yet precise characterization of the geodesics on a torus. We use only simple tools from the standard introductory courses in single and multivariable calculus, and no specialized language or notation from differential geometry, so our presentation is self contained for anyone who is familiar with the contents of these courses.