Carol Schumacher, Professor of Mathematics at Kenyon College

Afternoon Talk: Zeroing in on the Implicit Function Theorem

Monday, 09/29 @4:15 pm, Pettengill Hall G65

Abstract:

In mathematics, it often happens that baroque, highly technical results disguise beautiful underlying principles. This talk traces the path from the elegant contraction mapping principle to the rather inscrutable implicit function theorem—a path that passes through Newton’s method for finding roots, linear algebra and linear approximation, and the geometry of multidimensional surfaces.

General Audience Talk: All Tangled Up

Monday, 09/29 @7:30 pm, Pettengill Hall G65

Abstract:

Toys have inspired a lot of interesting mathematics. The Spirograph^TM helps children create lovely curves by rolling a small circle around the inside or the outside of a larger circle. These curves are called hypotrochoids and epitrochoids and are special cases of mathematical curves called roulettes. A roulette is created by following a point attached to one curve as that curve “rolls” along another curve. Another children’s toy, the Tangle^TM, inspired some students and me to investigate roulettes that we get by rolling a circle around the inside of a “tangle curve,” which is made up of quarter circles. The resulting roulettes we named “tangloids.” In this talk, we will look at many pretty pictures and animations of these curves and discuss some of their interesting properties. As a bonus, I will discuss the nature of generalization, which is very important in mathematics.

Accessibility: Bates is committed to creating inclusive and accessible events. If you need a reasonable accommodation, please contact Peter Philbin (pphilbin@bates.edu). All requests should be made 5 business days prior to the event to aid ability to meet your needs.