##### July 31, 2020 | 10:00 am | Zoom

**Title: **The Trefoil: An Analysis in Curve Minimization and Spline Theory

**Abstract **

We will consider a variational problem arising out of the localized induction equation. We are motivated by the idea of finding “fair” splines, by considering an energy functional involving the derivative of the curvature. Among the solutions to the Euler-Lagrange equations are two elastic curves and the Kiepert Trefoil. We will introduce features and properties of the trefoil. One of the features of the trefoil is that it is an algebraic curve with a simple parametrization to handle. In addition to this, we will show that the trefoil is a model for a two-parameter spline and provide examples of how pieces of the trefoil can be cut, transformed and fitted so that the resulting curve is aesthetically “fair”.

**Advisor: **Dr. David Singer

**Dissertation Committee**

- Dr. Joel Langer
- Dr. Elisabeth Werner
- Dr. Colin McLarty

Please contact *mams-staff@case.edu* for Zoom access.