The ellipse and its evolute and the distance problem

 Frederick Hartmann and Robert Jantzen
Department of Mathematical Sciences, Villanova University

4-mar-2004

[about 110K with output removed, about 3.4 MEG when executed]

Abstract.  Inspired by a simple max/min distance problem from a calculus course, we were naturally led to explore the geometry of the evolute of an ellipse, ignorant of many classical results that we later found by web/library searching. This is a beautiful example of how, empowered by a computer algebra system, one can follow one's nose so to speak in uncovering elegant mathematical structure that would otherwise be unreachable in practice. A knowledge of parametrized plane curves and their geometry as covered in a typical multivariable calculus course is assumed, including the osculating circle which is not typically covered but which requires little extra effort. It is not necessary to understand the MAPLE graphing code: its purpose is to visualize the geometry and allow user interaction.