Number Theory Seminar
Presented by: Michelle Bouthillier
Title: “Representations of Epitrochoids and Hypotrochoids”
Representations of a given curve may consist of implicit or parametric equations, along with any envelopes that produce that curve. We will describe the different methods of passing from one of these representa-tions to another, then apply these methods with regards to epitrochoids and hypotrochoids. These are the families of curves that are produced by tracing the path of a point affixed to a circle as it rolls around the inside or outside of a stationary circle. When the point affixed to the moving circle is on the circumference, epicycloids and hypocycloids are produced. We will provide several conjectures and results on the represen-tations of epitrochoids and hypotrochoids, with emphasis on epicycloids and hypocycloids, including their implicit representations and their con-struction as envelopes.
Seminar Room #227, Chase Building
Ellen LynchNumber Theory Seminar