Tracing closed curves with epicycles A fun application of the discrete Fourier transform

Abstract

The Discrete Fourier Transform has many applications in our modern digital world. In particu- lar, it allows us to approximate periodic functions by means of trigonometric polynomials which provides the required information to define a system of epicycles that can be animated to trace out closed curves. In this paper, I present a method in GeoGebra to create artistic animations con- sisting of systems of epicycles tracing out closed curves. The geometric construction presented here can also be used as an introductory learning activity to study the Discrete Fourier Transform from a geometric point of view.