“Animation of Mathematical Concepts using Polynomiography” by Kalantari, Kalantari and Andreev

In this paper we demonstrate how a medium called polynomiography, which consists of techniques for visualization of polynomial equations, can be used to animate mathematical concepts, thereby offering a valuable tool for education. More specifically, we will show how it can be used to visualize the following topics: Voronoi regions of points in the plane; multiplication of complex numbers and their interpretation as rotation; sensitivity of polynomial roots as coefficients change; visualization of classes of special polynomial equations arising from two problems from the American Mathematical Monthly; as well as animation for the sake of visual art. Each of these will be exhibited through a series of images and we give the Internet links to the corresponding animations. These sites can be accessed for educational purposes and will be upgraded and expanded from time to time.