A Classification of Closed Hypocycloids and Epicycloids

Abstract

Summary The paper describes a classification of closed epicycloids and hypocycloids into three classes: “odd/odd,” “even/odd,” “odd/even.” A subset of “perfect” epicycloids and hypocycloids that do not have self-intersection points has been identified. A new composite geometric object is constructed: the Euler Ring of Rings, consisting of a perfect epicycloid and a perfect hypocycloid with the same indices.