The Spirograph and the Greatest Common Factor

Abstract

One of the more interesting toys that has been developed recently is the Spirograph (a product of Kenner Products, Cincinnati, Ohio)—interesting not only for the designs that can be made from it but also for the mathematics that can be related to it. It consists of a collection of different-sized wheels; the larger wheels are rings with gears both inside and outside the rings, and the small wheels have only the outside gears, or teeth. In addition, the wheels have a series of holes in them so that a pen can be set at different locations.