A disk of radius rolls around the outside of the circumference of a unit circle, while a pen fixed on the disk traces out a"Spirograph™" pattern. The pen's distance from the center of the rolling disk is .
An epitrochoid is traced by a point attached to a circle of radius rolling around the outside of a fixed circle of radius , where the point is at a distance from the center of the exterior circle. The Spirograph™ toy, using toothed gears, is constrained to a set of rational values for , giving closed curves. Here, and is constrained to rational values . Animating the parameter portrays the familiar drawing mechanism.
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