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Epitrochoids


	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 .


	Contributed by: Bruce Fast
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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.

Contributed by: Bruce Fast

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