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,
is constrained to rational values
. Animating the parameter
portrays the familiar drawing mechanism.