An animated image showing the construction of a hypotrochoid (view animation), a roulette curve traced by a point attached to a circle of radius r rolling around the inside of a fixed circle of radius R, where the point is a distance d from the center of the interior circle. The red curve is a hypotrochoid drawn as the smaller black circle rolls around inside the larger blue circle. The Spirograph toy traces out hypotrochoids, as well as epitrochoid curves.Image: Sam Derbyshire