Rolling a Coin inside a Circle

A coin or a disk is placed inside a circle of diameter 2, with the edge of the disk touching the inside of the circle. The disk is then rolled around the circle, with the edge always touching. A simple problem, but if you trace the path made by a point at distance from the center of the disk, you get some very cool patterns! These are called spirograph patterns, roulettes, or hypotrochoids.

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