Epicycloids and hypocycloids are curves that can be defined by circles. Let a fixed circle (black) be given. A second, movable circle (blue) rolls on the outside (in the case of the epicycloid) or on the inside (in the case of the hypocycloid) of the fixed circle. By a point at the border of the moving circle the curve (red) is generated. If the radii of the two circles have an integer ratio, the curve is closed.