Centered trochoid
In geometry, a centered trochoid is the roulette formed by a circle rolling along another circle. That is, it is the path traced by a point attached to a circle as the circle rolls without slipping along a fixed circle. The term encompasses both epitrochoid and hypotrochoid. The center of this curve is defined to be the center of the fixed circle. Alternatively, a centered trochoid can be defined as the path traced by the sum of two vectors, each moving at a uniform speed in a circle. Specifically, a centered trochoid is a curve that can be parameterized in the complex plane by or in the Cartesian plane by where If is rational then the curve is closed and algebraic. Otherwise the curve winds around the origin an infinite number of times, and is dense in the annulus with outer radius and inner radius . (Wikipedia).
