Hypocycloid

In geometry, a hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. It is comparable to the cycloid but instead of the circle rolling along a line, it rolls within a circle.k=3 — a deltoidk=4 — an astroidk=5k=6k=2.1 = 21/10k=3.8 = 19/5k=5.5 = 11/2k=7.2 = 36/5 In geometry, a hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. It is comparable to the cycloid but instead of the circle rolling along a line, it rolls within a circle. If the smaller circle has radius r, and the larger circle has radius R = kr, then the parametric equations for the curve can be given by either: