The hypercycloid is the path traced by a point on the circumference of a small circle rolling around inside a larger circle, the larger circle having radius n times that of the smaller circle, usually n is taken to be an integer. For n = 2, the path is along a diameter, this degenerate case is the Tusi Couple. For n = 3, the curve is called a deltoid, from its resemblance to the Greek letter delta. In the limit of large n, taken as infinite outer circle radius, the curve approaches the cycloid, the path of a point on the edge of a wheel rolling along a straight line.
Code by Casey Bowler