[font=Trebuchet MS][b][size=150]If the smaller circle has radius r, and the larger circle has radius R = kr[br][color=#ff7700][br]x = (R-r)*cos(theta) + r*cos((R-r)/r*theta)[br][br]y = (R-r)*sin(theta) - r*sin((R-r)/r*theta)[/color][br][br]If k is an integer, then the curve is closed and has k cusps.[br][br]If k is a rational number, say k = p/q expressed in simplest terms, then the curve has p cusps.[/size][/b][/font]