Anticycloid curves are defined by an inverse problem: when a circle rolls on an anticycloid then a fixed point in the circle moves on a straight line. The trace of a focus of an ellipse rolling on a straight line generates these curves.

The relationship between the anticycloid curves of this Demonstration and those when a circle is rolling on an anticyloid is described in detail in the book by H. Dirnböck, Die Antizykloidenbewegung, Klagenfurt, Austria: Verlag Heyn, 1987 pp. 83–88.