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.
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