# Anticycloid Curves I: A Rolling Circle

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The curve traced out by a point on the rim of a circle rolling along a straight line is called a cycloid. Now change the situation: the point moves on a straight line when the circle rolls on a suitable trace. What is the shape of this trace? We call this curve an anticycloid. If is the distance from the point to the center of the circle, a parametrization of an anticycloid is given by

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Contributed by: Ralf Schaper (March 2011)

After work by: Hans Dirnböck

Open content licensed under CC BY-NC-SA

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The relationship between the the road (the anticycloid) and the wheel (the circle) that rolls smoothly on it is described in detail in the book by H. Dirnböck, *Die Antizykloidenbewegung,* Klagenfurt, Austria: Verlag Heyn, 1987.

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