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Roses from Rolling Circles

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A rose is obtained from a hypocycloid, but the green circle slips as well as rolls on the inside of the white circle.

Contributed by: Tomas Garza (August 2020)
Open content licensed under CC BY-NC-SA

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A point fixed to the green circle rolling inside the white circle traces a hypocycloid. With slipping allowed, the angular speeds of the yellow center and the revolving green point differ, which produces loops in the path described by the green point, known as a rosette.

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