Epicycloid.

The parametric equations of the epicycloid can be given by

x=(a+b)costbcos(a+bbt),y=(a+b)sintbsin(a+bbt)x = \left(a+b \right) \cos t – b \cos \left( \frac{a+b}{b} t \right), \, y = \left(a+b \right) \sin t – b \sin \left( \frac{a+b}{b} t \right)

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