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**Parametric Cartesian equation: x = (***a - b*)cos(*t*) + *c*cos((*a/b* -1)*t*), y = (*a - b*)sin(*t*) - *c*sin((*a/b* -1)*t*)

There are four curves which are closely related. These are the epicycloid, the epitrochoid, the hypocycloid and the hypotrochoid and they are traced by a point **P** on a circle of radius **b** which rolls round a fixed circle of radius **a**.

For the hypotrochoid, shown above in hit or miss ASCII, the circle of radius **b** rolls on the inside of the circle of radius **a**. The point **P** is at distance **c** from the centre of the circle of radius **b**. For this example **a** = 5, **b** = 7 and **c** = 2.2.

These curves were studied by Newton, la Hire, Desargues, and Leibniz amoung others.