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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 which are traced by a point **P** on a circle of radius **b** which rolls round a fixed circle of radius **a**.

For the epitrochoid, an example of which is shown above, the circle of radius **b** rolls on the outside of the circle of radius **a**. The point **P** is at distance **c** from the centre of the circle of radius **b**. For the example **a** = 5, **b** = 3 and **c** = 5 (so **P** is actually inside the circle of radius **a**).

An example of an epitrochoid appears in Durer's work "Instruction in Measurement With Compasses and Straight Edge". He called them "spider lines" due to the graph looking (slightly, I guess) like a spider.