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Parametric Cartesian equation: x = (a + b)cos(t) - bcos((a/b + 1)t), y = (a + b)sin(t) - bsin((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 epicycloid, shown above in clarity-reducing ASCII, the circle of radius b rolls on the outside of the circle of radius a. The point P is on the circumference of the circle of radius b. For the example drawn here a = 8 and b = 5.
Special cases
Also, the
evolute of an
epicycloid is a similar
epicycloid.