x = (a + b) cos (t) - b cos [(a/b + 1)t ],
y = (a + b) sin (t) - b sin [(a/b + 1)t ].
An epicycloid is like a cycloid on the circumference of a circle and is closely related to the epitrochoid, hypocycloid, and hypotrochoid.
An epicycloid with one cusp is called a cardioid, one with two cusps is called a nephroid, and one with five cusps is called a ranunculoid (after the buttercup genus Ranunculus).
Related category PLANE CURVES
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