Epicycloid
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In geometry, an epicycloid is a plane curve produced by tracing the path of a chosen point of a circle — called epicycle — which rolls around without slipping around a fixed circle. It is a particular kind of roulette.
An epicycloid with n − 1 cusps is given by the parametric equations
- [ x(\theta) = \cos \theta + \cos n \theta, ]
- [ y(\theta) = \sin \theta + \sin n \theta. ]
An epicycle with one cusp is a cardioid.
An epicycloid and its evolute are similar.[link]
See also: cycloid, hypocycloid, deferent and epicycle.
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