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
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Epicycloid.png
Epicycloid with n=1,2,3,4
Epicycloid.png
Epicycloid with n=1,2,3,4
An epicycloid with n − 1 cusps is given by the parametric equations
- <math> x(\theta) = \cos \theta + {1 \over n} \cos n \theta, <math>
- <math> y(\theta) = \sin \theta + {1 \over n} \sin n \theta. <math>
The epicycloid is a special kind of epitrochoid.
An epicycle with one cusp is a cardioid.
An epicycloid and its evolute are similar.[1] (http://mathworld.wolfram.com/EpicycloidEvolute.html)
See also: cycloid, hypocycloid, deferent and epicycle.