Plotting an Epicycloid
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This animation shows how a point on a moving circle generates an epicycloid.
(See notes below.)
The curve traced out by a point fixed to a circle as the circle rolls without
slipping along the outside of another, fixed, circle is called an epicycloid. (The moving circle here has
radius one-fifth that of the stationary circle.) The epicycloid frequently appears
in elementary calculus textbooks as an example of how to determine the parametric
equations for a curve given a geometric definition for the curve. See also
the
cycloid
and the
hypocycloid.
(11/17/07)