Epicycloid Evolute

Author

Eric W. Weisstein
March 16, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PlaneCurves/EpicycloidEvolute.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/EpicycloidEvolute.html.

©2008 Wolfram Research, Inc. except for portions noted otherwise

Evolute

Epicycloid[{a,b},t]//ColumnForm//TraditionalForm

Simplify[Evolute[Epicycloid[{a,b},t],t]]//ColumnForm//TraditionalForm

Plot

movie=With[{a=1,b=1/3},
Show[#,AspectRatio->Automatic,PlotRange->2{{-1,1},{-1,1}}]&/@
EvoluteFrames[Epicycloid[{a,b},t],{t,.001,2Pi,2Pi/50}]
];

<<Utilities`GIF`;

Export[gifs<>"epicycev.gif",movie]//Timing