Cayley's Sextic Evolute

Author

Eric W. Weisstein
March 16, 2008

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

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

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

Equation

cayleys1=4Cos[t/3]^3{Cos[t],Sin[t]};

cayleys2={4 Cos[t/2]^4(2Cos[t]-1),4Cos[t/2]^3 Sin[3t/2]};

FullSimplify[Evolute[cayleys1,t]]

FullSimplify[Evolute[cayleys2,t]]

Plot

<<Graphics`ImplicitPlot`

EvolutePlot[cayleys1,{t,0,3Pi}]

EvolutePlot[cayleys2,{t,0,2Pi}]