Cardiod Catacaustic

Author

Eric W. Weisstein
March 16, 2008

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

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

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

Equation

cat=FullSimplify[Catacaustic[{Cos[t](1+Cos[t]),Sin[t](1+Cos[t])},{x,0},t]]

FullSimplify[cat /.x->0]

FullSimplify[cat-{1/2,0}/.x->0]

Plot

<<Graphics`Colors`;

CatacausticPlot[{Cos[t](1+Cos[t]),Sin[t](1+Cos[t])},{0,0},{t,0,2Pi,2Pi/50}]

Show[CatacausticPlot[{Cos[t](1+Cos[t]),Sin[t](1+Cos[t])},{10000,0},{t,0,2Pi,2Pi/100}],
PlotRange->{{-2,3},{-2,2}},
AspectRatio->Automatic
]