Cycloid Catacaustic

Author

Eric W. Weisstein
March 16, 2008

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

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

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

Equation

cat=FullSimplify[Catacaustic[{t-Sin[t],1-Cos[t]},{x,y},t]]

At origin

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

At x=∞

Limit[cat,x->∞]

At y=∞

Limit[cat,y->∞]

TrigReduce[FullSimplify[{t-Cos[t] Sin[t],((Sin[t])^2)}/.t->t/2]]

Plot

ParametricPlot[{t-Sin[t],1-Cos[t]},{t,0,2π},AspectRatio->Automatic]

CatacausticPlot[{t-Sin[t],1-Cos[t]},{0,100000},{t,0,2π,2π/30}]