Quadrifolium Catacaustic

Author

Eric W. Weisstein
March 16, 2008

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

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

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

Catacaustics for Various Radiant Points

General

cat=FullSimplify[Catacaustic[{Cos[t]Sin[2t],Sin[t]Sin[2t]},{x,y},t]]

x=0

FullSimplify[cat/.x->0]

x=∞

FullSimplify[Limit[cat,x->∞]]

y=0

FullSimplify[cat/.y->0]

y=∞

FullSimplify[Limit[cat,y->∞]]

Origin

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

Plot

g1=CatacausticPlot[{Cos[t]Sin[2t],Sin[t]Sin[2t]},{0,0},{t,0,2π,2π/100}]

g2=CatacausticPlot[{Cos[t]Sin[2t],Sin[t]Sin[2t]},{10000,0},{t,0,2π,2π/100}]

g3=CatacausticPlot[{Cos[t]Sin[2t],Sin[t]Sin[2t]},{10000,10000},{t,0,2π,2π/100}]

g4=CatacausticPlot[{Cos[t]Sin[2t],Sin[t]Sin[2t]},.6{1,1},{t,0,2π,2π/100}]

Show[GraphicsArray[{{g1,g2},{g3,g4}}]]