Deltoid Pedal Curve

Author

Eric W. Weisstein
March 16, 2008

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

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

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

Plot

deltoid={2/3 Cos[t]+1/3 Cos[2t],2/3 Sin[t]-1/3 Sin[2t]};

pedal=FullSimplify[PedalCurve[deltoid,{x,y},t]]

Cusp

deltoid/.t->0

FullSimplify[pedal/.{x->1,y->0}]

PedalCurvePlot[deltoid,{3,0},{t,0,2Pi},{0,Pi,.2}]

Negative x-intercept

deltoid/.t->π

FullSimplify[pedal/.{x->-1/3,y->0}]

PedalCurvePlot[deltoid,{-1,0},{t,0,2Pi},{0,Pi,.2},PlotRange->{{-3,3.2},Automatic}]

Origin

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

PedalCurvePlot[deltoid,{0,0},{t,0,2Pi},{0,Pi/2,.2}]