Pedal Curve

Author

Eric W. Weisstein
January 25, 2011

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

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

©2010 Wolfram Research, Inc. except for portions noted otherwise

Equation

Simplify[Solve[{
y-g[t]==g'[t]/f'[t](x-f[t]),
y-y0==-f'[t]/g'[t](x-x0)},
{x,y}]
]

Simplify[PedalCurve[{f[t],g[t]},{(Subscript[x, 0]),(Subscript[y, 0])},t]]//TraditionalForm

Plot

V5

Off[ParametricPlot::"ppcom"]

movie=PedalCurvePlot[{Sin[t],.5Cos[t]},{0,0},{t,0, 2Pi-2Pi/50,2Pi/50},{0,2Pi},PlotRange->{1.1{-1,1},.7{-1,1}},AspectRatio->Automatic]

<<Utilities`GIF`

Export[gifs<>"pedal.gif",movie]//Timing

Show[Take[movie,{1,13,3}]]

V6

Show[{
PedalCurvePlot[{Sin[t],.5Cos[t]},{0,0},{t,0, 2Pi}],
PedalCurvePlot[{Sin[t],.5Cos[t]},{0,0},{t,0, π/2,.2},{0,2Pi},"ShowCurve"->False]
},PlotRange -> All]