Semicubical Parabola Involute

Author

Eric W. Weisstein
March 16, 2008

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

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

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

Equation

FullSimplify[Involute[{t^2,a t^3},t]]

Image

g=InvolutePlot[{t^2,t^3},{t,0,5},
PlotRange->{{-2,5},{-2,5}},ImageSize->200][[1]];

Show[Graphics[{
g,
g/.Line[x_]:>{Dashing[{.02}],Line[{#[[1]],-#[[2]]}&/@x]
}}],Axes->True,Ticks->None,PlotRange->{{-1,5},{-4,4}},
AspectRatio->Automatic,ImageSize->200]

Animation

Off[ParametricPlot::"ppcom"]

movie=InvoluteMovie[{t^2,t^3},{t,5,0,-.2},{0,5},
Axes->True,Ticks->False,
PlotRange->{{-1,5},{-4,4}},ImageSize->200];

<<Utilities`GIF`;

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

Show[Take[movie,{1,24,2}]]