Note

This Mathematica notebook is from the WWW project A Visual Dictionary of Special Plane Curves. Copyright © 1995-2000 by Xah Lee. (http://xahlee.org/)

Packages and Initializations

Needs["ParaPlot`"]
Needs["PlaneCurveFormulas`"]

plotting Sine curve's parallel and evolute

tMin = 0; tMax = 5*π;
pr = {{-6, 21}, {-1.5, 9}};

curves = 
      Parallel[{t, Sin[t]}, t, 
        Range[0, 7]]

parallelsGP = 
        First@ParametricPlot[Evaluate@curves, {t, tMin, tMax}, 
            AspectRatio -> Automatic, PlotRange -> pr, 
            PlotStyle -> 
              Table[Hue@i, {i, 0, 1, 1/Length[curves]}]];

evoluteGP = 
        First@ParaPlot[Evaluate@Evolute[{t, Sin[t]}, t], {t, tMin, tMax}, 
            AspectRatio -> Automatic, PlotRange -> pr, 
            PlotDot -> False];

sineGP = 
        First@Plot[Sin[t], {t, tMin, tMax}, AspectRatio -> Automatic, 
            PlotRange -> pr];

Show[Graphics[{evoluteGP, parallelsGP}], AspectRatio -> Automatic, 
      PlotRange -> pr]