Hypotrochoid Evolute

Author

Eric W. Weisstein
March 16, 2008

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

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

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

Equation

FullSimplify[Evolute[Hypotrochoid[{a,b},h,t],t],a>0&&b>0&&h>0]//TraditionalForm

Plot

MakeBoxes[label[{a_,b_,h_}],TraditionalForm]:=RowBox[{RowBox[{"a","==",MakeBoxes[a,TraditionalForm]}],",",RowBox[{"b","==",MakeBoxes[b,TraditionalForm]}],",",RowBox[{"h","==",MakeBoxes[h,TraditionalForm]}]}]

Show[GraphicsArray[
Partition[Block[{$DisplayFunction=Identity},EvolutePlot[Hypotrochoid[Take[#,2],Last[#],t],{t,0,2Pi},
PlotLabel->TraditionalForm[label[#]]]&/@{{16,2,3},{8,2,3},{8,2,5},{8,2,7},{6,1,2},{8,4,1}}
],3,3,{1,1},{}]]]