Reuleaux Polygon

Author

Eric W. Weisstein
October 19, 2003

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PlaneGeometry/ReuleauxPolygon.nb.

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

©2005 Wolfram Research, Inc. except for portions noted otherwise

Code

ReuleauxPolygon::usage="ReuleauxPolygon[n,a] gives a Reuleaux polygon of n (n odd) sides and side length a."

ReuleauxGon[n_Integer?OddQ,a_:1][t_]:=Module[{k,nn=(n-1)/2},Which@@Evaluate[Flatten[Table[{k/n≤t≤(k+1)/n,a{Re[Exp[2Pi I k/n]+2I Sin[Pi nn/n] Exp[Pi I((k+nn)/n+t)]],Im[Exp[2Pi I k/n]+2I Sin[Pi nn/n]Exp[Pi I((k+nn)/n+t)]]}},{k,0,2nn}],1]]]

ReuleauxPolygon[n_Integer?OddQ,a_:1,opts___]:=Module[{t},ParametricPlot[ReuleauxGon[n,a][t],{t,0,1},opts,Ticks->None,AspectRatio->Automatic,Axes->False,MaxBend->.25]]

Reuleaux Polygons

Show[GraphicsArray[Table[ReuleauxPolygon[n,1,DisplayFunction->Identity],{n,3,7,2}]]]