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{1000, 700}, Alignment -> {Left, Center}, ImageSizeAction -> Automatic]], "Specifications" :> {{{$CellContext`n$$, 3, Spacer[250]}, { 3 -> "Triangle", 4 -> "Rectangle", 5 -> "Pentagon", 6 -> "Hexagon", 8 -> "Octagon", 10 -> "Decagon"}, ControlType -> RadioButtonBar}}, "Options" :> { ContinuousAction -> True, SynchronousUpdating -> True, TrackedSymbols -> Manipulate}, "DefaultOptions" :> {}], ImageSizeCache->{1054., {396., 401.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>({$CellContext`Circle1 = ParametricPlot[{ Cos[$CellContext`t], Sin[$CellContext`t]}, {$CellContext`t, 0, 2 Pi}, PlotStyle -> Dashed, Axes -> False, ImageSize -> 350]; $CellContext`Ix[{{ Pattern[$CellContext`x1, Blank[]], Pattern[$CellContext`y1, Blank[]]}, { Pattern[$CellContext`x2, Blank[]], Pattern[$CellContext`y2, Blank[]]}, { Pattern[$CellContext`x3, Blank[]], Pattern[$CellContext`y3, Blank[]]}}] := (-0.5) Integrate[($CellContext`y2 - $CellContext`y1) (( 1 - $CellContext`t) $CellContext`x1 + $CellContext`t \ $CellContext`x2)^2 + ($CellContext`y3 - $CellContext`y2) (( 1 - $CellContext`t) $CellContext`x2 + $CellContext`t \ $CellContext`x3)^2 + ($CellContext`y1 - $CellContext`y3) (( 1 - $CellContext`t) $CellContext`x3 + $CellContext`t \ $CellContext`x1)^2, {$CellContext`t, 0, 1}]; $CellContext`Iy[{{ Pattern[$CellContext`x1, Blank[]], Pattern[$CellContext`y1, Blank[]]}, { Pattern[$CellContext`x2, Blank[]], Pattern[$CellContext`y2, Blank[]]}, { Pattern[$CellContext`x3, Blank[]], Pattern[$CellContext`y3, Blank[]]}}] := 0.5 Integrate[($CellContext`x2 - $CellContext`x1) (( 1 - $CellContext`t) $CellContext`y1 + $CellContext`t \ $CellContext`y2)^2 + ($CellContext`x3 - $CellContext`x2) (( 1 - $CellContext`t) $CellContext`y2 + $CellContext`t \ $CellContext`y3)^2 + ($CellContext`x1 - $CellContext`x3) (( 1 - $CellContext`t) $CellContext`y3 + $CellContext`t \ $CellContext`y1)^2, {$CellContext`t, 0, 1}]; $CellContext`Ia[{{ Pattern[$CellContext`x1, Blank[]], Pattern[$CellContext`y1, Blank[]]}, { Pattern[$CellContext`x2, Blank[]], Pattern[$CellContext`y2, Blank[]]}, { Pattern[$CellContext`x3, Blank[]], Pattern[$CellContext`y3, Blank[]]}}] := - Integrate[($CellContext`y2 - $CellContext`y1) (( 1 - $CellContext`t) $CellContext`x1 + $CellContext`t \ $CellContext`x2) + ($CellContext`y3 - $CellContext`y2) (( 1 - $CellContext`t) $CellContext`x2 + $CellContext`t \ $CellContext`x3) + ($CellContext`y1 - $CellContext`y3) (( 1 - $CellContext`t) $CellContext`x3 + $CellContext`t \ $CellContext`x1), {$CellContext`t, 0, 1}]; Null}; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{3.421164247515625*^9}] }, Open ]] }, WindowSize->{1272, 903}, WindowMargins->{{0, Automatic}, {Automatic, 6}}, FrontEndVersion->"6.0 for Microsoft Windows (32-bit) (April 20, 2007)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[590, 23, 33979, 707, 775, "Input"], Cell[34572, 732, 10790, 218, 814, "Output"] }, Open ]] } ] *) (* End of internal cache information *)