(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 44652, 865] NotebookOptionsPosition[ 28184, 570] NotebookOutlinePosition[ 44737, 867] CellTagsIndexPosition[ 44694, 864] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`high$$ = False, $CellContext`n$$ = 3, $CellContext`pt1$$ = {0, 0.7}, $CellContext`pt2$$ = { 0, 0.3}, $CellContext`pt3$$ = {Rational[1, 6] Pi, 0.4}, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[ Style["\:6bcd\:7dda\:306e\:9577\:3055(\:534a\:5f84\:306f 1 )", Bold]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`n$$], 3, "n"}, 2, 12, 1}, { Hold[ Style["\:5b9f\:969b\:306e\:6bd4\:7387\:3067 \:898b\:308b ", Bold]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`high$$], False, "Yes"}, {True, False}}, { Hold[ Style[$CellContext`\:4e09\:89d2\:5f62ABC, Bold]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`pt1$$], {0, 0.7}, "\:70b9A"}, {0.1, 0}, { 2 Pi, 0.99999}}, {{ Hold[$CellContext`pt2$$], {0, 0.3}, "\:70b9B"}, {0.1, 0}, { 2 Pi, 0.99999}}, {{ Hold[$CellContext`pt3$$], {Rational[1, 6] Pi, 0.4}, "\:70b9C"}, { 0.1, 0}, {2 Pi, 0.99999}}, { Hold[ Style[ "\:9577\:3055\:3068\:89d2\:ff08\:6bcd\:7dda\:306e\:9577\:3055\:304c1\ \:5358\:4f4d\:9577\:ff09", Bold]], Manipulate`Dump`ThisIsNotAControl}, { Hold[ Dynamic[ Graphics[{ Inset[ Style["\:8fbaAB\:306e\:9577\:3055=", 12], {0.6, 1.6}], Inset[ Style[Round[$CellContext`AB 100] 0.01, 12], {1.5, 1.6}], Inset[ Style["\:8fbaBC\:306e\:9577\:3055=", 12], {0.6, 1.5}], Inset[ Style[Round[$CellContext`BC 100] 0.01, 12], {1.5, 1.5}], Inset[ Style["\:8fbaCA\:306e\:9577\:3055=", 12], {0.6, 1.4}], Inset[ Style[Round[$CellContext`CA 100] 0.01, 12], {1.5, 1.4}], Inset[ Style["\[Angle]A=", 12], {0.8, 1.2}], Inset[ Style[Round[$CellContext`angleA] Degree, 12], {1.5, 1.2}], Inset[ Style["\[Angle]B=", 12], {0.8, 1.1}], Inset[ Style[Round[$CellContext`angleB] Degree, 12], {1.5, 1.1}], Inset[ Style["\[Angle]C=", 12], {0.8, 1.}], Inset[ Style[Round[$CellContext`angleC] Degree, 12], {1.5, 1.}], Inset[ Style["\[Angle]A+\[Angle]B+\[Angle]C=", 12], {0.8, 0.85}], Inset[ Style[ Round[$CellContext`angleA + $CellContext`angleB + \ $CellContext`angleC] Degree, 12], {1.5, 0.85}]}]]], Manipulate`Dump`ThisIsNotAControl}}, Typeset`size$$ = { 540., {510., 519.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`n$243120$$ = 0, $CellContext`high$243121$$ = False, $CellContext`pt1$243122$$ = {0, 0}, $CellContext`pt2$243123$$ = {0, 0}, $CellContext`pt3$243124$$ = {0, 0}}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`high$$ = False, $CellContext`n$$ = 3, $CellContext`pt1$$ = {0, 0.7}, $CellContext`pt2$$ = { 0, 0.3}, $CellContext`pt3$$ = {Rational[1, 6] Pi, 0.4}}, "ControllerVariables" :> { Hold[$CellContext`n$$, $CellContext`n$243120$$, 0], Hold[$CellContext`high$$, $CellContext`high$243121$$, False], Hold[$CellContext`pt1$$, $CellContext`pt1$243122$$, {0, 0}], Hold[$CellContext`pt2$$, $CellContext`pt2$243123$$, {0, 0}], Hold[$CellContext`pt3$$, $CellContext`pt3$243124$$, {0, 0}]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> ($CellContext`xmax = 2 Pi; $CellContext`rmax = $CellContext`n$$; $CellContext`single = False; $CellContext`type := "ABC"; $CellContext`f := Sqrt[$CellContext`n$$^2 - 1] (1 - $CellContext`x); If[ Not[$CellContext`single], {$CellContext`\[Theta]1 := Part[$CellContext`pt1$$, 1] $CellContext`n$$; $CellContext`\[Theta]2 := Part[$CellContext`pt2$$, 1] $CellContext`n$$; $CellContext`\[Theta]3 := Part[$CellContext`pt3$$, 1] $CellContext`n$$}, {$CellContext`\[Theta]1 := Part[$CellContext`pt1$$, 1]; $CellContext`\[Theta]2 := Part[$CellContext`pt2$$, 1]; $CellContext`\[Theta]3 := Part[$CellContext`pt3$$, 1]}]; $CellContext`\[Theta]4 := Part[$CellContext`pt3$$, 1] + (2 Pi) ( 2 UnitStep[ Part[$CellContext`pt1$$, 1] - Part[$CellContext`pt3$$, 1]] - 1); $CellContext`\[Theta]5 := Part[$CellContext`pt2$$, 1] + (2 Pi) ( 2 UnitStep[ Part[$CellContext`pt1$$, 1] - Part[$CellContext`pt3$$, 1]] - 1); $CellContext`r1 := $CellContext`rmax - Part[$CellContext`pt1$$, 2] $CellContext`n$$; $CellContext`r2 := $CellContext`rmax - Part[$CellContext`pt2$$, 2] $CellContext`n$$; $CellContext`r3 := $CellContext`rmax - Part[$CellContext`pt3$$, 2] $CellContext`n$$; $CellContext`x1 := $CellContext`r1 Cos[$CellContext`\[Theta]1/$CellContext`n$$]; $CellContext`y1 := \ $CellContext`r1 Sin[$CellContext`\[Theta]1/$CellContext`n$$]; $CellContext`x2 := \ $CellContext`r2 Cos[$CellContext`\[Theta]2/$CellContext`n$$]; $CellContext`y2 := \ $CellContext`r2 Sin[$CellContext`\[Theta]2/$CellContext`n$$]; $CellContext`x3 := \ $CellContext`r3 Cos[$CellContext`\[Theta]3/$CellContext`n$$]; $CellContext`y3 := \ $CellContext`r3 Sin[$CellContext`\[Theta]3/$CellContext`n$$]; $CellContext`x4 := \ $CellContext`r3 Cos[$CellContext`\[Theta]4/$CellContext`n$$]; $CellContext`y4 := \ $CellContext`r3 Sin[$CellContext`\[Theta]4/$CellContext`n$$]; $CellContext`x5 := \ $CellContext`r2 Cos[$CellContext`\[Theta]5/$CellContext`n$$]; $CellContext`y5 := \ $CellContext`r2 Sin[$CellContext`\[Theta]5/$CellContext`n$$]; $CellContext`\[Alpha]1 := N[ ArcTan[ Sin[$CellContext`\[Theta]1/$CellContext`n$$ - \ $CellContext`\[Theta]2/$CellContext`n$$] ($CellContext`y1 - $CellContext`y2), Sin[$CellContext`\[Theta]1/$CellContext`n$$ - \ $CellContext`\[Theta]2/$CellContext`n$$] (-$CellContext`x1 + \ $CellContext`x2)]]; $CellContext`\[Alpha]2 := N[ ArcTan[ Sin[$CellContext`\[Theta]2/$CellContext`n$$ - \ $CellContext`\[Theta]3/$CellContext`n$$] ($CellContext`y2 - $CellContext`y3), Sin[$CellContext`\[Theta]2/$CellContext`n$$ - \ $CellContext`\[Theta]3/$CellContext`n$$] (-$CellContext`x2 + \ $CellContext`x3)]]; $CellContext`\[Alpha]3 := N[ ArcTan[ Sin[$CellContext`\[Theta]3/$CellContext`n$$ - \ $CellContext`\[Theta]1/$CellContext`n$$] ($CellContext`y3 - $CellContext`y1), Sin[$CellContext`\[Theta]3/$CellContext`n$$ - \ $CellContext`\[Theta]1/$CellContext`n$$] (-$CellContext`x3 + \ $CellContext`x1)]]; $CellContext`\[Alpha]4 := N[ ArcTan[ Sin[$CellContext`\[Theta]4/$CellContext`n$$ - \ $CellContext`\[Theta]1/$CellContext`n$$] ($CellContext`y4 - $CellContext`y1), Sin[$CellContext`\[Theta]4/$CellContext`n$$ - \ $CellContext`\[Theta]1/$CellContext`n$$] (-$CellContext`x4 + \ $CellContext`x1)]]; $CellContext`h1 := ($CellContext`r1 $CellContext`r2) (Abs[ Sin[$CellContext`\[Theta]1/$CellContext`n$$ - $CellContext`\ \[Theta]2/$CellContext`n$$]]/ Sqrt[$CellContext`r1^2 + $CellContext`r2^2 - (( 2 $CellContext`r1) $CellContext`r2) Cos[$CellContext`\[Theta]1/$CellContext`n$$ - \ $CellContext`\[Theta]2/$CellContext`n$$]]); $CellContext`h2 := \ ($CellContext`r2 $CellContext`r3) (Abs[ Sin[$CellContext`\[Theta]2/$CellContext`n$$ - $CellContext`\ \[Theta]3/$CellContext`n$$]]/ Sqrt[$CellContext`r2^2 + $CellContext`r3^2 - (( 2 $CellContext`r2) $CellContext`r3) Cos[$CellContext`\[Theta]2/$CellContext`n$$ - \ $CellContext`\[Theta]3/$CellContext`n$$]]); $CellContext`h3 := \ ($CellContext`r3 $CellContext`r1) (Abs[ Sin[$CellContext`\[Theta]3/$CellContext`n$$ - $CellContext`\ \[Theta]1/$CellContext`n$$]]/ Sqrt[$CellContext`r3^2 + $CellContext`r1^2 - (( 2 $CellContext`r3) $CellContext`r1) Cos[$CellContext`\[Theta]3/$CellContext`n$$ - \ $CellContext`\[Theta]1/$CellContext`n$$]]); $CellContext`h4 := \ ($CellContext`r3 $CellContext`r1) (Abs[ Sin[$CellContext`\[Theta]4/$CellContext`n$$ - $CellContext`\ \[Theta]1/$CellContext`n$$]]/ Sqrt[$CellContext`r3^2 + $CellContext`r1^2 - (( 2 $CellContext`r3) $CellContext`r1) Cos[$CellContext`\[Theta]4/$CellContext`n$$ - \ $CellContext`\[Theta]1/$CellContext`n$$]]); $CellContext`\[Beta]1 := ArcCos[$CellContext`h1/$CellContext`n$$]; $CellContext`\[Beta]2 := ArcCos[$CellContext`h2/$CellContext`n$$]; $CellContext`\[Beta]3 := ArcCos[$CellContext`h3/$CellContext`n$$]; $CellContext`\[Beta]4 := ArcCos[$CellContext`h4/$CellContext`n$$]; $CellContext`mesh := Which[$CellContext`n$$ <= 3, 8 $CellContext`n$$ - 1, Inequality[8, Greater, $CellContext`n$$, GreaterEqual, 4], 4 $CellContext`n$$ - 1, $CellContext`n$$ >= 8, 2 $CellContext`n$$ - 1]; $CellContext`colors := { Blue, Green, Black, Red}; $CellContext`colorName := { "\:9752", "\:7dd1", "\:9ed2", "\:8d64"}; $CellContext`ptA3D := {($CellContext`r1/$CellContext`n$$) Cos[$CellContext`\[Theta]1], ($CellContext`r1/$CellContext`n$$) Sin[$CellContext`\[Theta]1], Part[$CellContext`pt1$$, 2] Sqrt[$CellContext`n$$^2 - 1]}; $CellContext`ptB3D := {($CellContext`r2/$CellContext`n$$) Cos[$CellContext`\[Theta]2], ($CellContext`r2/$CellContext`n$$) Sin[$CellContext`\[Theta]2], Part[$CellContext`pt2$$, 2] Sqrt[$CellContext`n$$^2 - 1]}; $CellContext`ptC3D := {($CellContext`r3/$CellContext`n$$) Cos[$CellContext`\[Theta]3], ($CellContext`r3/$CellContext`n$$) Sin[$CellContext`\[Theta]3], Part[$CellContext`pt3$$, 2] Sqrt[$CellContext`n$$^2 - 1]}; $CellContext`ptABC3D := Graphics3D[{ PointSize[Large], Part[$CellContext`colors, 3], Point[$CellContext`ptA3D], Part[$CellContext`colors, 1], Point[$CellContext`ptB3D], Part[$CellContext`colors, 2], Point[$CellContext`ptC3D], Black, Text["A", $CellContext`ptA3D], Text["B", $CellContext`ptB3D], Text[ "C", $CellContext`ptC3D]}]; $CellContext`nsegAB3D := \ ($CellContext`R1 := $CellContext`h1/ Cos[$CellContext`t1 - $CellContext`\[Alpha]1]; Which[$CellContext`\[Theta]1 - $CellContext`\[Theta]2 > \ $CellContext`n$$ Pi, {$CellContext`\[Theta]max1 := $CellContext`\[Theta]2 + ( 2 $CellContext`n$$) Pi, $CellContext`\[Theta]min1 := $CellContext`\[Theta]1}, \ $CellContext`\[Theta]2 - $CellContext`\[Theta]1 > $CellContext`n$$ Pi, {$CellContext`\[Theta]max1 := $CellContext`\[Theta]1 + ( 2 $CellContext`n$$) Pi, $CellContext`\[Theta]min1 := $CellContext`\[Theta]2}, Abs[$CellContext`\[Theta]1 - $CellContext`\[Theta]2] <= \ $CellContext`n$$ Pi, {$CellContext`\[Theta]max1 := Max[$CellContext`\[Theta]1, $CellContext`\[Theta]2], \ $CellContext`\[Theta]min1 := Min[$CellContext`\[Theta]1, $CellContext`\[Theta]2]}]; ParametricPlot3D[{($CellContext`R1/$CellContext`n$$) Cos[$CellContext`n$$ $CellContext`t1], \ ($CellContext`R1/$CellContext`n$$) Sin[$CellContext`n$$ $CellContext`t1], ( 1 - $CellContext`R1/$CellContext`n$$) Sqrt[$CellContext`n$$^2 - 1]}, {$CellContext`t1, \ $CellContext`\[Theta]min1/$CellContext`n$$, \ $CellContext`\[Theta]max1/$CellContext`n$$}, PlotStyle -> {Thick, Part[$CellContext`colors, 2]}]); $CellContext`osegAB3D := Graphics3D[{Thick, Part[$CellContext`colors, 2], Line[{$CellContext`ptA3D, $CellContext`ptB3D}]}]; \ $CellContext`segAB3D := If[Part[$CellContext`pt1$$, 1] != Part[$CellContext`pt2$$, 1], $CellContext`nsegAB3D, $CellContext`osegAB3D]; \ $CellContext`nsegBC3D := ($CellContext`R2 := $CellContext`h2/ Cos[$CellContext`t2 - $CellContext`\[Alpha]2]; Which[$CellContext`\[Theta]2 - $CellContext`\[Theta]3 > \ $CellContext`n$$ Pi, {$CellContext`\[Theta]max2 := $CellContext`\[Theta]3 + ( 2 $CellContext`n$$) Pi, $CellContext`\[Theta]min2 := $CellContext`\[Theta]2}, \ $CellContext`\[Theta]3 - $CellContext`\[Theta]2 > $CellContext`n$$ Pi, {$CellContext`\[Theta]max2 := $CellContext`\[Theta]2 + ( 2 $CellContext`n$$) Pi, $CellContext`\[Theta]min2 := $CellContext`\[Theta]3}, Abs[$CellContext`\[Theta]2 - $CellContext`\[Theta]3] <= \ $CellContext`n$$ Pi, {$CellContext`\[Theta]max2 := Max[$CellContext`\[Theta]2, $CellContext`\[Theta]3], \ $CellContext`\[Theta]min2 := Min[$CellContext`\[Theta]2, $CellContext`\[Theta]3]}]; ParametricPlot3D[{($CellContext`R2/$CellContext`n$$) Cos[$CellContext`n$$ $CellContext`t2], \ ($CellContext`R2/$CellContext`n$$) Sin[$CellContext`n$$ $CellContext`t2], ( 1 - $CellContext`R2/$CellContext`n$$) Sqrt[$CellContext`n$$^2 - 1]}, {$CellContext`t2, \ $CellContext`\[Theta]min2/$CellContext`n$$, \ $CellContext`\[Theta]max2/$CellContext`n$$}, PlotStyle -> {Thick, Part[$CellContext`colors, 3]}]); $CellContext`osegBC3D := Graphics3D[{Thick, Part[$CellContext`colors, 3], Line[{$CellContext`ptB3D, $CellContext`ptC3D}]}]; \ $CellContext`segBC3D := If[Part[$CellContext`pt2$$, 1] != Part[$CellContext`pt3$$, 1], $CellContext`nsegBC3D, $CellContext`osegBC3D]; \ $CellContext`nsegCA3D := ($CellContext`R3 := $CellContext`h3/ Cos[$CellContext`t3 - $CellContext`\[Alpha]3]; Which[$CellContext`\[Theta]3 - $CellContext`\[Theta]1 > \ $CellContext`n$$ Pi, {$CellContext`\[Theta]max3 := $CellContext`\[Theta]1 + ( 2 $CellContext`n$$) Pi, $CellContext`\[Theta]min3 := $CellContext`\[Theta]3}, \ $CellContext`\[Theta]1 - $CellContext`\[Theta]3 > $CellContext`n$$ Pi, {$CellContext`\[Theta]max3 := $CellContext`\[Theta]3 + ( 2 $CellContext`n$$) Pi, $CellContext`\[Theta]min3 := $CellContext`\[Theta]1}, Abs[$CellContext`\[Theta]3 - $CellContext`\[Theta]1] <= \ $CellContext`n$$ Pi, {$CellContext`\[Theta]max3 := Max[$CellContext`\[Theta]3, $CellContext`\[Theta]1], \ $CellContext`\[Theta]min3 := Min[$CellContext`\[Theta]3, $CellContext`\[Theta]1]}]; ParametricPlot3D[{($CellContext`R3/$CellContext`n$$) Cos[$CellContext`n$$ $CellContext`t3], \ ($CellContext`R3/$CellContext`n$$) Sin[$CellContext`n$$ $CellContext`t3], ( 1 - $CellContext`R3/$CellContext`n$$) Sqrt[$CellContext`n$$^2 - 1]}, {$CellContext`t3, \ $CellContext`\[Theta]min3/$CellContext`n$$, \ $CellContext`\[Theta]max3/$CellContext`n$$}, PlotStyle -> {Thick, Part[$CellContext`colors, 1]}]); $CellContext`osegCA3D := Graphics3D[{Thick, Part[$CellContext`colors, 1], Line[{$CellContext`ptC3D, $CellContext`ptA3D}]}]; \ $CellContext`segCA3D := If[Part[$CellContext`pt3$$, 1] != Part[$CellContext`pt1$$, 1], $CellContext`nsegCA3D, $CellContext`osegCA3D]; \ $CellContext`seg3D := ($CellContext`R := $CellContext`h4/ Cos[$CellContext`t - $CellContext`\[Alpha]4]; Which[$CellContext`\[Theta]4 - $CellContext`\[Theta]1 > \ $CellContext`n$$ Pi, {$CellContext`\[Theta]mx := $CellContext`\[Theta]1 + ( 2 $CellContext`n$$) Pi, $CellContext`\[Theta]mn := $CellContext`\[Theta]4}, \ $CellContext`\[Theta]1 - $CellContext`\[Theta]4 > $CellContext`n$$ Pi, {$CellContext`\[Theta]mx := $CellContext`\[Theta]4 + ( 2 $CellContext`n$$) Pi, $CellContext`\[Theta]mn := $CellContext`\[Theta]1}, Abs[$CellContext`\[Theta]4 - $CellContext`\[Theta]1] <= \ $CellContext`n$$ Pi, {$CellContext`\[Theta]mx := Max[$CellContext`\[Theta]4, $CellContext`\[Theta]1], \ $CellContext`\[Theta]mn := Min[$CellContext`\[Theta]4, $CellContext`\[Theta]1]}]; ParametricPlot3D[{($CellContext`R/$CellContext`n$$) Cos[$CellContext`n$$ $CellContext`t], \ ($CellContext`R/$CellContext`n$$) Sin[$CellContext`n$$ $CellContext`t], ( 1 - $CellContext`R/$CellContext`n$$) Sqrt[$CellContext`n$$^2 - 1]}, {$CellContext`t, $CellContext`\[Theta]mn/$CellContext`n$$, \ $CellContext`\[Theta]mx/$CellContext`n$$}, PlotStyle -> {Thick, Part[$CellContext`colors, 1]}]); $CellContext`segAB2D := Graphics[{Thick, Part[$CellContext`colors, 2], Line[{{$CellContext`x1, $CellContext`y1}, {$CellContext`x2, \ $CellContext`y2}}]}]; $CellContext`segBC2D := Graphics[{Thick, Part[$CellContext`colors, 3], Line[{{$CellContext`x2, $CellContext`y2}, {$CellContext`x3, \ $CellContext`y3}}]}]; $CellContext`segCA2D := Graphics[{Thick, Part[$CellContext`colors, 1], Line[{{$CellContext`x3, $CellContext`y3}, {$CellContext`x1, \ $CellContext`y1}}]}]; $CellContext`seg2D := Graphics[{Thick, Part[$CellContext`colors, 1], Line[{{$CellContext`x4, $CellContext`y4}, {$CellContext`x1, \ $CellContext`y1}}]}]; $CellContext`ptC := Switch[$CellContext`type, "ABC", { Part[$CellContext`colors, 2], Point[{$CellContext`r3 Cos[$CellContext`\[Theta]3/$CellContext`n$$], $CellContext`r3 Sin[$CellContext`\[Theta]3/$CellContext`n$$]}], Black, Text[ "C", {$CellContext`r3 Cos[$CellContext`\[Theta]3/$CellContext`n$$], $CellContext`r3 Sin[$CellContext`\[Theta]3/$CellContext`n$$]}, {-2, 0}]}, "ABCC", { Part[$CellContext`colors, 2], Point[{$CellContext`r3 Cos[$CellContext`\[Theta]4/$CellContext`n$$], $CellContext`r3 Sin[$CellContext`\[Theta]4/$CellContext`n$$]}], Point[{$CellContext`r3 Cos[$CellContext`\[Theta]3/$CellContext`n$$], $CellContext`r3 Sin[$CellContext`\[Theta]3/$CellContext`n$$]}], Black, Text[ "C", {$CellContext`r3 Cos[$CellContext`\[Theta]3/$CellContext`n$$], $CellContext`r3 Sin[$CellContext`\[Theta]3/$CellContext`n$$]}, {-2, 0}], Text[ "C", {$CellContext`r3 Cos[$CellContext`\[Theta]4/$CellContext`n$$], $CellContext`r3 Sin[$CellContext`\[Theta]4/$CellContext`n$$]}, {-2, 0}]}]; $CellContext`ptABC2D := Graphics[{ PointSize[Large], Black, Point[{$CellContext`r1 Cos[$CellContext`\[Theta]1/$CellContext`n$$], $CellContext`r1 Sin[$CellContext`\[Theta]1/$CellContext`n$$]}], Part[$CellContext`colors, 1], Point[{$CellContext`r2 Cos[$CellContext`\[Theta]2/$CellContext`n$$], $CellContext`r2 Sin[$CellContext`\[Theta]2/$CellContext`n$$]}], Black, Text[ "A", {$CellContext`r1 Cos[$CellContext`\[Theta]1/$CellContext`n$$], $CellContext`r1 Sin[$CellContext`\[Theta]1/$CellContext`n$$]}, {-2, 0}], Text[ "B", {$CellContext`r2 Cos[$CellContext`\[Theta]2/$CellContext`n$$], $CellContext`r2 Sin[$CellContext`\[Theta]2/$CellContext`n$$]}, {-2, 0}], $CellContext`ptC}]; $CellContext`basic3D := \ ($CellContext`ratio := If[$CellContext`high$$, {2, 2, Sqrt[$CellContext`n$$^2 - 1]}, Automatic]; RevolutionPlot3D[$CellContext`f, {$CellContext`x, 0, 1}, BoxRatios -> $CellContext`ratio]); $CellContext`basic2D := { Graphics[{Blue, Table[ Line[{{0, 0}, {$CellContext`n$$ Cos[($CellContext`k 2) ( Pi/$CellContext`n$$)], $CellContext`n$$ Sin[($CellContext`k 2) ( Pi/$CellContext`n$$)]}}], {$CellContext`k, 0, $CellContext`n$$ - 1}]}], ParametricPlot[{$CellContext`r Cos[$CellContext`t], $CellContext`r Sin[$CellContext`t]}, {$CellContext`r, 0, $CellContext`rmax}, {$CellContext`t, 0, 2 Pi}, PlotStyle -> Gray, Mesh -> {15, $CellContext`mesh}]}; $CellContext`AB1 := Sqrt[($CellContext`x1 - $CellContext`x2)^2 + ($CellContext`y1 - \ $CellContext`y2)^2]; $CellContext`AB2 := Sqrt[($CellContext`x1 - $CellContext`x5)^2 + ($CellContext`y1 - \ $CellContext`y5)^2]; $CellContext`B1C1 := Sqrt[($CellContext`x2 - $CellContext`x3)^2 + ($CellContext`y2 - \ $CellContext`y3)^2]; $CellContext`B1C2 := Sqrt[($CellContext`x2 - $CellContext`x4)^2 + ($CellContext`y2 - \ $CellContext`y4)^2]; $CellContext`B2C2 := Sqrt[($CellContext`x5 - $CellContext`x4)^2 + ($CellContext`y5 - \ $CellContext`y4)^2]; $CellContext`C1A := Sqrt[($CellContext`x3 - $CellContext`x1)^2 + ($CellContext`y3 - \ $CellContext`y1)^2]; $CellContext`C2A := Sqrt[($CellContext`x4 - $CellContext`x1)^2 + ($CellContext`y4 - \ $CellContext`y1)^2]; $CellContext`angleC2AB1 := (180/Pi) ArcCos[($CellContext`C2A^2 + $CellContext`AB1^2 - \ $CellContext`B1C2^2)/(( 2 $CellContext`C2A) $CellContext`AB1)]; $CellContext`angleC1AB1 := \ (180/Pi) ArcCos[($CellContext`C1A^2 + $CellContext`AB1^2 - \ $CellContext`B1C1^2)/(( 2 $CellContext`C1A) $CellContext`AB1)]; $CellContext`angleB := ( 180/Pi) ArcCos[($CellContext`AB1^2 + $CellContext`B1C1^2 - \ $CellContext`C1A^2)/(( 2 $CellContext`AB1) $CellContext`B1C1)]; $CellContext`angleB1C1A := \ (180/Pi) ArcCos[($CellContext`B1C1^2 + $CellContext`C1A^2 - \ $CellContext`AB1^2)/(( 2 $CellContext`B1C1) $CellContext`C1A)]; $CellContext`angleB2C2A := \ (180/Pi) ArcCos[($CellContext`B2C2^2 + $CellContext`C2A^2 - \ $CellContext`AB2^2)/((2 $CellContext`B2C2) $CellContext`C2A)]; Switch[$CellContext`type, "ABCC", {$CellContext`angleA := $CellContext`angleC2AB1; \ $CellContext`angleC := $CellContext`angleB2C2A; $CellContext`AB := \ $CellContext`AB1; $CellContext`BC := $CellContext`B1C1; $CellContext`CA := \ $CellContext`C2A}, "ABC", {$CellContext`angleA := $CellContext`angleC1AB1; \ $CellContext`angleC := $CellContext`angleB1C1A; $CellContext`AB := \ $CellContext`AB1; $CellContext`BC := $CellContext`B1C1; $CellContext`CA := \ $CellContext`C1A}]; $CellContext`cone := Switch[$CellContext`type, "ABCC", {$CellContext`basic3D, $CellContext`segAB3D, \ $CellContext`segBC3D, $CellContext`seg3D, $CellContext`ptABC3D}, "ABC", {$CellContext`basic3D, $CellContext`segAB3D, \ $CellContext`segBC3D, $CellContext`segCA3D, $CellContext`ptABC3D}]; \ $CellContext`development := Switch[$CellContext`type, "ABCC", {$CellContext`basic2D, $CellContext`segAB2D, \ $CellContext`segBC2D, $CellContext`seg2D, $CellContext`ptABC2D}, "ABC", {$CellContext`basic2D, $CellContext`segAB2D, \ $CellContext`segBC2D, $CellContext`segCA2D, 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