(* Content-type: application/mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 6.0' *)

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Notebook[{
Cell[BoxData[
 TagBox[
  StyleBox[
   DynamicModuleBox[{$CellContext`high$$ = False, $CellContext`pt1$$ = {
    0.0001, 2}, $CellContext`pt2$$ = {0, 1}, $CellContext`pt3$$ = {0, 
    2}, $CellContext`Rh$$ = 0.5, $CellContext`showR$$ = 
    False, $CellContext`type$$ = "gikyu", $CellContext`ymax$$ = 2 
    Pi, $CellContext`\[Theta]$$ = -1.5706963267948966`, Typeset`show$$ = True,
     Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", 
    Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = 
    "\"untitled\"", Typeset`specs$$ = {{
      Hold[
       Style["\:5b9f\:969b\:306e\:6bd4\:7387\:3067 \:898b\:308b", Bold]], 
      Manipulate`Dump`ThisIsNotAControl}, {{
       Hold[$CellContext`high$$], False, "Yes"}, {True, False}}, {{
       Hold[$CellContext`type$$], "gikyu", 
       Style["\:8868\:793a\:56f3\:5f62", Bold]}, {
      "gikyu" -> "\:64ec\:7403\:306e\:307f", "lines" -> "\:76f4\:7dda", 
       "circles" -> "\:5186", "both" -> "\:5168\:3066"}}, {
      Hold[
       Style[$CellContext`\:30dd\:30a2\:30f3\:30ab\:30ec\:5e73\:9762, Bold]], 
      Manipulate`Dump`ThisIsNotAControl}, {{
       Hold[$CellContext`ymax$$], 2 Pi, "\:9ad8\:3055"}, 2 Pi, 10 Pi}, {
      Hold[
       Style[$CellContext`\:76f4\:7dda, Bold]], 
      Manipulate`Dump`ThisIsNotAControl}, {{
       Hold[$CellContext`pt2$$], {0, 1}, "\:70b9A"}, {0, 1}, {2 Pi, 2 Pi}}, {{
       Hold[$CellContext`pt3$$], {0, 2}, "\:70b9B"}, {0, 1}, {2 Pi, 2 Pi}}, {
      Hold[
       Style[$CellContext`\:5186, Bold]], 
      Manipulate`Dump`ThisIsNotAControl}, {{
       Hold[$CellContext`Rh$$], 0.5, "\:534a\:5f84R"}, 0.1, 5}, {{
       Hold[$CellContext`pt1$$], {0.0001, 2}, "\:4e2d\:5fc3"}, {0, 0.1}, {
      6.2830853071795865`, 2 Pi}}, {{
       Hold[$CellContext`showR$$], False, "\:534a\:5f84\:8868\:793a"}, {
      True, False}}, {{
       Hold[$CellContext`\[Theta]$$], -1.5706963267948966`, 
       "\:534a\:5f84\:306e\:7aef"}, -1.5706963267948966`, 4.71228898038469}}, 
    Typeset`size$$ = {540., {510., 519.}}, Typeset`update$$ = 0, 
    Typeset`initDone$$, Typeset`skipInitDone$$ = 
    False, $CellContext`high$156683$$ = False, $CellContext`type$156684$$ = 
    False, $CellContext`ymax$156685$$ = 0, $CellContext`pt2$156686$$ = {0, 
    0}, $CellContext`pt3$156687$$ = {0, 0}, $CellContext`Rh$156688$$ = 
    0, $CellContext`pt1$156689$$ = {0, 0}, $CellContext`showR$156690$$ = 
    False, $CellContext`\[Theta]$156691$$ = 0}, 
    DynamicBox[Manipulate`ManipulateBoxes[
     1, StandardForm, 
      "Variables" :> {$CellContext`high$$ = 
        False, $CellContext`pt1$$ = {0.0001, 2}, $CellContext`pt2$$ = {0, 
         1}, $CellContext`pt3$$ = {0, 2}, $CellContext`Rh$$ = 
        0.5, $CellContext`showR$$ = False, $CellContext`type$$ = 
        "gikyu", $CellContext`ymax$$ = 
        2 Pi, $CellContext`\[Theta]$$ = -1.5706963267948966`}, 
      "ControllerVariables" :> {
        Hold[$CellContext`high$$, $CellContext`high$156683$$, False], 
        Hold[$CellContext`type$$, $CellContext`type$156684$$, False], 
        Hold[$CellContext`ymax$$, $CellContext`ymax$156685$$, 0], 
        Hold[$CellContext`pt2$$, $CellContext`pt2$156686$$, {0, 0}], 
        Hold[$CellContext`pt3$$, $CellContext`pt3$156687$$, {0, 0}], 
        Hold[$CellContext`Rh$$, $CellContext`Rh$156688$$, 0], 
        Hold[$CellContext`pt1$$, $CellContext`pt1$156689$$, {0, 0}], 
        Hold[$CellContext`showR$$, $CellContext`showR$156690$$, False], 
        Hold[$CellContext`\[Theta]$$, $CellContext`\[Theta]$156691$$, 0]}, 
      "OtherVariables" :> {
       Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, 
        Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, 
        Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
         Typeset`skipInitDone$$}, 
      "Body" :> ($CellContext`Ax = 
        Part[$CellContext`pt1$$, 1]; $CellContext`Ay := 
        Part[$CellContext`pt1$$, 2]; $CellContext`Bx := 
        Part[$CellContext`pt2$$, 1]; $CellContext`Cx := 
        Part[$CellContext`pt3$$, 1]; $CellContext`By := 
        Part[$CellContext`pt2$$, 2]; $CellContext`Cy := 
        Part[$CellContext`pt3$$, 2]; $CellContext`Au := $CellContext`Ay 
         Cosh[$CellContext`Rh$$]; $CellContext`Ru := $CellContext`Ay 
         Sinh[$CellContext`Rh$$]; $CellContext`Px := $CellContext`Ru 
          Cos[$CellContext`\[Theta]$$] + $CellContext`Ax; $CellContext`Py := \
$CellContext`Ru 
          Sin[$CellContext`\[Theta]$$] + $CellContext`Au; $CellContext`Qx := (
          1/$CellContext`Py) 
         Cos[$CellContext`Px]; $CellContext`Qy := (1/$CellContext`Py) 
         Sin[$CellContext`Px]; 
       If[$CellContext`Bx != $CellContext`Cx, {$CellContext`c1 := \
(($CellContext`Bx^2 + $CellContext`By^2 - $CellContext`Cx^2 - \
$CellContext`Cy^2)/2)/($CellContext`Bx - $CellContext`Cx); $CellContext`R1 := 
           Sqrt[($CellContext`Bx - $CellContext`c1)^2 + $CellContext`By^2]}]; \
$CellContext`basic2D := Graphics[{
           Line[{{0, 0}, {2 Pi, 0}}], Dotted, Black, Thin, 
           Line[{{0, 0}, {0, $CellContext`ymax$$}}], 
           Line[{{2 Pi, 0}, {2 Pi, $CellContext`ymax$$}}], 
           
           Line[{{2 Pi, 0}, {
             2 Pi, $CellContext`ymax$$}}]}]; $CellContext`line2D := 
        Graphics[{Thick, 
           If[$CellContext`Cx != $CellContext`Bx, 
            Circle[{$CellContext`c1, 0}, $CellContext`R1], 
            
            Line[{{$CellContext`Bx, 
               0}, {$CellContext`Bx, $CellContext`ymax$$}}]], 
           PointSize[Large], Red, 
           Point[{$CellContext`Bx, $CellContext`By}], Purple, 
           Point[{$CellContext`Cx, $CellContext`Cy}], Black, 
           Text["A", {$CellContext`Bx, $CellContext`By}, {-2, 0}], 
           Text[
           "B", {$CellContext`Cx, $CellContext`Cy}, {-2, 
            0}]}]; $CellContext`circle2D := Graphics[{Thick, Blue, 
           Circle[{$CellContext`Ax, $CellContext`Au}, $CellContext`Ru], 
           PointSize[Large], Green, 
           Point[{$CellContext`Ax, $CellContext`Ay}]}]; $CellContext`radius2D := 
        Graphics[{Thick, Green, 
           PointSize[Large], 
           Point[{$CellContext`Px, $CellContext`Py}], Red, 
           
           Circle[{$CellContext`c, 
             0}, $CellContext`r, {$CellContext`vmin, $CellContext`vmax}]}]; \
$CellContext`circles2D := 
        If[$CellContext`showR$$, {$CellContext`circle2D, \
$CellContext`radius2D}, $CellContext`circle2D]; $CellContext`h := Show[
          Plot[
          1, {$CellContext`x, 0, 2 Pi}, 
           PlotRange -> {{0, 2 Pi}, {0, $CellContext`ymax$$}}, PlotStyle -> 
           Dashed, Axes -> True, Ticks -> {
             Table[$CellContext`k (Pi/2), {$CellContext`k, 0, 4}]}, GridLines -> {
             Table[$CellContext`k (Pi/2), {$CellContext`k, 0, 4}], 
             Table[$CellContext`k, {$CellContext`k, 2, $CellContext`ymax$$}]},
            GridLinesStyle -> Directive[Dashed]], 
          
          Switch[$CellContext`type$$, 
           "both", {$CellContext`circles2D, $CellContext`line2D, \
$CellContext`basic2D}, "lines", {$CellContext`line2D, $CellContext`basic2D}, 
           "circles", {$CellContext`circles2D, $CellContext`basic2D}, 
           "gikyu", $CellContext`basic2D], AspectRatio -> 
          Automatic]; $CellContext`dummy := Graphics3D[
          Point[{0, 0, 10}]]; $CellContext`circle3D := {
          
          If[$CellContext`Au + $CellContext`Ru >= 
           1, $CellContext`circle, $CellContext`dummy], 
          If[$CellContext`Ay >= 1, 
           Graphics3D[{
             PointSize[Large], Green, 
             
             Point[{(1/$CellContext`Ay) 
               Cos[$CellContext`Ax], (1/$CellContext`Ay) Sin[$CellContext`Ax], 
               
               ReplaceAll[$CellContext`f, $CellContext`x -> 
                1/$CellContext`Ay]}]}], $CellContext`dummy]}; \
$CellContext`line3D := {
          
          If[$CellContext`Bx != $CellContext`Cx, $CellContext`line, \
$CellContext`oline], 
          Graphics3D[{
            PointSize[Large], Red, 
            
            Point[{(1/$CellContext`By) 
              Cos[$CellContext`Bx], (1/$CellContext`By) Sin[$CellContext`Bx], 
              ReplaceAll[$CellContext`f, $CellContext`x -> 
               1/$CellContext`By]}], Purple, 
            
            Point[{(1/$CellContext`Cy) 
              Cos[$CellContext`Cx], (1/$CellContext`Cy) Sin[$CellContext`Cx], 
              
              ReplaceAll[$CellContext`f, $CellContext`x -> 
               1/$CellContext`Cy]}], Black, 
            Text[
            "A", {(1/$CellContext`By) 
              Cos[$CellContext`Bx], (1/$CellContext`By) Sin[$CellContext`Bx], 
              
              ReplaceAll[$CellContext`f, $CellContext`x -> 
               1/$CellContext`By]}], 
            Text[
            "B", {(1/$CellContext`Cy) 
              Cos[$CellContext`Cx], (1/$CellContext`Cy) Sin[$CellContext`Cx], 
              
              ReplaceAll[$CellContext`f, $CellContext`x -> 
               1/$CellContext`Cy]}]}]}; $CellContext`radius3D := {
          
          If[$CellContext`Ax != $CellContext`Px, $CellContext`segment, \
$CellContext`osegment], 
          Graphics3D[{Green, 
            PointSize[Large], 
            If[
             And[$CellContext`Py >= 1, 
              Inequality[0, LessEqual, $CellContext`Px, Less, 2 Pi]], 
             Point[{$CellContext`Qx, $CellContext`Qy, 
               
               ReplaceAll[$CellContext`f, $CellContext`x -> 
                1/$CellContext`Py]}], 
             
             Point[{0, 0, 
              10}]]}]}; $CellContext`basic3D := ($CellContext`boxratio := 
          If[$CellContext`high$$, {2, 2, 3}, Automatic]; {
           
           RevolutionPlot3D[$CellContext`f, {$CellContext`x, 0, 1}, 
            BoxRatios -> $CellContext`boxratio], 
           ParametricPlot3D[{$CellContext`u, 0, 
             
             ReplaceAll[$CellContext`f, $CellContext`x -> $CellContext`u]}, \
{$CellContext`u, 0.03, 1}, 
            PlotStyle -> {Thick, Dashed, Brown}]}); $CellContext`circles3D := 
        If[$CellContext`showR$$, {$CellContext`circle3D, \
$CellContext`radius3D}, $CellContext`circle3D]; $CellContext`gikyu := Show[
          
          Switch[$CellContext`type$$, 
           "both", {$CellContext`basic3D, $CellContext`circles3D, \
$CellContext`line3D}, "lines", {$CellContext`basic3D, $CellContext`line3D}, 
           "circles", {$CellContext`basic3D, $CellContext`circles3D}, 
           "gikyu", $CellContext`basic3D]]; 
       GraphicsColumn[{$CellContext`gikyu, $CellContext`h}]), 
      "Specifications" :> {
        Style[
        "\:5b9f\:969b\:306e\:6bd4\:7387\:3067 \:898b\:308b", 
         Bold], {{$CellContext`high$$, False, "Yes"}, {True, False}}, 
        Delimiter, {{$CellContext`type$$, "gikyu", 
          Style["\:8868\:793a\:56f3\:5f62", Bold]}, {
         "gikyu" -> "\:64ec\:7403\:306e\:307f", "lines" -> "\:76f4\:7dda", 
          "circles" -> "\:5186", "both" -> "\:5168\:3066"}, ControlType -> 
         PopupMenu}, Delimiter, 
        Style[$CellContext`\:30dd\:30a2\:30f3\:30ab\:30ec\:5e73\:9762, 
         Bold], {{$CellContext`ymax$$, 2 Pi, "\:9ad8\:3055"}, 2 Pi, 10 Pi}, 
        Delimiter, 
        Style[$CellContext`\:76f4\:7dda, 
         Bold], {{$CellContext`pt2$$, {0, 1}, "\:70b9A"}, {0, 1}, {
         2 Pi, 2 Pi}}, {{$CellContext`pt3$$, {0, 2}, "\:70b9B"}, {0, 1}, {
         2 Pi, 2 Pi}}, Delimiter, 
        Style[$CellContext`\:5186, 
         Bold], {{$CellContext`Rh$$, 0.5, "\:534a\:5f84R"}, 0.1, 
         5}, {{$CellContext`pt1$$, {0.0001, 2}, "\:4e2d\:5fc3"}, {0, 0.1}, {
         6.2830853071795865`, 2 Pi}}, {{$CellContext`showR$$, False, 
          "\:534a\:5f84\:8868\:793a"}, {
         True, False}}, {{$CellContext`\[Theta]$$, -1.5706963267948966`, 
          "\:534a\:5f84\:306e\:7aef"}, -1.5706963267948966`, 
         4.71228898038469}, Delimiter}, 
      "Options" :> {ControlPlacement -> Left}, "DefaultOptions" :> {}],
     ImageSizeCache->{1018., {541.5, 548.5}},
     SingleEvaluation->True],
    Deinitialization:>None,
    DynamicModuleValues:>{},
    Initialization:>(($CellContext`xmax = 2 Pi; $CellContext`myArcTan[
         Pattern[$CellContext`x, 
          Blank[]], 
         Pattern[$CellContext`y, 
          Blank[]]] = If[Abs[$CellContext`x] > 0.01, 
         If[ArcTan[$CellContext`x, $CellContext`y] >= 0, 
          ArcTan[$CellContext`x, $CellContext`y], 
          ArcTan[$CellContext`x, $CellContext`y] + Pi], (Pi/2) 
         Sign[$CellContext`x]]; $CellContext`f := 
       Log[(1 + Sqrt[1 - $CellContext`x^2])/$CellContext`x] - Sqrt[
        1 - $CellContext`x^2]; $CellContext`circle := ($CellContext`t1 := 
         If[$CellContext`Ru > $CellContext`Au - 1, 
           ArcSin[(1 - $CellContext`Au)/$CellContext`Ru], (-Pi)/
           2]; $CellContext`t2 := Pi - $CellContext`t1; $CellContext`t3 := 
         If[$CellContext`Ax/$CellContext`Ru < 1, 
           ArcCos[-($CellContext`Ax/$CellContext`Ru)], Pi]; $CellContext`t4 := 
         If[Abs[(2 Pi - $CellContext`Ax)/$CellContext`Ru] < 1, 
           ArcCos[(2 Pi - $CellContext`Ax)/$CellContext`Ru], 0]; {
          
          ParametricPlot3D[{(
             1/($CellContext`Au + $CellContext`Ru Sin[$CellContext`t])) 
            Cos[$CellContext`Ru Cos[$CellContext`t] + $CellContext`Ax], (
             1/($CellContext`Au + $CellContext`Ru Sin[$CellContext`t])) 
            Sin[$CellContext`Ru Cos[$CellContext`t] + $CellContext`Ax], 
            
            ReplaceAll[$CellContext`f, $CellContext`x -> 
             1/($CellContext`Au + $CellContext`Ru 
               Sin[$CellContext`t])]}, {$CellContext`t, $CellContext`t3, \
$CellContext`t4}, PlotStyle -> {Thick, Blue}], 
          
          ParametricPlot3D[{(
             1/($CellContext`Au + $CellContext`Ru Sin[$CellContext`t])) 
            Cos[$CellContext`Ru Cos[$CellContext`t] + $CellContext`Ax], (
             1/($CellContext`Au + $CellContext`Ru Sin[$CellContext`t])) 
            Sin[$CellContext`Ru Cos[$CellContext`t] + $CellContext`Ax], 
            
            ReplaceAll[$CellContext`f, $CellContext`x -> 
             1/($CellContext`Au + $CellContext`Ru 
               Sin[$CellContext`t])]}, {$CellContext`t, -$CellContext`t4, \
-$CellContext`t3}, 
           PlotStyle -> {
            Thick, Blue}]}); $CellContext`segment := ($CellContext`c = \
(($CellContext`Ax^2 + $CellContext`Ay^2 - $CellContext`Px^2 - \
$CellContext`Py^2)/2)/($CellContext`Ax - $CellContext`Px); $CellContext`r = 
         Sqrt[($CellContext`Ax - $CellContext`c)^2 + $CellContext`Ay^2]; \
$CellContext`v3 := $CellContext`myArcTan[-$CellContext`c, 
           
           Sqrt[$CellContext`r^2 - $CellContext`c^2]]; $CellContext`v4 := \
$CellContext`myArcTan[2 Pi - $CellContext`c, 
           
           Sqrt[$CellContext`r^2 - (
             2 Pi - $CellContext`c)^2]]; $CellContext`v1 := \
$CellContext`myArcTan[$CellContext`Ax - $CellContext`c, $CellContext`Ay]; \
$CellContext`v2 := $CellContext`myArcTan[$CellContext`Px - $CellContext`c, \
$CellContext`Py]; 
        Which[$CellContext`Px < 
          0, {$CellContext`vmin := $CellContext`v1, $CellContext`vmax := \
$CellContext`v3}, $CellContext`Px > 
          2 Pi, {$CellContext`vmin := $CellContext`v4, $CellContext`vmax := \
$CellContext`v1}, 
          Inequality[
          0, LessEqual, $CellContext`Px, Less, 2 Pi], {$CellContext`vmin := 
           Min[$CellContext`v1, $CellContext`v2], $CellContext`vmax := 
           Max[$CellContext`v1, $CellContext`v2]}]; 
        ParametricPlot3D[{(1/($CellContext`r Sin[$CellContext`v])) 
           Cos[$CellContext`r Cos[$CellContext`v] + $CellContext`c], (
            1/($CellContext`r Sin[$CellContext`v])) 
           Sin[$CellContext`r Cos[$CellContext`v] + $CellContext`c], 
           
           ReplaceAll[$CellContext`f, $CellContext`x -> 
            1/($CellContext`r 
             Sin[$CellContext`v])]}, {$CellContext`v, $CellContext`vmin, \
$CellContext`vmax}, 
          PlotStyle -> {
           Thick, Red}]); $CellContext`osegment := ($CellContext`vmin0 := 
         Min[$CellContext`Ay + 
           Sin[$CellContext`\[Theta]$$] $CellContext`Rh$$, $CellContext`Ay]; \
$CellContext`vmax0 := 
         Max[$CellContext`Ay + 
           Sin[$CellContext`\[Theta]$$] $CellContext`Rh$$, $CellContext`Ay]; 
        ParametricPlot3D[{$CellContext`v Cos[$CellContext`Ax], $CellContext`v 
           Sin[$CellContext`Ax], 
           
           ReplaceAll[$CellContext`f, $CellContext`x -> $CellContext`v]}, \
{$CellContext`v, 1/$CellContext`vmax0, 1/$CellContext`vmin0}, 
          PlotStyle -> {Thick, Red}]); $CellContext`line := ($CellContext`s1 := 
         ArcSin[1/$CellContext`R1]; $CellContext`s2 := 
         Pi - ArcSin[1/$CellContext`R1]; $CellContext`s3 := If[
           Element[
            ArcCos[(2 Pi - $CellContext`c1)/$CellContext`R1], Reals], 
           ArcCos[(2 Pi - $CellContext`c1)/$CellContext`R1], 
           0]; $CellContext`s4 := If[
           Element[
            ArcCos[-($CellContext`c1/$CellContext`R1)], Reals], 
           ArcCos[-($CellContext`c1/$CellContext`R1)], Pi]; $CellContext`smin := 
         Max[$CellContext`s1, $CellContext`s3]; $CellContext`smax := 
         Min[$CellContext`s2, $CellContext`s4]; 
        ParametricPlot3D[{(1/($CellContext`R1 Sin[$CellContext`s])) 
           Cos[$CellContext`R1 Cos[$CellContext`s] + $CellContext`c1], (
            1/($CellContext`R1 Sin[$CellContext`s])) 
           Sin[$CellContext`R1 Cos[$CellContext`s] + $CellContext`c1], 
           
           ReplaceAll[$CellContext`f, $CellContext`x -> 
            1/($CellContext`R1 
             Sin[$CellContext`s])]}, {$CellContext`s, $CellContext`smin, \
$CellContext`smax}, PlotStyle -> {Thick, Black}]); $CellContext`oline := 
       ParametricPlot3D[{$CellContext`s Cos[$CellContext`Bx], $CellContext`s 
          Sin[$CellContext`Bx], 
          
          ReplaceAll[$CellContext`f, $CellContext`x -> $CellContext`s]}, \
{$CellContext`s, 0.03, 1}, PlotStyle -> {Thick, Black}]; Null); 
     Typeset`initDone$$ = True),
    SynchronousInitialization->True,
    UnsavedVariables:>{Typeset`initDone$$},
    UntrackedVariables:>{Typeset`size$$}], "Manipulate",
   Deployed->True,
   StripOnInput->False],
  Manipulate`InterpretManipulate[1]]], "Output",
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},
WindowSize->{1272, 905},
WindowMargins->{{0, Automatic}, {Automatic, 0}},
DockedCells->FEPrivate`If[
  FEPrivate`SameQ[FEPrivate`$ProductIDName, "MathematicaPlayer"], 
  FEPrivate`Join[{
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