(* 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[ 38092, 725] NotebookOptionsPosition[ 21562, 428] NotebookOutlinePosition[ 38177, 727] CellTagsIndexPosition[ 38134, 724] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`high$$ = False, $CellContext`linetype$$ = "line", $CellContext`pt2$$ = {-5.026548245743668, 5.857875658030852}, $CellContext`pt3$$ = {(-4) Pi, 3.5446015351590177`}, $CellContext`pt4$$ = {(-4) Pi, 5.395220833456485}, $CellContext`pt5$$ = {(-4) Pi, 3.949424506661589}, $CellContext`type$$ = "gikyu", $CellContext`width$$ = 12.566370614359172`, $CellContext`ymax$$ = 6.283185307179586, Typeset`show$$ = 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", Bold]}, { "gikyu" -> "\:64ec\:7403\:306e\:307f", "lines" -> "\:76f4\:7dda / \:6700\:77ed\:8ddd\:96e2\:7dda", "seg" -> "\:6700\:77ed\:8ddd\:96e2\:7dda\:5206", "all" -> "\:4e21\:65b9"}}, { Hold[ Style["\:30dd\:30a2\:30f3\:30ab\:30ec\:5e73\:9762", Bold]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`ymax$$], 2 Pi, "\:9ad8\:3055"}, 2 Pi, 10 Pi}, {{ Hold[$CellContext`width$$], 4 Pi, "\:5e45"}, 4 Pi, 10 Pi}, { Hold[ Style["\:76f4\:7dda/\:6700\:77ed\:8ddd\:96e2\:7dda", Bold]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`linetype$$], "line", "\:7a2e\:985e"}, { "line" -> "\:76f4\:7dda\:306e\:307f", "geoline" -> "\:6700\:77ed\:8ddd\:96e2\:7dda\:306e\:307f", "both" -> "\:4e21\:65b9"}}, {{ Hold[$CellContext`pt2$$], {0, 1}, "\:70b9A"}, {(-4) Pi, 1}, { 6 Pi, 4 Pi}}, {{ Hold[$CellContext`pt3$$], {0, 2}, "\:70b9B"}, {(-4) Pi, 1}, { 6 Pi, 4 Pi}}, { Hold[ Style["\:6700\:77ed\:8ddd\:96e2\:7dda\:5206", Bold]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`pt4$$], {0, 1}, "\:70b9P"}, {(-4) Pi, 1}, { 6 Pi, 4 Pi}}, {{ Hold[$CellContext`pt5$$], {0, 2}, "\:70b9Q"}, {(-4) Pi, 1}, { 6 Pi, 4 Pi}}}, Typeset`size$$ = {540., {381., 391.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`high$14876$$ = False, $CellContext`type$14877$$ = False, $CellContext`ymax$14878$$ = 0, $CellContext`width$14879$$ = 0, $CellContext`linetype$14880$$ = False, $CellContext`pt2$14881$$ = {0, 0}, $CellContext`pt3$14882$$ = {0, 0}, $CellContext`pt4$14883$$ = {0, 0}, $CellContext`pt5$14884$$ = {0, 0}}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`high$$ = False, $CellContext`linetype$$ = "line", $CellContext`pt2$$ = {0, 1}, $CellContext`pt3$$ = {0, 2}, $CellContext`pt4$$ = {0, 1}, $CellContext`pt5$$ = {0, 2}, $CellContext`type$$ = "gikyu", $CellContext`width$$ = 4 Pi, $CellContext`ymax$$ = 2 Pi}, "ControllerVariables" :> { Hold[$CellContext`high$$, $CellContext`high$14876$$, False], Hold[$CellContext`type$$, $CellContext`type$14877$$, False], Hold[$CellContext`ymax$$, $CellContext`ymax$14878$$, 0], Hold[$CellContext`width$$, $CellContext`width$14879$$, 0], Hold[$CellContext`linetype$$, $CellContext`linetype$14880$$, False], Hold[$CellContext`pt2$$, $CellContext`pt2$14881$$, {0, 0}], Hold[$CellContext`pt3$$, $CellContext`pt3$14882$$, {0, 0}], Hold[$CellContext`pt4$$, $CellContext`pt4$14883$$, {0, 0}], Hold[$CellContext`pt5$$, $CellContext`pt5$14884$$, {0, 0}]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> ($CellContext`By := Part[$CellContext`pt2$$, 2]; $CellContext`Cy := Part[$CellContext`pt3$$, 2]; $CellContext`Bx := Mod[ Part[$CellContext`pt2$$, 1], 2 Pi] + (2 Pi) UnitStep[Mod[ Part[$CellContext`pt3$$, 1], 2 Pi] - Mod[ Part[$CellContext`pt2$$, 1], 2 Pi] - Pi]; $CellContext`bx := Part[$CellContext`pt2$$, 1]; $CellContext`cx := Part[$CellContext`pt3$$, 1]; $CellContext`Cx := Mod[ Part[$CellContext`pt3$$, 1], 2 Pi] + (2 Pi) UnitStep[Mod[ Part[$CellContext`pt2$$, 1], 2 Pi] - Mod[ Part[$CellContext`pt3$$, 1], 2 Pi] - Pi]; $CellContext`Dy := Part[$CellContext`pt4$$, 2]; $CellContext`Ey := Part[$CellContext`pt5$$, 2]; $CellContext`Dx := Mod[ Part[$CellContext`pt4$$, 1], 2 Pi] + (2 Pi) UnitStep[Mod[ Part[$CellContext`pt5$$, 1], 2 Pi] - Mod[ Part[$CellContext`pt4$$, 1], 2 Pi] - Pi]; $CellContext`Ex := Mod[ Part[$CellContext`pt5$$, 1], 2 Pi] + (2 Pi) UnitStep[Mod[ Part[$CellContext`pt4$$, 1], 2 Pi] - Mod[ Part[$CellContext`pt5$$, 1], 2 Pi] - Pi]; 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 + $CellContext`By^2]}]; If[$CellContext`bx != $CellContext`cx, {$CellContext`c3 := \ (($CellContext`bx^2 + $CellContext`By^2 - $CellContext`cx^2 - \ $CellContext`Cy^2)/2)/($CellContext`bx - $CellContext`cx); $CellContext`R3 := Sqrt[($CellContext`bx - $CellContext`c3)^2 + $CellContext`By^2]}]; \ $CellContext`Xmin := Pi - $CellContext`width$$/2; $CellContext`Xmax := Pi + $CellContext`width$$/2; $CellContext`basic2D := Graphics[{ Line[{{$CellContext`Xmin, 0}, {$CellContext`Xmax, 0}}], Dotted, Black, Thin, Line[{{$CellContext`Xmin, 0}, {$CellContext`Xmin, $CellContext`ymax$$}}], Line[{{$CellContext`Xmax, 0}, {$CellContext`Xmax, $CellContext`ymax$$}}], Line[{{$CellContext`Xmax, 0}, {$CellContext`Xmax, $CellContext`ymax$$}}]}]; \ $CellContext`line2D := Graphics[{Thick, Black, If[$CellContext`Cx != $CellContext`Bx, Circle[{$CellContext`c1, 0}, $CellContext`R1], Line[{{$CellContext`Bx, 0}, {$CellContext`Bx, $CellContext`ymax$$}}]], 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}]}]; $CellContext`hline2D := Graphics[{Thick, Green, If[$CellContext`cx != $CellContext`bx, Circle[{$CellContext`c3, 0}, $CellContext`R3], Line[{{$CellContext`bx, 0}, {$CellContext`bx, $CellContext`ymax$$}}]], PointSize[Large], Red, Point[{$CellContext`bx, $CellContext`By}], Purple, Point[{$CellContext`cx, $CellContext`Cy}], Black, Text["A", {$CellContext`bx, $CellContext`By}, {-2, 0}], Text[ "B", {$CellContext`cx, $CellContext`Cy}, {-2, 0}]}]; $CellContext`segment2D := Graphics[{Thick, Red, If[$CellContext`Dx != $CellContext`Ex, Circle[{$CellContext`c2, 0}, $CellContext`R2, {$CellContext`smin, $CellContext`smax}], Line[{{$CellContext`Dx, 0}, {$CellContext`Dx, $CellContext`ymax$$}}]], PointSize[Large], Red, Point[{$CellContext`Dx, $CellContext`Dy}], Purple, Point[{$CellContext`Ex, $CellContext`Ey}], Black, Text["P", {$CellContext`Dx, $CellContext`Dy}, {-2, 0}], Text[ "Q", {$CellContext`Ex, $CellContext`Ey}, {-2, 0}]}]; $CellContext`lines2D := Switch[$CellContext`linetype$$, "line", $CellContext`hline2D, "geoline", $CellContext`line2D, "both", {$CellContext`line2D, $CellContext`hline2D}]; \ $CellContext`h := Show[ Plot[ 1, {$CellContext`x, $CellContext`Xmin, $CellContext`Xmax}, PlotRange -> {{$CellContext`Xmin, $CellContext`Xmax}, { 0, $CellContext`ymax$$}}, PlotStyle -> Dashed, Axes -> True, Ticks -> { Table[$CellContext`k Pi, {$CellContext`k, Floor[$CellContext`Xmin/Pi], Floor[$CellContext`Xmax/Pi]}]}, GridLines -> { Table[$CellContext`k (Pi/2), {$CellContext`k, Floor[2 ($CellContext`Xmin/Pi)], Floor[2 ($CellContext`Xmax/Pi)]}], Table[$CellContext`k, {$CellContext`k, 2, $CellContext`ymax$$}]}, GridLinesStyle -> Directive[Dashed]], Switch[$CellContext`type$$, "all", {$CellContext`lines2D, $CellContext`segment2D, \ $CellContext`basic2D}, "lines", {$CellContext`lines2D, $CellContext`basic2D}, "seg", {$CellContext`segment2D, $CellContext`basic2D}, "gikyu", $CellContext`basic2D], AspectRatio -> Automatic]; $CellContext`segment3D := { If[$CellContext`Dx != $CellContext`Ex, $CellContext`segment, \ $CellContext`osegment], Graphics3D[{ PointSize[Large], Red, Point[{(1/$CellContext`Dy) Cos[$CellContext`Dx], (1/$CellContext`Dy) Sin[$CellContext`Dx], ReplaceAll[$CellContext`f, $CellContext`x -> 1/$CellContext`Dy]}], Purple, Point[{(1/$CellContext`Ey) Cos[$CellContext`Ex], (1/$CellContext`Ey) Sin[$CellContext`Ex], ReplaceAll[$CellContext`f, $CellContext`x -> 1/$CellContext`Ey]}], Black, Text[ "P", {(1/$CellContext`Dy) Cos[$CellContext`Dx], (1/$CellContext`Dy) Sin[$CellContext`Dx], ReplaceAll[$CellContext`f, $CellContext`x -> 1/$CellContext`Dy]}], Text[ "Q", {(1/$CellContext`Ey) Cos[$CellContext`Ex], (1/$CellContext`Ey) Sin[$CellContext`Ex], ReplaceAll[$CellContext`f, $CellContext`x -> 1/$CellContext`Ey]}]}]}; $CellContext`lines3D := Switch[$CellContext`linetype$$, "line", $CellContext`hline3D, "geoline", $CellContext`line3D, "both", {$CellContext`line3D, $CellContext`hline3D}]; \ $CellContext`line3D := { If[$CellContext`Bx != $CellContext`Cx, $CellContext`line, \ $CellContext`oline], Graphics3D[{ PointSize[Large], Red, Point[{(1/$CellContext`By) Cos[$CellContext`Bx], (1/$CellContext`By) Sin[$CellContext`Bx], ReplaceAll[$CellContext`f, $CellContext`x -> 1/$CellContext`By]}], Purple, Point[{(1/$CellContext`Cy) Cos[$CellContext`Cx], (1/$CellContext`Cy) Sin[$CellContext`Cx], ReplaceAll[$CellContext`f, $CellContext`x -> 1/$CellContext`Cy]}], Black, Text[ "A", {(1/$CellContext`By) Cos[$CellContext`Bx], (1/$CellContext`By) Sin[$CellContext`Bx], ReplaceAll[$CellContext`f, $CellContext`x -> 1/$CellContext`By]}], Text[ "B", {(1/$CellContext`Cy) Cos[$CellContext`Cx], (1/$CellContext`Cy) Sin[$CellContext`Cx], ReplaceAll[$CellContext`f, $CellContext`x -> 1/$CellContext`Cy]}]}]}; $CellContext`hline3D := { If[$CellContext`bx != $CellContext`cx, $CellContext`hline, \ $CellContext`holine], Graphics3D[{ PointSize[Large], Red, Point[{(1/$CellContext`By) Cos[$CellContext`bx], (1/$CellContext`By) Sin[$CellContext`bx], ReplaceAll[$CellContext`f, $CellContext`x -> 1/$CellContext`By]}], Purple, Point[{(1/$CellContext`Cy) Cos[$CellContext`cx], (1/$CellContext`Cy) Sin[$CellContext`cx], ReplaceAll[$CellContext`f, $CellContext`x -> 1/$CellContext`Cy]}], Black, Text[ "A", {(1/$CellContext`By) Cos[$CellContext`bx], (1/$CellContext`By) Sin[$CellContext`bx], ReplaceAll[$CellContext`f, $CellContext`x -> 1/$CellContext`By]}], Text[ "B", {(1/$CellContext`Cy) Cos[$CellContext`cx], (1/$CellContext`Cy) Sin[$CellContext`cx], ReplaceAll[$CellContext`f, $CellContext`x -> 1/$CellContext`Cy]}]}]}; $CellContext`basic3D := \ ($CellContext`ratio := If[ Not[$CellContext`high$$], Automatic, {2, 2, 3}]; RevolutionPlot3D[$CellContext`f, {$CellContext`x, 0, 1}, BoxRatios -> $CellContext`ratio]); $CellContext`gikyu := Show[ Switch[$CellContext`type$$, "all", {$CellContext`basic3D, $CellContext`lines3D, \ $CellContext`segment3D}, "lines", {$CellContext`basic3D, $CellContext`lines3D}, "seg", {$CellContext`basic3D, $CellContext`segment3D}, "gikyu", $CellContext`basic3D]]; GraphicsColumn[{$CellContext`gikyu, $CellContext`h}]), "Specifications" :> { Style[ "\:5b9f\:969b\:306e\:6bd4\:7387\:3067\:898b\:308b", Bold], {{$CellContext`high$$, False, "Yes"}, {True, False}}, Delimiter, {{$CellContext`type$$, "gikyu", Style["\:8868\:793a", Bold]}, { "gikyu" -> "\:64ec\:7403\:306e\:307f", "lines" -> "\:76f4\:7dda / \:6700\:77ed\:8ddd\:96e2\:7dda", "seg" -> "\:6700\:77ed\:8ddd\:96e2\:7dda\:5206", "all" -> "\:4e21\:65b9"}, ControlType -> PopupMenu}, Delimiter, Style[ "\:30dd\:30a2\:30f3\:30ab\:30ec\:5e73\:9762", Bold], {{$CellContext`ymax$$, 2 Pi, "\:9ad8\:3055"}, 2 Pi, 10 Pi}, {{$CellContext`width$$, 4 Pi, "\:5e45"}, 4 Pi, 10 Pi}, Delimiter, Style[ "\:76f4\:7dda/\:6700\:77ed\:8ddd\:96e2\:7dda", Bold], {{$CellContext`linetype$$, "line", "\:7a2e\:985e"}, { "line" -> "\:76f4\:7dda\:306e\:307f", "geoline" -> "\:6700\:77ed\:8ddd\:96e2\:7dda\:306e\:307f", "both" -> "\:4e21\:65b9"}}, {{$CellContext`pt2$$, {0, 1}, "\:70b9A"}, {(-4) Pi, 1}, { 6 Pi, 4 Pi}}, {{$CellContext`pt3$$, {0, 2}, "\:70b9B"}, {(-4) Pi, 1}, {6 Pi, 4 Pi}}, Delimiter, Style[ "\:6700\:77ed\:8ddd\:96e2\:7dda\:5206", Bold], {{$CellContext`pt4$$, {0, 1}, "\:70b9P"}, {(-4) Pi, 1}, { 6 Pi, 4 Pi}}, {{$CellContext`pt5$$, {0, 2}, "\:70b9Q"}, {(-4) Pi, 1}, {6 Pi, 4 Pi}}, Delimiter}, "Options" :> {ControlPlacement -> Left}, "DefaultOptions" :> {}], ImageSizeCache->{972., {463.5, 470.5}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>(($CellContext`xmax = 6 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]; $CellContext`line := ($CellContext`s1 := ArcSin[1/$CellContext`R1]; $CellContext`s2 := Pi - ArcSin[1/$CellContext`R1]; $CellContext`smin := Max[$CellContext`s1, $CellContext`s2]; $CellContext`smax := Min[$CellContext`s1, $CellContext`s2]; ParametricPlot3D[{(1/($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}]; $CellContext`hline := ($CellContext`t1 := ArcSin[1/$CellContext`R3]; $CellContext`t2 := Pi - ArcSin[1/$CellContext`R3]; $CellContext`tmin := Max[$CellContext`t1, $CellContext`t2]; $CellContext`tmax := Min[$CellContext`t1, $CellContext`t2]; ParametricPlot3D[{(1/($CellContext`R3 Sin[$CellContext`t])) Cos[$CellContext`R3 Cos[$CellContext`t] + $CellContext`c3], ( 1/($CellContext`R3 Sin[$CellContext`t])) Sin[$CellContext`R3 Cos[$CellContext`t] + $CellContext`c3], ReplaceAll[$CellContext`f, $CellContext`x -> 1/($CellContext`R3 Sin[$CellContext`t])]}, {$CellContext`t, $CellContext`tmin, \ $CellContext`tmax}, PlotStyle -> {Thick, Green}]); $CellContext`holine := ParametricPlot3D[{$CellContext`t Cos[$CellContext`bx], $CellContext`t Sin[$CellContext`bx], ReplaceAll[$CellContext`f, $CellContext`x -> $CellContext`t]}, \ {$CellContext`t, 0.03, 1}, PlotStyle -> { Thick, Green}]; $CellContext`segment := ($CellContext`c2 = \ (($CellContext`Ex^2 + $CellContext`Ey^2 - $CellContext`Dx^2 - \ $CellContext`Dy^2)/2)/($CellContext`Ex - $CellContext`Dx); $CellContext`R2 = Sqrt[($CellContext`Ex - $CellContext`c2)^2 + $CellContext`Ey^2]; \ $CellContext`smin = Min[ ArcTan[$CellContext`Ex - $CellContext`c2, $CellContext`Ey], ArcTan[$CellContext`Dx - $CellContext`c2, $CellContext`Dy]]; \ $CellContext`smax = Max[ ArcTan[$CellContext`Ex - $CellContext`c2, $CellContext`Ey], ArcTan[$CellContext`Dx - $CellContext`c2, $CellContext`Dy]]; ParametricPlot3D[{(1/($CellContext`R2 Sin[$CellContext`s])) Cos[$CellContext`R2 Cos[$CellContext`s] + $CellContext`c2], ( 1/($CellContext`R2 Sin[$CellContext`s])) Sin[$CellContext`R2 Cos[$CellContext`s] + $CellContext`c2], ReplaceAll[$CellContext`f, $CellContext`x -> 1/($CellContext`R2 Sin[$CellContext`s])]}, {$CellContext`s, $CellContext`smin, \ $CellContext`smax}, PlotStyle -> {Thick, Red}]); $CellContext`osegment := ParametricPlot3D[{$CellContext`u Cos[$CellContext`Ex], $CellContext`u Sin[$CellContext`Ex], ReplaceAll[$CellContext`f, $CellContext`x -> $CellContext`u]}, \ {$CellContext`u, 1/Max[$CellContext`Dy, $CellContext`Ey], 1/ Min[$CellContext`Dy, $CellContext`Ey]}, PlotStyle -> {Thick, Red}]; Null); Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{ 3.46369031371875*^9, 3.463690405921875*^9, 3.46369052703125*^9, 3.46369059834375*^9, 3.4636907709375*^9, 3.463690843578125*^9, 3.46369098890625*^9, 3.46369260909375*^9, 3.46369317896875*^9, 3.463693234265625*^9, 3.463693326203125*^9, 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