(* 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[ 29305, 553] NotebookOptionsPosition[ 12837, 258] NotebookOutlinePosition[ 29390, 555] CellTagsIndexPosition[ 29347, 552] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`height$$ = 2 Pi, $CellContext`high$$ = False, $CellContext`pt1$$ = {0.0001, 2}, $CellContext`Rh$$ = 0.5, $CellContext`showR$$ = False, $CellContext`width$$ = 4 Pi, $CellContext`\[Theta]$$ = -1.5697963267948967`, Typeset`show$$ = 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$$], False, "Yes"}, {True, False}}, { Hold[ Style[$CellContext`\:30dd\:30a2\:30f3\:30ab\:30ec\:5e73\:9762, Bold]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`height$$], 2 Pi, "\:9ad8\:3055"}, 2 Pi, 10 Pi}, {{ Hold[$CellContext`width$$], 4 Pi, "\:5e45"}, 4 Pi, 10 Pi}, { Hold[ Style[$CellContext`\:5186, Bold]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`Rh$$], 0.5, "\:534a\:5f84R"}, 0.1, 5}, {{ Hold[$CellContext`pt1$$], {0.0001, 2}, "\:4e2d\:5fc3"}, {(-4) Pi, 0.1}, {18.84945592153876, 2 Pi}}, {{ Hold[$CellContext`showR$$], False, "\:534a\:5f84\:8868\:793a"}, { True, False}}, {{ Hold[$CellContext`\[Theta]$$], -1.5697963267948967`, "\:534a\:5f84\:306e\:7aef"}, Rational[-1, 2] Pi, 4.71228898038469}}, Typeset`size$$ = {540., {381., 391.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`high$142702$$ = False, $CellContext`height$142703$$ = 0, $CellContext`width$142704$$ = 0, $CellContext`Rh$142705$$ = 0, $CellContext`pt1$142706$$ = {0, 0}, $CellContext`showR$142707$$ = False, $CellContext`\[Theta]$142708$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`height$$ = 2 Pi, $CellContext`high$$ = False, $CellContext`pt1$$ = {0.0001, 2}, $CellContext`Rh$$ = 0.5, $CellContext`showR$$ = False, $CellContext`width$$ = 4 Pi, $CellContext`\[Theta]$$ = -1.5697963267948967`}, "ControllerVariables" :> { Hold[$CellContext`high$$, $CellContext`high$142702$$, False], Hold[$CellContext`height$$, $CellContext`height$142703$$, 0], Hold[$CellContext`width$$, $CellContext`width$142704$$, 0], Hold[$CellContext`Rh$$, $CellContext`Rh$142705$$, 0], Hold[$CellContext`pt1$$, $CellContext`pt1$142706$$, {0, 0}], Hold[$CellContext`showR$$, $CellContext`showR$142707$$, False], Hold[$CellContext`\[Theta]$$, $CellContext`\[Theta]$142708$$, 0]}, "OtherVariables" :> { Typeset`show$$, 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`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]$$] + $CellContext`Au; $CellContext`Qx := ( 1/$CellContext`Py) Cos[$CellContext`Px]; $CellContext`Qy := (1/$CellContext`Py) Sin[$CellContext`Px]; $CellContext`Xmin := Pi - $CellContext`width$$/2; $CellContext`Xmax := Pi + $CellContext`width$$/2; $CellContext`basic2D := Graphics[{ Line[{{$CellContext`Xmin, 0}, {$CellContext`Xmax, 0}}], Dotted, Black, Thin, Line[{{$CellContext`Xmin, 0}, {$CellContext`Xmin, $CellContext`height$$}}], Line[{{$CellContext`Xmax, 0}, {$CellContext`Xmax, $CellContext`height$$}}], Line[{{$CellContext`Xmax, 0}, {$CellContext`Xmax, $CellContext`height$$}}]}]; \ $CellContext`circle2D := Graphics[{Thick, Blue, Circle[{$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}]}]; \ $CellContext`h := Show[ Plot[ 1, {$CellContext`x, $CellContext`Xmin, $CellContext`Xmax}, PlotRange -> {{$CellContext`Xmin, $CellContext`Xmax}, { 0, $CellContext`height$$}}, PlotStyle -> Dashed, Axes -> True, Ticks -> { Table[$CellContext`k Pi, {$CellContext`k, Floor[$CellContext`Xmin/Pi], Floor[$CellContext`Xmax/Pi]}]}, GridLines -> { Table[$CellContext`k (Pi/2), {$CellContext`k, Floor[2 ($CellContext`Xmin/Pi)], Floor[2 ($CellContext`Xmax/Pi)]}], Table[$CellContext`k, {$CellContext`k, 2, $CellContext`ymax}]}, GridLinesStyle -> Directive[Dashed]], If[$CellContext`showR$$, {$CellContext`circle2D, \ $CellContext`radius2D, $CellContext`basic2D}, {$CellContext`circle2D, \ $CellContext`basic2D}], AspectRatio -> Automatic]; $CellContext`dummy := Graphics3D[ Point[{0, 0, 10}]]; $CellContext`circle3D := { If[$CellContext`Ru + $CellContext`Au >= 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]}; \ $CellContext`radius3D := { If[$CellContext`Ax != $CellContext`Px, $CellContext`radius, \ $CellContext`oradius], Graphics3D[{Green, PointSize[Large], If[$CellContext`Py >= 1, Point[{$CellContext`Qx, $CellContext`Qy, ReplaceAll[$CellContext`f, $CellContext`x -> 1/$CellContext`Py]}], Point[{0, 0, 10}]]}]}; $CellContext`basic3D := ($CellContext`ratio := If[ Not[$CellContext`high$$], Automatic, {2, 2, 3}]; RevolutionPlot3D[$CellContext`f, {$CellContext`x, 0, 1}, BoxRatios -> $CellContext`ratio]); $CellContext`gikyu := Show[ If[$CellContext`showR$$, Show[$CellContext`basic3D, $CellContext`circle3D, \ $CellContext`radius3D], Show[$CellContext`basic3D, $CellContext`circle3D]]]; GraphicsColumn[{$CellContext`gikyu, $CellContext`h}]), "Specifications" :> { Style[ "\:5b9f\:969b\:306e\:6bd4\:7387\:3067 \:898b\:308b", Bold], {{$CellContext`high$$, False, "Yes"}, {True, False}}, Delimiter, Style[$CellContext`\:30dd\:30a2\:30f3\:30ab\:30ec\:5e73\:9762, Bold], {{$CellContext`height$$, 2 Pi, "\:9ad8\:3055"}, 2 Pi, 10 Pi}, {{$CellContext`width$$, 4 Pi, "\:5e45"}, 4 Pi, 10 Pi}, Delimiter, Style[$CellContext`\:5186, Bold], {{$CellContext`Rh$$, 0.5, "\:534a\:5f84R"}, 0.1, 5}, {{$CellContext`pt1$$, {0.0001, 2}, "\:4e2d\:5fc3"}, {(-4) Pi, 0.1}, {18.84945592153876, 2 Pi}}, {{$CellContext`showR$$, False, "\:534a\:5f84\:8868\:793a"}, { True, False}}, {{$CellContext`\[Theta]$$, -1.5697963267948967`, "\:534a\:5f84\:306e\:7aef"}, Rational[-1, 2] Pi, 4.71228898038469}, Delimiter}, "Options" :> {ControlPlacement -> Left}, "DefaultOptions" :> {}], ImageSizeCache->{1014., {413.5, 420.5}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>(( Clear["Global`*"]; $CellContext`xmax = 6 Pi; $CellContext`ymax = 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]; $CellContext`circle := ($CellContext`t1 := If[$CellContext`Ru > $CellContext`Au - 1, ArcSin[(1 - $CellContext`Au)/$CellContext`Ru], (-Pi)/ 2]; $CellContext`t2 := Pi - $CellContext`t1; $CellContext`tmax := Max[$CellContext`t1, $CellContext`t2]; $CellContext`tmin := Min[$CellContext`t1, $CellContext`t2]; ParametricPlot3D[{( 1/($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`tmin, \ $CellContext`tmax}, PlotStyle -> { Thick, Blue}]); $CellContext`radius := ($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`v1 := $CellContext`myArcTan[$CellContext`Ax - $CellContext`c, \ $CellContext`Ay]; $CellContext`v2 := $CellContext`myArcTan[$CellContext`Px - \ $CellContext`c, $CellContext`Py]; $CellContext`vmin := Min[$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}]); $CellContext`oradius := ($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}]); Null); Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{{3.465359739857391*^9, 3.4653597877345357`*^9}, 3.4653598376898985`*^9, 3.4653598727227182`*^9, 3.4653599893060656`*^9, 3.4653601309842873`*^9, 3.465360624081917*^9, 3.4653607661967487`*^9, 3.4653687811388564`*^9, 3.465368912374071*^9, 3.46536916368818*^9, 3.465369218860408*^9, 3.465369250313734*^9, 3.4653693094703627`*^9, 3.4653693813926983`*^9, 3.465369472908909*^9, {3.465369591503418*^9, 3.4653696124879274`*^9}}] }, WindowSize->{1272, 905}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, DockedCells->FEPrivate`If[ FEPrivate`SameQ[FEPrivate`$ProductIDName, "MathematicaPlayer"], FEPrivate`Join[{ Cell[ BoxData[ GraphicsBox[ RasterBox[CompressedData[" 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