(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 63161, 1222] NotebookOptionsPosition[ 46307, 921] NotebookOutlinePosition[ 63247, 1224] CellTagsIndexPosition[ 63204, 1221] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`d$$ = 0, $CellContext`n$$ = 0, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`d$$], 0, Row[{ Spacer[200], Style["Transformation", 15, Bold], Spacer[300]}]}, { 0 -> Style["Hyperbolic", 13, Bold], 1 -> Style["Circular", 13, Bold]}}, {{ Hold[$CellContext`n$$], 0, Row[{ 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$CellContext`x^2 + $CellContext`y^2 < Max[Part[ Part[$CellContext`pts, 1], 1]^2 + Part[ Part[$CellContext`pts, 1], 2]^2, 2 Part[ Part[$CellContext`pts, 2], 1]^2 + Part[ Part[$CellContext`pts, 1], 2]^2 - Part[ Part[$CellContext`pts, 1], 1]^2], $CellContext`x^2 - $CellContext`y^2 < Max[2 Part[ Part[$CellContext`pts, 3], 1]^2 - Part[ Part[$CellContext`pts, 1], 1]^2 - Part[ Part[$CellContext`pts, 1], 2]^2, Part[ Part[$CellContext`pts, 1], 1]^2 - Part[ Part[$CellContext`pts, 1], 2]^2], $CellContext`x^2 - $CellContext`y^2 > Min[2 Part[ Part[$CellContext`pts, 3], 1]^2 - Part[ Part[$CellContext`pts, 1], 1]^2 - Part[ Part[$CellContext`pts, 1], 2]^2, Part[ Part[$CellContext`pts, 1], 1]^2 - Part[ Part[$CellContext`pts, 1], 2]^2]], {$CellContext`x, -0.1, 5}, {$CellContext`y, -0.1, 5}, PlotStyle -> { Directive[Green, Opacity[0.4]]}], Plot[($CellContext`x^2 + Part[ Part[$CellContext`pts, 1], 2]^2 - Part[ Part[$CellContext`pts, 1], 1]^2)^ Rational[1, 2], {$CellContext`x, 0, 5}, PlotStyle -> {Cyan, Thickness[0.003]}], Plot[($CellContext`x^2 + Part[ Part[$CellContext`pts, 1], 2]^2 - Part[ Part[$CellContext`pts, 1], 1]^2)^ Rational[1, 2], {$CellContext`x, -5, 0}, PlotStyle -> {Cyan, Thickness[0.003]}], Plot[-($CellContext`x^2 + Part[ Part[$CellContext`pts, 1], 2]^2 - Part[ Part[$CellContext`pts, 1], 1]^2)^ Rational[1, 2], {$CellContext`x, -5, 0}, PlotStyle -> {Cyan, Thickness[0.003]}], Plot[-($CellContext`x^2 + Part[ Part[$CellContext`pts, 1], 2]^2 - Part[ Part[$CellContext`pts, 1], 1]^2)^ Rational[1, 2], {$CellContext`x, 0, 5}, PlotStyle -> {Cyan, Thickness[0.003]}], Plot[($CellContext`x^2 + Part[ Part[$CellContext`pts, 1], 1]^2 + Part[ Part[$CellContext`pts, 1], 2]^2 - 2 Part[ Part[$CellContext`pts, 3], 1]^2)^ Rational[1, 2], {$CellContext`x, 0, 5}, PlotStyle -> {Cyan, Thickness[0.003]}], Plot[($CellContext`x^2 + Part[ Part[$CellContext`pts, 1], 1]^2 + Part[ Part[$CellContext`pts, 1], 2]^2 - 2 Part[ Part[$CellContext`pts, 3], 1]^2)^ Rational[1, 2], {$CellContext`x, -5, 0}, PlotStyle -> {Cyan, Thickness[0.003]}], Plot[-($CellContext`x^2 + Part[ Part[$CellContext`pts, 1], 1]^2 + Part[ Part[$CellContext`pts, 1], 2]^2 - 2 Part[ Part[$CellContext`pts, 3], 1]^2)^ Rational[1, 2], {$CellContext`x, 0, 5}, PlotStyle -> {Cyan, Thickness[0.003]}], Plot[-($CellContext`x^2 + Part[ Part[$CellContext`pts, 1], 1]^2 + Part[ Part[$CellContext`pts, 1], 2]^2 - 2 Part[ Part[$CellContext`pts, 3], 1]^2)^ Rational[1, 2], {$CellContext`x, -5, 0}, PlotStyle -> {Cyan, Thickness[0.003]}], Axes -> True, AxesStyle -> Red, AxesLabel -> { Style["X", Black, Bold, 15], Style["Y", Black, Bold, 15]}, ImageSize -> {500, 600}, PlotRange -> If[$CellContext`n$$ == 1, All, {{-0.4, 5}, {-0.4, 5}}], PlotLabel -> Style["\!\(\*\nStyleBox[\"S\",\nFontColor->RGBColor[0, 1, \ 0]]\)=T(\!\(\*\nStyleBox[\"R\",\nFontColor->RGBColor[0, 0, 1]]\)), \!\(\*\n\ StyleBox[SubscriptBox[\"Q\", \"i\"],\nFontColor->RGBColor[0, 1, \ 0]]\)=T(\!\(\*\nStyleBox[SubscriptBox[\"P\", \"i\"],\nFontColor->RGBColor[0, \ 0, 1]]\))", Bold, 20]]]], {{0, 0}, {5, 5}}, Appearance -> Automatic]}, Center]}], Row[{ LocatorPane[ Dynamic[$CellContext`pts], Framed[ Graphics[{{ Inset[ Style["R", Bold, 17], Scaled[{0.5, 0.5}]], Blue, Opacity[0.5], EdgeForm[Black], Polygon[ Dynamic[$CellContext`pts]]}, Point[ Dynamic[$CellContext`pts]]}, PlotRange -> {{-0.1, 3}, {-0.1, 3}}, Axes -> True, AxesLabel -> { Style["U", Bold, 15], Style["V", Bold, 15]}, ImageSize -> {400, 400}]], {{0, 0}, { 3, 3}}], Null, Null, Null, Null, Null, Style[ "\!\(\*OverscriptBox[\(\[DoubleLongRightArrow]\), \(\((x, y)\)\\ \ = \\ T \((u, v)\)\)]\)", Bold, 20], Null, Null, Null, Null, Null, LocatorPane[ Dynamic[$CellContext`pts], Dynamic[ Framed[ Show[ Graphics[{{Dashed, $CellContext`createCircle[{ Part[$CellContext`pts, 1], Part[$CellContext`pts, 2]}]}, { Inset[ Style["T(R)", Bold, 17], Scaled[{0.5, 0.5}]], Dashed, $CellContext`createCircle[{ Part[$CellContext`pts, 3], Part[$CellContext`pts, 4]}]}, {Dashed, $CellContext`createCircle[{ Part[$CellContext`pts, 1], Part[$CellContext`pts, 4]}]}, {Dashed, $CellContext`createCircle[{ Part[$CellContext`pts, 3], Part[$CellContext`pts, 2]}]}}], RegionPlot[ And[($CellContext`x - Part[ $CellContext`center[{ Part[$CellContext`pts, 1], Part[$CellContext`pts, 2]}], 1])^2 + ($CellContext`y - Part[ $CellContext`center[{ Part[$CellContext`pts, 1], Part[$CellContext`pts, 2]}], 2])^2 > $CellContext`radius[{ Part[$CellContext`pts, 1], Part[$CellContext`pts, 2]}]^2, ($CellContext`x - Part[ $CellContext`center[{ Part[$CellContext`pts, 3], Part[$CellContext`pts, 4]}], 1])^2 + ($CellContext`y - Part[ $CellContext`center[{ Part[$CellContext`pts, 3], Part[$CellContext`pts, 4]}], 2])^2 < $CellContext`radius[{ Part[$CellContext`pts, 3], Part[$CellContext`pts, 4]}]^2, ($CellContext`x - Part[ $CellContext`center[{ Part[$CellContext`pts, 3], Part[$CellContext`pts, 2]}], 1])^2 + ($CellContext`y - Part[ $CellContext`center[{ Part[$CellContext`pts, 3], Part[$CellContext`pts, 2]}], 2])^2 < $CellContext`radius[{ Part[$CellContext`pts, 3], Part[$CellContext`pts, 2]}]^2, ($CellContext`x - Part[ $CellContext`center[{ Part[$CellContext`pts, 1], Part[$CellContext`pts, 4]}], 1])^2 + ($CellContext`y - Part[ $CellContext`center[{ Part[$CellContext`pts, 1], Part[$CellContext`pts, 4]}], 2])^2 > $CellContext`radius[{ Part[$CellContext`pts, 1], Part[$CellContext`pts, 4]}]^2], {$CellContext`x, -0.1, 3}, {$CellContext`y, -0.1, 3}, PlotStyle -> { Directive[Yellow, Opacity[0.4]]}], PlotRange -> {{-0.1, 3}, {-0.1, 3}}, Axes -> True, AxesLabel -> { Style["X", Bold, 15], Style["Y", Bold, 15]}, ImageSize -> {400, 400}]]], {{-0.1, -0.1}, {3, 3}}, Appearance -> { Graphics[{ Inset[ "\!\(\*\nStyleBox[SubscriptBox[\"P\", \"1\"],\n\ FontSize->16]\)", Scaled[{0.5, 0.35}]], {Red, PointSize[0.07], Point[ Dynamic[ Part[$CellContext`pts, 1]]]}}], Graphics[{ Inset[ "\!\(\*\nStyleBox[SubscriptBox[\"P\", \"2\"],\n\ FontSize->16]\)", Scaled[{0.5, 0.35}]], {Red, PointSize[0.07], Point[ Dynamic[ Part[$CellContext`pts, 1]]]}}], Graphics[{ Inset[ "\!\(\*\nStyleBox[SubscriptBox[\"P\", \"3\"],\n\ FontSize->16]\)", Scaled[{0.5, 0.65}]], {Red, PointSize[0.07], Point[ Dynamic[ Part[$CellContext`pts, 1]]]}}], Graphics[{ Inset[ "\!\(\*\nStyleBox[SubscriptBox[\"P\", \"4\"],\n\ FontSize->16]\)", Scaled[{0.5, 0.65}]], {Red, PointSize[0.07], Point[ Dynamic[ Part[$CellContext`pts, 1]]]}}]}]}]]], {1000, 620}, Alignment -> {Center, Center}, ImageSizeAction -> Automatic]], "Specifications" :> {{{$CellContext`d$$, 0, Row[{ Spacer[200], Style["Transformation", 15, Bold], Spacer[300]}]}, { 0 -> Style["Hyperbolic", 13, Bold], 1 -> Style["Circular", 13, Bold]}, ControlType -> RadioButtonBar}, {{$CellContext`n$$, 0, Row[{"\!\(\*\nStyleBox[\"\[Copyright]\",\nFontSize->14]\)\!\(\*\n\ StyleBox[\" \",\nFontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\"N\",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\".\",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\" \",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\"Bykov\",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\",\",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\" \",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\"SJ\",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\" \",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\"Delta\",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\" \",\n\ FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\"College\",\n\ FontColor->RGBColor[0, 0, 1]]\)", Spacer[500]}]}, { 0 -> Style["Quadrant I View", 13, Bold], 1 -> Style["Full View", 13, Bold]}, ControlType -> RadioButtonBar, Enabled -> Dynamic[ If[$CellContext`d$$ == 1, False, True]]}}, "Options" :> { ControlPlacement -> {Top, Bottom}, TrackedSymbols -> Manipulate}, "DefaultOptions" :> {}], ImageSizeCache->{1055., {365., 370.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>({{$CellContext`createCircle[{{ Pattern[$CellContext`x1, Blank[]], Pattern[$CellContext`y1, Blank[]]}, { Pattern[$CellContext`x2, Blank[]], Pattern[$CellContext`y2, Blank[]]}}] := With[{$CellContext`a = Det[{{$CellContext`x1, $CellContext`y1, 1}, {$CellContext`x2, $CellContext`y2, 1}, {0, 0, 1}}], $CellContext`d = - Det[{{$CellContext`x1^2 + $CellContext`y1^2, $CellContext`y1, 1}, {$CellContext`x2^2 + $CellContext`y2^2, $CellContext`y2, 1}, {0, 0, 1}}], $CellContext`e = Det[{{$CellContext`x1^2 + $CellContext`y1^2, $CellContext`x1, 1}, {$CellContext`x2^2 + $CellContext`y2^2, $CellContext`x2, 1}, {0, 0, 1}}], $CellContext`f = - Det[{{$CellContext`x1^2 + $CellContext`y1^2, $CellContext`x1, \ $CellContext`y1}, {$CellContext`x2^2 + $CellContext`y2^2, $CellContext`x2, \ $CellContext`y2}, {0, 0, 0}}]}, Circle[{-($CellContext`d/(2 $CellContext`a)), -($CellContext`e/( 2 $CellContext`a))}, Sqrt[($CellContext`d^2 + $CellContext`e^2)/( 4 $CellContext`a^2) - $CellContext`f/$CellContext`a]]], \ $CellContext`f[{ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`y, Blank[]]}] := ($CellContext`x - $CellContext`y) Exp[$CellContext`x^2 - $CellContext`y^2], $CellContext`center[{{ Pattern[$CellContext`x1, Blank[]], Pattern[$CellContext`y1, Blank[]]}, { Pattern[$CellContext`x2, Blank[]], Pattern[$CellContext`y2, Blank[]]}}] := With[{$CellContext`a = Det[{{$CellContext`x1, $CellContext`y1, 1}, {$CellContext`x2, $CellContext`y2, 1}, {0, 0, 1}}], $CellContext`d = - Det[{{$CellContext`x1^2 + $CellContext`y1^2, $CellContext`y1, 1}, {$CellContext`x2^2 + $CellContext`y2^2, $CellContext`y2, 1}, {0, 0, 1}}], $CellContext`e = Det[{{$CellContext`x1^2 + $CellContext`y1^2, $CellContext`x1, 1}, {$CellContext`x2^2 + $CellContext`y2^2, $CellContext`x2, 1}, {0, 0, 1}}], $CellContext`f = - Det[{{$CellContext`x1^2 + $CellContext`y1^2, $CellContext`x1, \ $CellContext`y1}, {$CellContext`x2^2 + $CellContext`y2^2, $CellContext`x2, \ $CellContext`y2}, {0, 0, 0}}]}, {-($CellContext`d/( 2 $CellContext`a)), -($CellContext`e/( 2 $CellContext`a))}], $CellContext`radius[{{ Pattern[$CellContext`x1, Blank[]], Pattern[$CellContext`y1, Blank[]]}, { Pattern[$CellContext`x2, Blank[]], Pattern[$CellContext`y2, Blank[]]}}] := With[{$CellContext`a = Det[{{$CellContext`x1, $CellContext`y1, 1}, {$CellContext`x2, $CellContext`y2, 1}, {0, 0, 1}}], $CellContext`d = - Det[{{$CellContext`x1^2 + $CellContext`y1^2, $CellContext`y1, 1}, {$CellContext`x2^2 + $CellContext`y2^2, $CellContext`y2, 1}, {0, 0, 1}}], $CellContext`e = Det[{{$CellContext`x1^2 + $CellContext`y1^2, $CellContext`x1, 1}, {$CellContext`x2^2 + $CellContext`y2^2, $CellContext`x2, 1}, {0, 0, 1}}], $CellContext`f = - Det[{{$CellContext`x1^2 + $CellContext`y1^2, $CellContext`x1, \ $CellContext`y1}, {$CellContext`x2^2 + $CellContext`y2^2, $CellContext`x2, \ $CellContext`y2}, {0, 0, 0}}]}, Sqrt[($CellContext`d^2 + $CellContext`e^2)/( 4 $CellContext`a^2) - $CellContext`f/$CellContext`a]]}; \ {$CellContext`createCircle[{{ Pattern[$CellContext`x1, Blank[]], Pattern[$CellContext`y1, Blank[]]}, { Pattern[$CellContext`x2, Blank[]], Pattern[$CellContext`y2, Blank[]]}}] := With[{$CellContext`a = Det[{{$CellContext`x1, $CellContext`y1, 1}, {$CellContext`x2, $CellContext`y2, 1}, {0, 0, 1}}], $CellContext`d = - Det[{{$CellContext`x1^2 + $CellContext`y1^2, $CellContext`y1, 1}, {$CellContext`x2^2 + $CellContext`y2^2, $CellContext`y2, 1}, {0, 0, 1}}], $CellContext`e = Det[{{$CellContext`x1^2 + $CellContext`y1^2, $CellContext`x1, 1}, {$CellContext`x2^2 + $CellContext`y2^2, $CellContext`x2, 1}, {0, 0, 1}}], $CellContext`f = - Det[{{$CellContext`x1^2 + $CellContext`y1^2, $CellContext`x1, \ $CellContext`y1}, {$CellContext`x2^2 + $CellContext`y2^2, $CellContext`x2, \ $CellContext`y2}, {0, 0, 0}}]}, Circle[{-($CellContext`d/(2 $CellContext`a)), -($CellContext`e/( 2 $CellContext`a))}, (($CellContext`d^2 + $CellContext`e^2)/( 4 $CellContext`a^2) - $CellContext`f/$CellContext`a)^ Rational[1, 2]]]; $CellContext`radius[{{ Pattern[$CellContext`x1, Blank[]], Pattern[$CellContext`y1, Blank[]]}, { Pattern[$CellContext`x2, Blank[]], Pattern[$CellContext`y2, Blank[]]}}] := With[{$CellContext`a = Det[{{$CellContext`x1, $CellContext`y1, 1}, {$CellContext`x2, $CellContext`y2, 1}, {0, 0, 1}}], $CellContext`d = - Det[{{$CellContext`x1^2 + $CellContext`y1^2, $CellContext`y1, 1}, {$CellContext`x2^2 + $CellContext`y2^2, $CellContext`y2, 1}, {0, 0, 1}}], $CellContext`e = Det[{{$CellContext`x1^2 + $CellContext`y1^2, $CellContext`x1, 1}, {$CellContext`x2^2 + $CellContext`y2^2, $CellContext`x2, 1}, {0, 0, 1}}], $CellContext`f = - Det[{{$CellContext`x1^2 + $CellContext`y1^2, $CellContext`x1, \ $CellContext`y1}, {$CellContext`x2^2 + $CellContext`y2^2, $CellContext`x2, \ $CellContext`y2}, {0, 0, 0}}]}, (($CellContext`d^2 + $CellContext`e^2)/( 4 $CellContext`a^2) - $CellContext`f/$CellContext`a)^ Rational[1, 2]]; $CellContext`center[{{ Pattern[$CellContext`x1, Blank[]], Pattern[$CellContext`y1, Blank[]]}, { Pattern[$CellContext`x2, Blank[]], Pattern[$CellContext`y2, Blank[]]}}] := With[{$CellContext`a = Det[{{$CellContext`x1, $CellContext`y1, 1}, {$CellContext`x2, $CellContext`y2, 1}, {0, 0, 1}}], $CellContext`d = - Det[{{$CellContext`x1^2 + $CellContext`y1^2, $CellContext`y1, 1}, {$CellContext`x2^2 + $CellContext`y2^2, $CellContext`y2, 1}, {0, 0, 1}}], $CellContext`e = Det[{{$CellContext`x1^2 + $CellContext`y1^2, $CellContext`x1, 1}, {$CellContext`x2^2 + $CellContext`y2^2, $CellContext`x2, 1}, {0, 0, 1}}], $CellContext`f = - Det[{{$CellContext`x1^2 + $CellContext`y1^2, $CellContext`x1, \ $CellContext`y1}, {$CellContext`x2^2 + $CellContext`y2^2, $CellContext`x2, \ $CellContext`y2}, {0, 0, 0}}]}, {-($CellContext`d/( 2 $CellContext`a)), -($CellContext`e/(2 $CellContext`a))}]; Null}}; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{3.470242685640625*^9}] }, 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