(* 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[ 44415, 860] NotebookOptionsPosition[ 27561, 559] NotebookOutlinePosition[ 44501, 862] CellTagsIndexPosition[ 44458, 859] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`ct$$ = False, $CellContext`fcn$$ = 1, $CellContext`m$$ = 20, $CellContext`n$$ = 20, $CellContext`nrm$$ = True, $CellContext`op$$ = 0.5, $CellContext`w$$ = 0.3, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`fcn$$], 1, Row[{ Spacer[30], Style[ "N={x,y,z}={Cos\[Theta] Sin\[Phi], Sin\[Theta] Sin\[Phi], 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$CellContext`u \ ($CellContext`w - 1)}; $CellContext`sp = 0, 4, $CellContext`h[{ Pattern[$CellContext`u, Blank[]], Pattern[$CellContext`v, Blank[]], Pattern[$CellContext`w, Blank[]]}] := {$CellContext`u^2/($CellContext`w - 1) + 1, $CellContext`u $CellContext`v/($CellContext`w - 1), $CellContext`u}; $CellContext`sp = 0, 5, $CellContext`h[ Pattern[$CellContext`u, Blank[]], Pattern[$CellContext`v, Blank[]]] := { Cos[$CellContext`u] Cos[$CellContext`v], Sin[$CellContext`u] Cos[$CellContext`v], -Sin[$CellContext`v]}; $CellContext`sp = 1, 6, $CellContext`h[ Pattern[$CellContext`u, Blank[]], Pattern[$CellContext`v, Blank[]]] := Sin[$CellContext`v] { Cos[$CellContext`u] Cos[$CellContext`v], Sin[$CellContext`u] Cos[$CellContext`v], -Sin[$CellContext`v]}; $CellContext`sp = 1]; $CellContext`mer = ParametricPlot3D[ $CellContext`Surf[0, $CellContext`v], {$CellContext`v, 0, 2 Pi}, PlotStyle -> {Red, Thick}]; $CellContext`NP = Graphics3D[{Blue, PointSize[0.015], Point[{0, 0, 1}]}]; $CellContext`SP = 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15]}, Center]]], Framed[ Show[ Plot3D[ Norm[ If[$CellContext`sp == 1, $CellContext`h[$CellContext`u, $CellContext`v], $CellContext`h[ $CellContext`Surf[$CellContext`u, $CellContext`v]]]], \ {$CellContext`u, 0, 2 Pi}, {$CellContext`v, 0, Pi}], Plot3D[ 0, {$CellContext`u, 0, 2 Pi}, {$CellContext`v, 0, Pi}, PlotStyle -> {Red}], PlotRange -> {{0, 2 Pi}, {0, Pi}, Automatic}, AxesLabel -> { Style["\[Theta]", Bold, 15], Style["\[Phi]", Bold, 15], ""}, PlotLabel -> Column[{ Style[ "\[LeftDoubleBracketingBar]\!\(\*\nStyleBox[\"F\",\n\ FontColor->RGBColor[0, 0, 1]]\)\[RightDoubleBracketingBar]", 20, Bold], Style[ "\!\(\*\nStyleBox[\"F\",\nFontColor->RGBColor[0, 0, 1]]\)\ \!\(\*\nStyleBox[\" \",\nFontColor->RGBColor[0, 0, 1]]\)is not zero", 15]}, Center], ImageSize -> {260, 240}]]}, Center]]}]], ImageSize -> {1080, 600}, Alignment -> {Center, Center}], "Specifications" :> {{{$CellContext`fcn$$, 1, Row[{ Spacer[30], Style[ "N={x,y,z}={Cos\[Theta] Sin\[Phi], Sin\[Theta] Sin\[Phi], Cos\ \[Phi]}", 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