(* 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[ 20957, 579] NotebookOptionsPosition[ 19701, 532] NotebookOutlinePosition[ 20059, 548] CellTagsIndexPosition[ 20016, 545] WindowFrame->Normal ContainsDynamic->False*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Triangle angles", "Title", CellChangeTimes->{{3.410560259357154*^9, 3.4105602623774853`*^9}, { 3.413876547345669*^9, 3.413876548853537*^9}, {3.416291007466495*^9, 3.416291015326582*^9}, {3.416546173678588*^9, 3.416546174904448*^9}, { 3.416750299945694*^9, 3.416750302594899*^9}, {3.4196897600002127`*^9, 3.4196897717154818`*^9}, {3.431370257113245*^9, 3.431370259079279*^9}, { 3.432401681829069*^9, 3.43240168511698*^9}, {3.434966422709402*^9, 3.434966424650836*^9}}, Background->RGBColor[ 0.7500114442664225, 0.7500114442664225, 0.7500114442664225]], Cell["JOR, 22Jan04; revised 6Nov08", "Subtitle", CellChangeTimes->{{3.410560275360083*^9, 3.410560281582642*^9}, 3.4105610555934*^9, {3.413876554034669*^9, 3.413876554703198*^9}, { 3.416290998841281*^9, 3.416291000542302*^9}, {3.416546178619573*^9, 3.416546179094122*^9}, 3.4167502971439342`*^9, {3.419689775221615*^9, 3.419689776246386*^9}, {3.43137026406847*^9, 3.4313702655215807`*^9}, { 3.432401665639081*^9, 3.432401677741083*^9}, {3.434966429715907*^9, 3.4349664434997597`*^9}, {3.434967387378859*^9, 3.434967388408984*^9}}, Background->RGBColor[ 0.7500114442664225, 0.7500114442664225, 0.7500114442664225]], Cell[TextData[{ StyleBox["a, b, c are the corners (in 2D or 3D -- doesn't matter).\nA, B, C \ the edge lengths, A from a to b, etc. [CC because C is protected!]\nalpha, \ beta, gamma the angles, with alpha opposite A etc.\nNote this means that the \ angle at a is beta, because B is opposite a.\nNot the best decision, I know, \ but that is why they are returned in the peculiar order.\nReturns angles in ", FontSize->14, FontColor->GrayLevel[0], Background->None], StyleBox["radians", FontSize->14, FontSlant->"Italic", FontColor->GrayLevel[0], Background->None], StyleBox[", first angle at a, etc. Return as list.\nNB: No error checking -- \ crashes if triangle has an edge of zero length.\nTriAngles[] is the main \ function, but TriMidAngle[] extracts just the middle angle, following the \ usual convention.", FontSize->14, FontColor->GrayLevel[0], Background->None] }], "Text", CellFrame->True, CellChangeTimes->{{3.4168060866424313`*^9, 3.416806102121842*^9}, { 3.416806550143208*^9, 3.4168065517862883`*^9}, {3.416806780684826*^9, 3.416806796852281*^9}, {3.418180164949278*^9, 3.41818021614887*^9}, { 3.418180353639224*^9, 3.418180385151347*^9}, {3.418180427574439*^9, 3.4181804363443413`*^9}, 3.4181804664334173`*^9, {3.4181808075326653`*^9, 3.418180819246889*^9}, {3.41818086609838*^9, 3.418180962161561*^9}, { 3.418228348278067*^9, 3.418228402808107*^9}, {3.4196897798203983`*^9, 3.419689790903858*^9}, {3.419768674350041*^9, 3.419768688381897*^9}, { 3.431370271008016*^9, 3.431370405176326*^9}, {3.4349664533835983`*^9, 3.43496645686248*^9}, 3.434966488800474*^9, {3.434966662471678*^9, 3.434966747050359*^9}, {3.434967405337968*^9, 3.4349674132342*^9}, { 3.435595080485433*^9, 3.435595123355618*^9}}, Background->GrayLevel[0.833326]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"FUZZ", " ", "=", " ", "0.000001"}], ";"}], StyleBox[" ", FontColor->RGBColor[0, 0, 1]], StyleBox[ RowBox[{"(*", " ", RowBox[{"Overly", " ", RowBox[{"generous", "!"}]}], " ", "*)"}], FontColor->RGBColor[0, 0, 1]], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"(*", RowBox[{"Conversion", " ", "functions"}], "*)"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"RadDeg", "[", "a_", "]"}], " ", ":=", " ", RowBox[{"N", "[", " ", RowBox[{"180", " ", RowBox[{"a", " ", "/", " ", "Pi"}]}], " ", "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"DegRad", "[", "a_", "]"}], " ", ":=", " ", RowBox[{"N", "[", " ", RowBox[{"Pi", " ", RowBox[{"a", "/", "180"}]}], " ", "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"DegRad", "[", "10", "]"}]}], "Input", CellChangeTimes->{{3.434966556788962*^9, 3.434966574180563*^9}, { 3.434967035866214*^9, 3.434967042418347*^9}, {3.436031977044414*^9, 3.436031980720495*^9}}], Cell[BoxData["0.17453292519943295`"], "Output", CellChangeTimes->{3.436031981549569*^9}] }, Open ]], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"TriAngles", "[", RowBox[{"a_", ",", "b_", ",", "c_"}], "]"}], " ", ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{ "A", ",", "B", ",", "CC", ",", "alpha", ",", "beta", ",", "gamma"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"A", " ", "=", " ", RowBox[{ RowBox[{"Sqrt", "[", " ", RowBox[{ RowBox[{"(", RowBox[{"b", "-", "a"}], ")"}], ".", RowBox[{"(", RowBox[{"b", "-", "a"}], ")"}]}], "]"}], "//", "N"}]}], ";", "\[IndentingNewLine]", RowBox[{"B", " ", "=", " ", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{ RowBox[{"(", RowBox[{"c", "-", "b"}], ")"}], ".", RowBox[{"(", RowBox[{"c", "-", "b"}], ")"}]}], "]"}], "//", "N"}]}], ";", "\[IndentingNewLine]", RowBox[{"CC", "=", " ", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{ RowBox[{"(", RowBox[{"a", "-", "c"}], ")"}], ".", RowBox[{"(", RowBox[{"a", "-", "c"}], ")"}]}], "]"}], "//", "N"}]}], ";", "\[IndentingNewLine]", RowBox[{"beta", " ", "=", " ", RowBox[{ RowBox[{"ArcCos", "[", " ", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"CC", "^", "2"}], " ", "+", RowBox[{"A", "^", "2"}], " ", "-", " ", RowBox[{"B", "^", "2"}]}], ")"}], "/", RowBox[{"(", RowBox[{"2", " ", "CC", " ", "A"}], ")"}]}], "]"}], "//", "N"}]}], ";", "\[IndentingNewLine]", RowBox[{"gamma", " ", "=", " ", RowBox[{ RowBox[{"ArcCos", "[", " ", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"A", "^", "2"}], " ", "+", " ", RowBox[{"B", "^", "2"}], " ", "-", " ", RowBox[{"CC", "^", "2"}]}], ")"}], "/", RowBox[{"(", RowBox[{"2", " ", "A", " ", "B"}], ")"}]}], "]"}], "//", "N"}]}], ";", "\[IndentingNewLine]", RowBox[{"alpha", " ", "=", " ", RowBox[{ RowBox[{"ArcCos", "[", " ", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"B", "^", "2"}], " ", "+", " ", RowBox[{"CC", "^", "2"}], " ", "-", RowBox[{"A", "^", "2"}]}], ")"}], "/", RowBox[{"(", RowBox[{"2", " ", "B", " ", "CC"}], " ", ")"}]}], "]"}], "//", "N"}]}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{ RowBox[{ RowBox[{"Abs", "[", " ", RowBox[{ "alpha", " ", "+", " ", "beta", " ", "+", " ", "gamma", " ", "-", " ", "Pi"}], "]"}], " ", ">", " ", "FUZZ"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ "Print", "[", "\"\\"", "]"}], ";", "\[IndentingNewLine]", "Break", ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", RowBox[{"If", "[", RowBox[{"DEBUG", ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"Print", "[", RowBox[{"\"\\"", ",", RowBox[{"{", RowBox[{"A", ",", "B", ",", "CC"}], "}"}]}], "]"}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", RowBox[{"\"\\"", ",", " ", RowBox[{"RadDeg", "[", "beta", "]"}], ",", "\"\<,\>\"", ",", " ", RowBox[{"RadDeg", "[", "gamma", "]"}], ",", "\"\<,\>\"", ",", " ", RowBox[{"RadDeg", "[", "alpha", "]"}], ",", "\"\<; Angle sum = \>\"", ",", " ", RowBox[{"RadDeg", "[", RowBox[{"alpha", "+", "beta", "+", "gamma"}], "]"}]}], "]"}], ";"}]}], "\[IndentingNewLine]", "]"}], ";", "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Return", "[", " ", RowBox[{"{", " ", RowBox[{"beta", ",", " ", "gamma", ",", " ", "alpha"}], "}"}], "]"}], ";"}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"TriLengths", "[", RowBox[{"a_", ",", "b_", ",", "c_"}], "]"}], " ", ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", RowBox[{"A", ",", "B", ",", "CC"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"A", " ", "=", " ", RowBox[{ RowBox[{"Sqrt", "[", " ", RowBox[{ RowBox[{"(", RowBox[{"b", "-", "a"}], ")"}], ".", RowBox[{"(", RowBox[{"b", "-", "a"}], ")"}]}], "]"}], "//", "N"}]}], ";", "\[IndentingNewLine]", RowBox[{"B", " ", "=", " ", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{ RowBox[{"(", RowBox[{"c", "-", "b"}], ")"}], ".", RowBox[{"(", RowBox[{"c", "-", "b"}], ")"}]}], "]"}], "//", "N"}]}], ";", "\[IndentingNewLine]", RowBox[{"CC", "=", " ", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{ RowBox[{"(", RowBox[{"a", "-", "c"}], ")"}], ".", RowBox[{"(", RowBox[{"a", "-", "c"}], ")"}]}], "]"}], "//", "N"}]}], ";", "\[IndentingNewLine]", RowBox[{"Return", "[", RowBox[{"{", RowBox[{"A", ",", "B", ",", "CC"}], "}"}], "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"TriDraw", "[", RowBox[{"a_", ",", "b_", ",", "c_"}], "]"}], " ", ":=", " ", RowBox[{"Module", "[", RowBox[{ RowBox[{"{", "g", "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"g", "=", RowBox[{"Graphics", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"Red", ",", " ", "Thick", ",", " ", RowBox[{"Line", "[", RowBox[{"{", RowBox[{"a", ",", "b", ",", "c", ",", "a"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"Text", "[", RowBox[{"\"\\"", ",", "a"}], "]"}], ",", RowBox[{"Text", "[", RowBox[{"\"\\"", ",", "b"}], "]"}], ",", RowBox[{"Text", "[", RowBox[{"\"\\"", ",", "b"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Text", "[", RowBox[{"\"\\"", ",", RowBox[{ RowBox[{"(", RowBox[{"a", "+", "b"}], ")"}], "/", "2"}]}], "]"}], ",", RowBox[{"Text", "[", RowBox[{"\"\\"", ",", RowBox[{ RowBox[{"(", RowBox[{"b", "+", "c"}], ")"}], "/", "2"}]}], "]"}], ",", RowBox[{"Text", "[", RowBox[{"\"\\"", ",", RowBox[{ RowBox[{"(", RowBox[{"c", "+", "a"}], ")"}], "/", "2"}]}], "]"}]}], "}"}]}], "\[IndentingNewLine]", "}"}], "\[IndentingNewLine]", ",", RowBox[{"Axes", "\[Rule]", "True"}], "\[IndentingNewLine]", ",", RowBox[{"AspectRatio", "\[Rule]", "Automatic"}]}], "\[IndentingNewLine]", "]"}]}], ";", "\[IndentingNewLine]", RowBox[{"Print", "[", "g", "]"}]}]}], "\[IndentingNewLine]", "]"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"TriMidAngle", "[", RowBox[{"a_", ",", "b_", ",", "c_"}], "]"}], " ", ":=", RowBox[{ RowBox[{"TriAngles", "[", RowBox[{"a", ",", "b", ",", "c"}], "]"}], "[", RowBox[{"[", "2", "]"}], "]"}]}], ";"}]}], "Input", CellChangeTimes->{{3.434966935321957*^9, 3.434966959468293*^9}, { 3.434967055170506*^9, 3.434967162158764*^9}, {3.43535490556082*^9, 3.43535493168505*^9}, {3.435355941273019*^9, 3.43535597279338*^9}, { 3.435591131870892*^9, 3.4355911834818125`*^9}}], Cell["Testing ....", "Text", CellChangeTimes->{{3.4349669024678307`*^9, 3.4349669083943996`*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"DEBUG", "=", "True"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"a", ",", "b", ",", "c"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"TriDraw", "[", RowBox[{"a", ",", "b", ",", "c"}], "]"}], ";", RowBox[{"TriAngles", "[", RowBox[{"a", ",", "b", ",", "c"}], "]"}]}]}], "Input", CellChangeTimes->{{3.4349669860717983`*^9, 3.434967030899016*^9}, 3.434967350640184*^9}], Cell[CellGroupData[{ Cell[BoxData[ GraphicsBox[{ {RGBColor[1, 0, 0], Thickness[Large], LineBox[{{0, 0}, {1, 0}, {1, 1}, {0, 0}}]}, { InsetBox["\<\"a\"\>", {0, 0}], InsetBox["\<\"b\"\>", {1, 0}], InsetBox["\<\"b\"\>", {1, 0}], InsetBox["\<\"A\"\>", NCache[{Rational[1, 2], 0}, {0.5, 0}]], InsetBox["\<\"B\"\>", NCache[{1, Rational[1, 2]}, {1, 0.5}]], InsetBox["\<\"C\"\>", NCache[{Rational[1, 2], Rational[1, 2]}, {0.5, 0.5}]]}}, AspectRatio->Automatic, Axes->True]], "Print", CellChangeTimes->{3.434967080507225*^9, 3.434967166450552*^9, 3.434967252197639*^9, 3.435355033729569*^9, 3.4355911880302005`*^9, 3.43603135552497*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"Lengths A,B,C=\"\>", "\[InvisibleSpace]", RowBox[{"{", RowBox[{"1.`", ",", "1.`", ",", "1.4142135623730951`"}], "}"}]}], SequenceForm["Lengths A,B,C=", {1., 1., 1.4142135623730951`}], Editable->False]], "Print", CellChangeTimes->{3.434967080507225*^9, 3.434967166450552*^9, 3.434967252197639*^9, 3.435355033729569*^9, 3.4355911880302005`*^9, 3.436031355571678*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"Angles at a,b,c = \"\>", "\[InvisibleSpace]", "45.`", "\[InvisibleSpace]", "\<\",\"\>", "\[InvisibleSpace]", "90.00000000000001`", "\[InvisibleSpace]", "\<\",\"\>", "\[InvisibleSpace]", "45.`", "\[InvisibleSpace]", "\<\"; Angle sum = \"\>", "\[InvisibleSpace]", "180.`"}], SequenceForm[ "Angles at a,b,c = ", 45., ",", 90.00000000000001, ",", 45., "; Angle sum = ", 180.], Editable->False]], "Print", CellChangeTimes->{3.434967080507225*^9, 3.434967166450552*^9, 3.434967252197639*^9, 3.435355033729569*^9, 3.4355911880302005`*^9, 3.436031355587248*^9}] }, Open ]], Cell[BoxData[ RowBox[{"{", RowBox[{ "0.7853981633974483`", ",", "1.5707963267948968`", ",", "0.7853981633974483`"}], "}"}]], "Output", CellChangeTimes->{3.435355033785405*^9, 3.4355911881239815`*^9, 3.436031355898634*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"{", RowBox[{"a", ",", "b", ",", "c"}], "}"}], "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"Sqrt", "[", "3", "]"}], "/", "2"}], ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"Sqrt", "[", "3", "]"}], "/", "2"}], ",", RowBox[{"1", "/", "2"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"TriDraw", "[", RowBox[{"a", ",", "b", ",", "c"}], "]"}], ";", RowBox[{"TriAngles", "[", RowBox[{"a", ",", "b", ",", "c"}], "]"}]}]}], "Input", CellChangeTimes->{3.4349672250207663`*^9, 3.4349673411848783`*^9}], Cell[CellGroupData[{ Cell[BoxData[ GraphicsBox[{ {RGBColor[1, 0, 0], Thickness[Large], LineBox[NCache[{{0, 0}, {Rational[1, 2] 3^Rational[1, 2], 0}, { Rational[1, 2] 3^Rational[1, 2], Rational[1, 2]}, {0, 0}}, {{0, 0}, { 0.8660254037844386, 0}, {0.8660254037844386, 0.5}, {0, 0}}]]}, { InsetBox["\<\"a\"\>", {0, 0}], InsetBox["\<\"b\"\>", NCache[{Rational[1, 2] 3^Rational[1, 2], 0}, {0.8660254037844386, 0}]], InsetBox["\<\"b\"\>", NCache[{Rational[1, 2] 3^Rational[1, 2], 0}, {0.8660254037844386, 0}]], InsetBox["\<\"A\"\>", NCache[{Rational[1, 4] 3^Rational[1, 2], 0}, {0.4330127018922193, 0}]], InsetBox["\<\"B\"\>", NCache[{Rational[1, 2] 3^Rational[1, 2], Rational[1, 4]}, { 0.8660254037844386, 0.25}]], InsetBox["\<\"C\"\>", NCache[{Rational[1, 4] 3^Rational[1, 2], Rational[1, 4]}, { 0.4330127018922193, 0.25}]]}}, AspectRatio->Automatic, Axes->True]], "Print", CellChangeTimes->{{3.434967237102046*^9, 3.4349672611194477`*^9}, 3.435355033880404*^9, 3.435591188155242*^9, 3.4360313559297724`*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"Lengths A,B,C=\"\>", "\[InvisibleSpace]", RowBox[{"{", RowBox[{"0.8660254037844386`", ",", "0.5`", ",", "1.`"}], "}"}]}], SequenceForm["Lengths A,B,C=", {0.8660254037844386, 0.5, 1.}], Editable->False]], "Print", CellChangeTimes->{{3.434967237102046*^9, 3.4349672611194477`*^9}, 3.435355033880404*^9, 3.435591188155242*^9, 3.4360313559453416`*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"Angles at a,b,c = \"\>", "\[InvisibleSpace]", "29.99999999999998`", "\[InvisibleSpace]", "\<\",\"\>", "\[InvisibleSpace]", "90.00000000000001`", "\[InvisibleSpace]", "\<\",\"\>", "\[InvisibleSpace]", "60.`", "\[InvisibleSpace]", "\<\"; Angle sum = \"\>", "\[InvisibleSpace]", "180.`"}], SequenceForm[ "Angles at a,b,c = ", 29.99999999999998, ",", 90.00000000000001, ",", 60., "; Angle sum = ", 180.], Editable->False]], "Print", CellChangeTimes->{{3.434967237102046*^9, 3.4349672611194477`*^9}, 3.435355033880404*^9, 3.435591188155242*^9, 3.4360313559453416`*^9}] }, Open ]], Cell[BoxData[ RowBox[{"{", RowBox[{ "0.5235987755982985`", ",", "1.5707963267948968`", ",", "1.0471975511965976`"}], "}"}]], "Output", CellChangeTimes->{3.43535503390834*^9, 3.435591188233393*^9, 3.436031355960911*^9}] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"DEBUG", "=", "False"}], ";"}]], "Input"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"TriMidAngle", "[", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.4355911907342253`*^9, 3.435591217368086*^9}}], Cell[BoxData["1.5707963267948968`"], "Output", CellChangeTimes->{3.435591217899513*^9, 3.43603135597648*^9}] }, Open ]] }, Open ]] }, WindowSize->{1272, 997}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, Magnification->2., FrontEndVersion->"6.0 for Microsoft Windows (32-bit) (May 21, 2008)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[590, 23, 575, 9, 196, "Title"], Cell[1168, 34, 639, 9, 131, "Subtitle"], Cell[1810, 45, 1814, 36, 406, "Text"], Cell[CellGroupData[{ Cell[3649, 85, 1078, 32, 228, "Input"], Cell[4730, 119, 89, 1, 82, "Output"] }, Open ]], Cell[4834, 123, 8238, 213, 1384, "Input"], Cell[13075, 338, 98, 1, 55, "Text"], Cell[CellGroupData[{ Cell[13198, 343, 706, 22, 160, "Input"], Cell[CellGroupData[{ Cell[13929, 369, 656, 14, 732, "Print"], Cell[14588, 385, 433, 9, 43, "Print"], Cell[15024, 396, 635, 13, 43, "Print"] }, Open ]], Cell[15674, 412, 235, 6, 82, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[15946, 423, 763, 24, 126, "Input"], Cell[CellGroupData[{ Cell[16734, 451, 1086, 22, 448, "Print"], Cell[17823, 475, 414, 8, 43, "Print"], Cell[18240, 485, 647, 13, 43, "Print"] }, Open ]], Cell[18902, 501, 232, 6, 82, "Output"] }, Open ]], Cell[19149, 510, 75, 2, 57, "Input"], Cell[CellGroupData[{ Cell[19249, 516, 312, 9, 57, "Input"], Cell[19564, 527, 109, 1, 82, "Output"] }, Open ]] }, Open ]] } ] *) (* End of internal cache information *)