(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 8.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 157, 7] NotebookDataLength[ 261884, 7601] NotebookOptionsPosition[ 237284, 6978] NotebookOutlinePosition[ 249331, 7264] CellTagsIndexPosition[ 248876, 7248] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell["Math 421 \[FilledSmallCircle] Fall 2010", "Subsubtitle", CellChangeTimes->{{3.490633146828125*^9, 3.490633147125*^9}}, TextAlignment->Center], Cell[CellGroupData[{ Cell[TextData[{ "Drawing geometric objects in the complex plane\nwith ", StyleBox["Presentations", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"] }], "Subtitle", CellChangeTimes->{{3.490633151109375*^9, 3.490633153640625*^9}, { 3.490638885796875*^9, 3.4906388860625*^9}, {3.4908943385625*^9, 3.490894370703125*^9}, {3.49346249421875*^9, 3.493462498578125*^9}}, TextAlignment->Center, TextJustification->0], Cell["26 September 2010", "Subsubtitle", CellChangeTimes->{{3.49063315875*^9, 3.49063316615625*^9}, 3.490789668859375*^9, 3.490898365109375*^9, 3.4909829021875*^9, { 3.49116718778125*^9, 3.491167189703125*^9}, 3.49122306675*^9, { 3.492292855203125*^9, 3.492292855875*^9}, {3.49251755234375*^9, 3.492517555046875*^9}, {3.493217492546875*^9, 3.49321749271875*^9}, 3.4932968269375*^9, 3.49346247953125*^9, {3.493817752640625*^9, 3.4938177531875*^9}, {3.494150149125*^9, 3.494150149453125*^9}, 3.494500334796875*^9}, TextAlignment->Center], Cell["\<\ Based in part upon documentation written by David Park; edited and amended by \ Murray Eisenberg.\ \>", "SmallText", CellChangeTimes->{ 3.490634020328125*^9, {3.490821544476466*^9, 3.490821570382716*^9}, { 3.490822149585841*^9, 3.490822149992091*^9}}, TextAlignment->Center, TextJustification->0], Cell[TextData[{ "When you open this notebook, you should see a pop-up window asking whether \ you want to evaluate the Initialization Cells. You should select ", StyleBox["Yes", FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain"], "." }], "EmphasisText", CellChangeTimes->{ 3.490633836984375*^9, {3.49089844703125*^9, 3.490898447765625*^9}}], Cell[TextData[{ StyleBox["Explanation", FontSlant->"Italic"], ": In the section \"Initialization\" below, there's an Input cell \ consisting of the expression\n\t", StyleBox["<"Courier", FontWeight->"Plain", FontSlant->"Plain"], "\nand I made that cell into an \"initialization cell\". When you answered \ yes, that cell was evaluated automatically, and this in effect loaded the ", StyleBox["Presentations", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], " application packages." }], "SmallText", CellChangeTimes->{{3.490633867953125*^9, 3.490633922609375*^9}, { 3.490650173484375*^9, 3.49065017828125*^9}, {3.490907105859375*^9, 3.490907106171875*^9}}, ParagraphSpacing->{0.7, 0}], Cell[TextData[{ "This notebook is a tutorial on doing complex graphics using the ", StyleBox["Presentations", FontSlant->"Italic"], " application. You may want to consult it before tackling the notebook ", StyleBox["nthRoots.nb", FontFamily->"Courier"], ". The latter provides additional examples." }], "Text", CellChangeTimes->{{3.490633826*^9, 3.4906338316875*^9}, { 3.490821625538966*^9, 3.490821675929591*^9}, {3.490898385265625*^9, 3.49089838665625*^9}}], Cell[CellGroupData[{ Cell["Prerequisites", "Section", CellChangeTimes->{{3.466616366328125*^9, 3.46661637828125*^9}, { 3.466616604453125*^9, 3.466616607390625*^9}}], Cell[CellGroupData[{ Cell[TextData[StyleBox["Mathematica", FontSlant->"Italic"]], "Subsection", CellChangeTimes->{{3.466616614109375*^9, 3.466616621015625*^9}}], Cell[TextData[{ "Most of this notebook requires that you have ", "David Park\[CloseCurlyQuote]s ", StyleBox["Presentations", FontSlant->"Italic"], " add-on for ", StyleBox["Mathematica", FontSlant->"Italic"], " available on the computer where you are using ", StyleBox["Mathematica", FontSlant->"Italic"], ".", " (See notebook ", StyleBox["AboutPresentations.nb", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], ".)" }], "Text", CellChangeTimes->{{3.46661644090625*^9, 3.466616483484375*^9}, { 3.466616542578125*^9, 3.466616591375*^9}, {3.4666167129375*^9, 3.466616714296875*^9}, {3.490983043921875*^9, 3.490983044875*^9}, { 3.490984276765625*^9, 3.4909843116875*^9}, {3.4910590243125*^9, 3.491059033125*^9}, {3.49116693490625*^9, 3.491166943421875*^9}}], Cell[TextData[{ "In order to reproduce graphics output from this notebook, you must have \ loaded ", StyleBox["Presentations", FontSlant->"Italic"], " by evaluating the expression:\n\t", StyleBox["<<", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Italic"], StyleBox["Presentations", FontFamily->"Courier", FontWeight->"Plain"], StyleBox["`", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], "\nThat initialization is done below, in the ", ButtonBox["Initialization section", BaseStyle->"Hyperlink", ButtonData->"initialization"], ", below." }], "Text", CellChangeTimes->{{3.46661644090625*^9, 3.466616483484375*^9}, { 3.466616542578125*^9, 3.466616591375*^9}, {3.4666167129375*^9, 3.46661679353125*^9}, {3.4666168744375*^9, 3.466616901171875*^9}, { 3.4909830825*^9, 3.4909830910625*^9}, {3.490984498375*^9, 3.49098451746875*^9}, {3.491058732328125*^9, 3.491058740734375*^9}, 3.491058892734375*^9, {3.491058930921875*^9, 3.491059018609375*^9}, { 3.491059057390625*^9, 3.491059075953125*^9}, {3.49105918140625*^9, 3.49105918140625*^9}, {3.491059247640625*^9, 3.49105924765625*^9}, { 3.491059412859375*^9, 3.491059447375*^9}}, ParagraphSpacing->{0.5, 0.}], Cell[TextData[{ "You should already know some of the basics about ", StyleBox["Mathematica", FontSlant->"Italic"], ": basic syntax; how to navigate around a ", StyleBox["Mathematica", FontSlant->"Italic"], " notebook; how to create an Input cell and type input into it; and how to \ evaluate an Input cell." }], "Text", CellChangeTimes->{{3.4911590738125*^9, 3.491159285734375*^9}, { 3.491166982578125*^9, 3.491166982953125*^9}}], Cell[TextData[{ "It\[CloseCurlyQuote]s a good idea to use this notebook as additional \ reference as you work through a notebook more substantial mathematical \ content, such as ", StyleBox["nthRoots.nb", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], "." }], "Text", CellChangeTimes->{{3.491222989953125*^9, 3.491223041359375*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["Mathematics", "Subsection", CellChangeTimes->{{3.46661662978125*^9, 3.466616631109375*^9}}], Cell["\<\ You should already know the basics of the algebra of complex numbers\ \[LongDash]how to add and multiply them\[LongDash]and the representation of \ complex numbers by points in the plane. \ \>", "Text", CellChangeTimes->{{3.466616634859375*^9, 3.46661670978125*^9}}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Initialization", "Section", ShowGroupOpener->True, CellChangeTimes->{{3.4906339376875*^9, 3.49063394653125*^9}, { 3.490638317984375*^9, 3.49063833975*^9}, {3.490735161125*^9, 3.490735165125*^9}, 3.490984367984375*^9}, CellTags->"initialization"], Cell[TextData[{ "When you opened this notebook, it should have prompted you whether you want \ to evaluate Initialization Cells. You should have answered \ \[OpenCurlyDoubleQuote]yes.\[CloseCurlyDoubleQuote]\nCheck now whether you \ did so by looking at the Input cell that follows. At its left it should have \ a label such as ", StyleBox["In[1]", FontFamily->"Helvetica", FontWeight->"Plain", FontSlant->"Plain"], ".\nIf you do not see such a label, then ", StyleBox["evaluate the following Input cell now", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], ". (Even if the cell was already evaluated, it won\[CloseCurlyQuote]t hurt \ if you evaluate it again.)" }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.490634229484375*^9, 3.49063436175*^9}, 3.490634682*^9, { 3.490634737515625*^9, 3.4906347940625*^9}, {3.490700557578125*^9, 3.49070056315625*^9}, 3.49073510265625*^9, 3.490735145640625*^9}, ParagraphSpacing->{0.5, 0.}], Cell[BoxData[ RowBox[{"<<", "Presentations`"}]], "Input", ShowGroupOpener->True, InitializationCell->True, CellChangeTimes->{{3.49063458959375*^9, 3.490634598328125*^9}, { 3.490650191265625*^9, 3.49065019440625*^9}}, CellTags->"load"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Forming ", StyleBox["Complex Graphics", FontSlant->"Italic"], " objects" }], "Section", ShowGroupOpener->True, CellChangeTimes->{{3.49381277684375*^9, 3.493812786546875*^9}}], Cell[TextData[{ "The basic method for plotting graphical objects with ", StyleBox["Mathematica", FontSlant->"Italic"], " is to use a ", StyleBox["Graphics[{", FontFamily->"Courier"], StyleBox["\[Ellipsis]", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], StyleBox["}]", FontFamily->"Courier"], " expression. Within the braces, you include commands that set the ", StyleBox["graphics directives", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], " to be used (such as color or line thickness) along with the ", StyleBox["graphics primitives", FontWeight->"Bold", FontSlant->"Plain", FontColor->RGBColor[0, 0, 1]], " that actually draw the objects (such as ", StyleBox["Point", FontFamily->"Courier"], " and ", StyleBox["Line", FontFamily->"Courier"], "). In this way, you can build up a rather complicated graphics." }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.4906394383125*^9, 3.4906394411875*^9}, { 3.49063983184375*^9, 3.490639873015625*^9}, {3.49065963978125*^9, 3.490659640765625*^9}, 3.493812906734375*^9}], Cell[TextData[{ "The ", Cell[BoxData[ StyleBox[ RowBox[{"Complex", " ", "Graphics"}], FontFamily->"Times", FontSlant->"Italic"]]], " part of ", StyleBox["Presentations", FontSlant->"Italic"], " contains a number of complex primitives that mirror the ordinary ", StyleBox["Mathematica", FontSlant->"Italic"], " graphics primitives, but allow complex numbers to be used instead of real \ coordinate pairs." }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.490639462546875*^9, 3.490639466640625*^9}, { 3.490639888765625*^9, 3.49063991753125*^9}, {3.490659732359375*^9, 3.490659736609375*^9}, 3.493658960984375*^9, {3.493812878421875*^9, 3.4938129015625*^9}}], Cell[TextData[{ StyleBox["To construct a complex point", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], " use the ", StyleBox["Presentations", FontSlant->"Italic"], " function ", StyleBox["ComplexPoint", FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"], ". For example:" }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.490639462546875*^9, 3.490639466640625*^9}, { 3.490639888765625*^9, 3.49063991753125*^9}, {3.490659732359375*^9, 3.490659736609375*^9}, {3.493658960984375*^9, 3.4936590105*^9}, 3.4938135083125*^9}], Cell[BoxData[ RowBox[{"ComplexPoint", "[", RowBox[{"1", "+", "\[ImaginaryI]"}], "]"}]], "Input", CellChangeTimes->{{3.490639493546875*^9, 3.490639499453125*^9}}], Cell[TextData[{ "The result is an ordinary ", StyleBox["Mathematica", FontSlant->"Italic"], " ", StyleBox["Point", FontFamily->"Courier"], " graphics primitive expression." }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.490639811921875*^9, 3.490639820375*^9}, { 3.49063992134375*^9, 3.490639957421875*^9}, {3.490659749453125*^9, 3.490659824609375*^9}, {3.4907010556875*^9, 3.49070108325*^9}, { 3.493659022640625*^9, 3.493659069234375*^9}}], Cell[TextData[{ "Similarly, ", StyleBox["to construct a polygonal curve", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], "\[LongDash]a \"broken line\"\[LongDash]use the ", StyleBox["Presentations", FontSlant->"Italic"], " function ComplexLine. For example, to construct the polygonal curve that \ goes from 0 to 1 to ", Cell[BoxData[ FormBox[ RowBox[{"1", "+", "\[ImaginaryI]"}], TraditionalForm]]], " to ", Cell[BoxData[ FormBox["\[ImaginaryI]", TraditionalForm]]], " and back to ", Cell[BoxData[ FormBox["0", TraditionalForm]]], ", you may use:" }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.490639811921875*^9, 3.490639820375*^9}, { 3.49063992134375*^9, 3.490639957421875*^9}, {3.490659749453125*^9, 3.490659824609375*^9}, {3.4907010556875*^9, 3.49070108325*^9}, { 3.493659022640625*^9, 3.493659070578125*^9}, 3.49381350109375*^9}], Cell[BoxData[ RowBox[{"ComplexLine", "[", RowBox[{"{", RowBox[{"0", ",", "1", ",", RowBox[{"1", "+", "\[ImaginaryI]"}], ",", "\[ImaginaryI]", ",", "0"}], "}"}], "]"}]], "Input", ShowGroupOpener->True, CellChangeTimes->{{3.490639968796875*^9, 3.490639975359375*^9}, { 3.490640739890625*^9, 3.490640751359375*^9}, {3.49070108734375*^9, 3.490701110125*^9}}], Cell[TextData[{ "The result is an ordinary ", StyleBox["Mathematica", FontSlant->"Italic"], " ", StyleBox["Line", FontFamily->"Courier"], " graphics primitive expression." }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.490639979734375*^9, 3.490639985125*^9}, { 3.490659834765625*^9, 3.490659840625*^9}}], Cell[TextData[{ "The ", StyleBox["Complex Graphics", FontSlant->"Italic"], " primitives of this type include: ", StyleBox["ComplexArrow", FontFamily->"Courier"], ", ", StyleBox["ComplexCircle", FontFamily->"Courier"], ", ", StyleBox["ComplexDisk", FontFamily->"Courier"], ", ", StyleBox["ComplexLine", FontFamily->"Courier"], ", ", StyleBox["ComplexPoint", FontFamily->"Courier"], ", ", StyleBox["ComplexPolygon", FontFamily->"Courier"], ", and ", StyleBox["ComplexText", FontFamily->"Courier"], ". Also available is the graphics primitive ", StyleBox["ComplexCurve", FontFamily->"Courier"], ", which draws a curve in the complex plane that is parameterized by a real \ variable." }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.49064001878125*^9, 3.49064003878125*^9}, 3.490640086078125*^9, 3.4938129148125*^9}], Cell[TextData[{ StyleBox["Exercise ", FontWeight->"Bold"], StyleBox[ CounterBox["Exercise"], FontWeight->"Bold"], StyleBox[".", FontWeight->"Bold"], " Use ", StyleBox["Complex Graphics", FontSlant->"Italic"], " primitives to form the triangle with vertices ", Cell[BoxData[ FormBox[ RowBox[{"-", "1"}], TraditionalForm]]], ", ", Cell[BoxData[ FormBox["1", TraditionalForm]]], ", and ", Cell[BoxData[ FormBox["\[ImaginaryI]", TraditionalForm]]], " along with the (circumference of the) circle that passes through its \ vertices." }], "Exercise", CellChangeTimes->{ 3.48969559478125*^9, 3.48969563040625*^9, {3.49073464525*^9, 3.490734718453125*^9}, 3.490734753*^9, 3.493812920015625*^9}] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Displaying ", StyleBox["Complex Graphics", FontSlant->"Italic"], ": ", StyleBox["Draw2D", FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"] }], "Section", ShowGroupOpener->True, CellChangeTimes->{{3.490640117609375*^9, 3.490640129453125*^9}, 3.4938127691875*^9, {3.49381380209375*^9, 3.49381380771875*^9}, { 3.493813878515625*^9, 3.493813879734375*^9}, {3.493813959515625*^9, 3.493813960859375*^9}}], Cell[TextData[{ "Just forming ordinary ", StyleBox["Mathematica", FontSlant->"Italic"], " graphics objects such as ", StyleBox["Point[{1,1}]", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " or ", StyleBox["Line[{{0,0},{1,0},{1,1},{0,1},{0,0}}]", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " does not display them. Rather, you have to include them in a ", StyleBox["Graphics[{", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], StyleBox["\[Ellipsis]", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], StyleBox["}]", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " expression. For example:" }], "Text", CellChangeTimes->{{3.49070115434375*^9, 3.490701250328125*^9}}], Cell[BoxData[ RowBox[{"Graphics", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"Point", "[", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], "]"}], ",", RowBox[{"Line", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}]}], "}"}], "]"}]}], "\[IndentingNewLine]", "}"}], "]"}]], "Input", CellChangeTimes->{{3.490701252671875*^9, 3.490701278796875*^9}, { 3.4907931876875*^9, 3.490793190625*^9}}], Cell[TextData[{ "Likewise, forming ", StyleBox["Complex Graphics", FontSlant->"Italic"], " primitives such as ", StyleBox["ComplexPoint[1+\[ImaginaryI]]", FontFamily->"Courier"], " or ", StyleBox["ComplexLine[{0,1,1+\[ImaginaryI],\[ImaginaryI],0}]", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " does not actually display the graphics!" }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.490640144265625*^9, 3.490640178859375*^9}, { 3.490640209546875*^9, 3.49064023459375*^9}, {3.490640628109375*^9, 3.490640631703125*^9}, {3.49064081090625*^9, 3.490640812109375*^9}, { 3.4906598845625*^9, 3.49065993234375*^9}, {3.49070131278125*^9, 3.4907014338125*^9}, {3.49073496765625*^9, 3.49073497953125*^9}, { 3.493659101359375*^9, 3.493659102421875*^9}, 3.4938127946875*^9}], Cell[TextData[{ StyleBox["To display complex graphics objects", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], ", include them within a ", StyleBox["Draw2D", FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"], " expression. The ", StyleBox["Presentations", FontSlant->"Italic"], " function ", StyleBox["Draw2D", FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"], " is essentially a \[OpenCurlyDoubleQuote]cover\[CloseCurlyDoubleQuote] for \ the built-in ", StyleBox["Mathematica", FontSlant->"Italic"], " function ", StyleBox["Graphics", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], "." }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.490640144265625*^9, 3.490640178859375*^9}, { 3.490640209546875*^9, 3.49064023459375*^9}, {3.490640628109375*^9, 3.490640631703125*^9}, {3.49064081090625*^9, 3.490640812109375*^9}, { 3.4906598845625*^9, 3.49065993234375*^9}, {3.49070131278125*^9, 3.4907014338125*^9}, {3.49073496765625*^9, 3.49073497953125*^9}, { 3.493659101359375*^9, 3.49365916746875*^9}}], Cell[TextData[{ "For example, draw a point at ", Cell[BoxData[ FormBox[ RowBox[{"\[ImplicitPlus]", Cell["1+\[ImaginaryI]"]}], TraditionalForm]]], " and the polygonal line\[LongDash]a square\[LongDash]with vertices 0, 1, ", Cell[BoxData[ FormBox[ RowBox[{"1", "+", "\[ImaginaryI]"}], TraditionalForm]]], ", and ", Cell[BoxData[ FormBox["\[ImaginaryI]", TraditionalForm]]], ":" }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.490640144265625*^9, 3.490640178859375*^9}, { 3.490640209546875*^9, 3.49064023459375*^9}, {3.490640628109375*^9, 3.490640631703125*^9}, {3.49064081090625*^9, 3.49064085646875*^9}, { 3.49073500646875*^9, 3.49073506971875*^9}}], Cell[BoxData[ RowBox[{"Draw2D", "[", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"ComplexPoint", "[", RowBox[{"1", "+", "\[ImaginaryI]"}], "]"}], ",", RowBox[{"ComplexLine", "[", RowBox[{"{", RowBox[{"0", ",", "1", ",", RowBox[{"1", "+", "\[ImaginaryI]"}], ",", "\[ImaginaryI]", ",", "0"}], "}"}], "]"}]}], "\[IndentingNewLine]", "}"}], "]"}]], "Input", CellChangeTimes->{{3.490640634953125*^9, 3.490640660515625*^9}, 3.490640761515625*^9, 3.49070145971875*^9, {3.490721452203125*^9, 3.49072146525*^9}, {3.490793197828125*^9, 3.490793217828125*^9}}], Cell[TextData[{ "To make the point more visible against the square, you may use color, size, \ or some other treatment. And to do that, use a graphics directive. 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(That\ \[CloseCurlyQuote]s not required, just a good style to make reading and \ writing code easier.) Comments, enclosed in ", StyleBox["(*", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " ", StyleBox["\[Ellipsis]", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], " ", StyleBox["*)", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " pairs, were included in order to make each action clear." }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.490640783390625*^9, 3.4906407999375*^9}, { 3.490660087375*^9, 3.49066021753125*^9}, {3.490660312234375*^9, 3.4906603300625*^9}, {3.4906604210625*^9, 3.49066042434375*^9}, { 3.49066052740625*^9, 3.490660529546875*^9}, {3.490703431953125*^9, 3.490703476140625*^9}, {3.49070361334375*^9, 3.4907036144375*^9}, { 3.490793253265625*^9, 3.490793293125*^9}}], Cell["\<\ Normally, such \[OpenCurlyDoubleQuote]obvious\[CloseCurlyDoubleQuote] \ comments will not be included. It\[CloseCurlyQuote]s a good idea, though, to \ use a separate line of code for each object to be drawn, and a separate line \ of code for each set of graphics directives that affect the subsequent \ objects.\ \>", "Text", ShowGroupOpener->True, CellChangeTimes->{{3.490640783390625*^9, 3.4906407999375*^9}, { 3.490660087375*^9, 3.49066021753125*^9}, {3.490660312234375*^9, 3.4906603300625*^9}, {3.4906604210625*^9, 3.49066042434375*^9}, { 3.49066052740625*^9, 3.490660529546875*^9}, {3.490703431953125*^9, 3.490703476140625*^9}, {3.49070361334375*^9, 3.490703687453125*^9}, { 3.490713159140625*^9, 3.4907131593125*^9}, {3.4938125160625*^9, 3.493812517046875*^9}}], Cell["See what happens if you make the square thick, too:", "Text", CellChangeTimes->{{3.490660538390625*^9, 3.490660686390625*^9}}], Cell[BoxData[ RowBox[{"Draw2D", "[", "\[IndentingNewLine]", RowBox[{"{", "\[IndentingNewLine]", RowBox[{"Blue", ",", RowBox[{"PointSize", "[", "Large", "]"}], ",", "\[IndentingNewLine]", RowBox[{"ComplexPoint", "[", RowBox[{"1", "+", "\[ImaginaryI]"}], "]"}], ",", "\[IndentingNewLine]", "Red", ",", "Thick", ",", "\[IndentingNewLine]", RowBox[{"ComplexLine", "[", RowBox[{"{", RowBox[{"0", ",", "1", ",", RowBox[{"1", "+", "\[ImaginaryI]"}], ",", "\[ImaginaryI]", ",", "0"}], "}"}], "]"}]}], "\[IndentingNewLine]", "}"}], "\[IndentingNewLine]", "]"}]], "Input", CellChangeTimes->{{3.490640240828125*^9, 3.490640380421875*^9}, { 3.490640424078125*^9, 3.490640546125*^9}, 3.490660244984375*^9, { 3.490660276359375*^9, 3.490660277265625*^9}, {3.490660449390625*^9, 3.490660508171875*^9}, {3.49066058084375*^9, 3.49066058159375*^9}, { 3.49066072190625*^9, 3.490660740015625*^9}, {3.49070350325*^9, 3.49070351478125*^9}, {3.49070427696875*^9, 3.490704296109375*^9}, 3.490709326203125*^9, {3.4907932313125*^9, 3.490793233734375*^9}}], Cell[TextData[{ "Now the point is harder to see. And one reason is that ", StyleBox["later items in the ", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], StyleBox["Draw3D", FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain", FontColor->RGBColor[0, 0, 1]], StyleBox[" list are drawn ", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], StyleBox["on top", FontWeight->"Bold", FontSlant->"Italic", FontColor->RGBColor[0, 0, 1]], StyleBox[" of the earlier items", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], ". If you look closely above, you will see the corner of the red square \ drawn on top of the blue point at ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"\[ImplicitPlus]", "1"}], "+", "\[ImaginaryI]"}], TraditionalForm]]], "." }], "Text", CellChangeTimes->{{3.49071318725*^9, 3.490713304171875*^9}}], Cell[TextData[{ StyleBox["Exercise ", FontWeight->"Bold"], StyleBox[ CounterBox["Exercise"], FontWeight->"Bold"], StyleBox[".", FontWeight->"Bold"], " Make it easier to see the blue point by experimenting with the effects of:\ \n\t(a) reversing the order of the objects;\n\t(b) changing the point size\ \[LongDash]", StyleBox["try, for example, ", FontFamily->"Times"], StyleBox["PointSize[0.0275]", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], StyleBox[";", FontFamily->"Times"], "\n\t(c) changing the thickness of the line\[LongDash]instead of ", StyleBox["Thick", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], ", try, for example, ", StyleBox["Thickness[0.005]", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], "." }], "Exercise", CellChangeTimes->{ 3.48969559478125*^9, 3.48969563040625*^9, {3.4907047248125*^9, 3.490704871984375*^9}, {3.490709375953125*^9, 3.490709425484375*^9}, { 3.490709480125*^9, 3.490709576*^9}, {3.49070967184375*^9, 3.4907097544375*^9}, {3.4907097945625*^9, 3.49070991465625*^9}, { 3.490713283828125*^9, 3.490713292734375*^9}, 3.490713332921875*^9}, ParagraphSpacing->{0.5, 0}], Cell[TextData[{ "There are several ways ", StyleBox["to select a color", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], ", including:\n\t\[FilledSmallCircle] By name, if you already know it. For \ example, ", StyleBox["Red", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], ", ", StyleBox["Blue", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], ", ", StyleBox["Orange", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], ", ", StyleBox["White", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], ", \[Ellipsis]. (This works only for colors in the ", StyleBox["Mathematica", FontSlant->"Italic"], " \[OpenCurlyDoubleQuote]System\[CloseCurlyDoubleQuote] color scheme.)\n\t\ \[FilledSmallCircle] By selecting a color from the ", StyleBox["Mathematica", FontSlant->"Italic"], " ", StyleBox["Color Schemes", FontFamily->"Helvetica", FontWeight->"Plain", FontSlant->"Plain"], " palette.\n\t\[FilledSmallCircle]", StyleBox[" By using the ", FontFamily->"Times"], StyleBox["Presentations", FontFamily->"Times", FontSlant->"Italic"], StyleBox[" function ", FontFamily->"Times"], StyleBox["Legacy", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], StyleBox[". For example, ", FontFamily->"Times"], StyleBox["Legacy[IndianRed]", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], StyleBox[" or, in prefix form, ", FontFamily->"Times"], StyleBox["Legacy@IndianRed", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], StyleBox[". This is just a shortcut for ", FontFamily->"Times"], StyleBox["ColorData[\[OpenCurlyDoubleQuote]Legacy\[CloseCurlyDoubleQuote], \ \[OpenCurlyDoubleQuote]IndianRed\[CloseCurlyDoubleQuote]]", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], StyleBox[".There are similar ", FontFamily->"Times"], StyleBox["Presentations", FontFamily->"Times", FontSlant->"Italic"], StyleBox[" shortcuts for other ", FontFamily->"Times"], StyleBox["Mathematica", FontFamily->"Times", FontSlant->"Italic"], StyleBox[" color schemes, for example, ", FontFamily->"Times"], StyleBox["HTML", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], StyleBox[".", FontFamily->"Times"] }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.490718848515625*^9, 3.490718863*^9}, { 3.490718904203125*^9, 3.4907190221875*^9}, {3.4907190604375*^9, 3.490719157859375*^9}, {3.4907192003125*^9, 3.49071942434375*^9}, { 3.490719469546875*^9, 3.49071956909375*^9}, {3.49071960484375*^9, 3.490719635046875*^9}, {3.4907196750625*^9, 3.49071969709375*^9}, { 3.493812709703125*^9, 3.493812736671875*^9}}, ParagraphSpacing->{0.75, 0}], Cell[TextData[{ StyleBox["To see what ", FontFamily->"Times"], StyleBox["Legacy", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], StyleBox[" colors are available, evaluate:", FontFamily->"Times"] }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.490718848515625*^9, 3.490718863*^9}, { 3.490718904203125*^9, 3.4907190221875*^9}, {3.4907190604375*^9, 3.490719157859375*^9}, {3.4907192003125*^9, 3.49071942434375*^9}, { 3.490719469546875*^9, 3.49071956909375*^9}, {3.49071960484375*^9, 3.490719635046875*^9}, {3.4907196750625*^9, 3.4907197038125*^9}, 3.4907200618125*^9}, ParagraphSpacing->{0.75, 0}], Cell[BoxData[ RowBox[{"ColorData", "[", RowBox[{"\"\\"", ",", "\"\\""}], "]"}]], "Input", CellChangeTimes->{{3.490719585453125*^9, 3.490719595515625*^9}, { 3.49071970984375*^9, 3.49071975434375*^9}, {3.49072001528125*^9, 3.4907200253125*^9}}], Cell[TextData[{ "For more about selecting colors, see ", ButtonBox["\[OpenCurlyDoubleQuote]How to Use Colors in ", BaseStyle->"Link", ButtonData->"paclet:howto/UseColorsInMathematica"], StyleBox[ButtonBox["Mathematica", BaseStyle->"Link", ButtonData->"paclet:howto/UseColorsInMathematica"], FontSlant->"Italic"], ButtonBox["\[CloseCurlyDoubleQuote]", BaseStyle->"Link", ButtonData->"paclet:howto/UseColorsInMathematica"], " in the Documentation Center." }], "Text", CellChangeTimes->{{3.49072008784375*^9, 3.49072009590625*^9}, { 3.490720162828125*^9, 3.490720218953125*^9}, {3.49072077521875*^9, 3.490720823984375*^9}, {3.490720866421875*^9, 3.4907208786875*^9}}], Cell[TextData[{ StyleBox["Exercise ", FontWeight->"Bold"], StyleBox[ CounterBox["Exercise"], FontWeight->"Bold"], StyleBox[".", FontWeight->"Bold"], " (a) Change the colors of the point and line to other ", StyleBox["System", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " colors.\n(b) Change them to the ", StyleBox["Legacy", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " colors ", StyleBox["DodgerBlue", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " and ", StyleBox["IndianRed", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], ".\n(c) Try some other colors." }], "Exercise", CellChangeTimes->{ 3.48969559478125*^9, 3.48969563040625*^9, {3.490720952109375*^9, 3.49072104490625*^9}, 3.4907210773125*^9}, ParagraphSpacing->{0.5, 0.}], Cell[TextData[{ StyleBox["Exercise ", FontWeight->"Bold"], StyleBox[ CounterBox["Exercise"], FontWeight->"Bold"], StyleBox[".", FontWeight->"Bold"], " (a) Use ", StyleBox["Complex Graphics", FontSlant->"Italic"], " primitives to draw the figure consisting of triangle with vertices ", Cell[BoxData[ FormBox[ RowBox[{"-", "1"}], TraditionalForm]]], ", ", Cell[BoxData[ FormBox["1", TraditionalForm]]], ", and ", Cell[BoxData[ FormBox["\[ImaginaryI]", TraditionalForm]]], " along with the (circumference of the) circle that passes through its \ vertices. 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You may \ override any of these defaults that affect the overall appearance of the \ entire drawing." }], "Text", CellChangeTimes->{ 3.4907046779375*^9, {3.490721174984375*^9, 3.490721279109375*^9}, { 3.490721612921875*^9, 3.490721635890625*^9}, {3.490735196859375*^9, 3.490735250515625*^9}, {3.4907869055625*^9, 3.490786984296875*^9}}], Cell[TextData[{ "For example, add the plot option ", StyleBox["ImageSize", FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"], ". You specify the size in printer's points, and there are supposed to be 72 \ points to the inch. (But that depends upon the details of your graphics \ display and the magnification of the notebook.)" }], "Text", CellChangeTimes->{{3.49072129753125*^9, 3.4907213934375*^9}, 3.4907214284375*^9, {3.490721546*^9, 3.4907215475625*^9}, { 3.490735287328125*^9, 3.490735304875*^9}, {3.490787002765625*^9, 3.49078702915625*^9}}, CellTags->"printers points"], Cell[BoxData[ RowBox[{"Draw2D", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{"Red", ",", "Thick", ",", "\[IndentingNewLine]", RowBox[{"ComplexLine", "[", RowBox[{"{", RowBox[{"0", ",", "1", ",", RowBox[{"1", "+", "\[ImaginaryI]"}], ",", "\[ImaginaryI]", ",", "0"}], "}"}], "]"}], ",", "\[IndentingNewLine]", "Blue", ",", RowBox[{"PointSize", "[", "Large", "]"}], ",", "\[IndentingNewLine]", RowBox[{"ComplexPoint", "[", RowBox[{"1", "+", "\[ImaginaryI]"}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", RowBox[{"3", " ", "72"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.490640240828125*^9, 3.490640380421875*^9}, { 3.490640424078125*^9, 3.490640546125*^9}, 3.490660244984375*^9, { 3.490660276359375*^9, 3.490660277265625*^9}, {3.490660449390625*^9, 3.490660508171875*^9}, {3.49066058084375*^9, 3.49066058159375*^9}, { 3.49066072190625*^9, 3.490660740015625*^9}, {3.49070350325*^9, 3.49070351478125*^9}, {3.49070427696875*^9, 3.490704296109375*^9}, 3.490709326203125*^9, {3.490721475140625*^9, 3.490721514296875*^9}, { 3.490735316921875*^9, 3.49073532009375*^9}, 3.490793111640625*^9}], Cell[TextData[{ "Because an option such as ", StyleBox["ImageSize", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " affects the entire drawing, not just individual object, it goes ", StyleBox["after", FontSlant->"Italic"], " the list of graphics objects and directives:\n\t", StyleBox["Draw2D[{", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], StyleBox["\[Ellipsis]", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], StyleBox["}, ", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], StyleBox["opts", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], StyleBox["]", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"] }], "Text", CellChangeTimes->{{3.49070431721875*^9, 3.490704456875*^9}, { 3.4907215575625*^9, 3.490721581640625*^9}, {3.490735327671875*^9, 3.490735340515625*^9}}, ParagraphSpacing->{0.5, 0.}], Cell[TextData[{ "The last drawing does not give a very good feel for what the objects are \ and where they are. To enhance it:\n\t\[FilledSmallCircle] add axes with tick \ marks and coordinates (by default ", StyleBox["Draw2D", FontFamily->"Courier"], " suppresses them);\n\t\[FilledSmallCircle] use the ", StyleBox["PlotRange", FontFamily->"Courier"], " option to enlarge the plot \"window\", so that the objects may be seen in \ a larger view;\n\t\[FilledSmallCircle] put a ", StyleBox["Legacy", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " color ", StyleBox["Honeydew", FontFamily->"Courier"], " background behind the plot to better set it off from the rest of the \ notebook; and\n\t\[FilledSmallCircle] add a descriptive plot label." }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.4907218409375*^9, 3.490721841828125*^9}, { 3.490721937953125*^9, 3.490722038234375*^9}, {3.490735349421875*^9, 3.49073537621875*^9}, {3.490787078125*^9, 3.49078713034375*^9}, { 3.49251751125*^9, 3.49251751790625*^9}}, ParagraphSpacing->{0.5, 0}], Cell[BoxData[ RowBox[{"Draw2D", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"Legacy", "@", "IndianRed"}], ",", "Thick", ",", "\[IndentingNewLine]", RowBox[{"ComplexLine", "[", RowBox[{"{", RowBox[{"0", ",", "1", ",", RowBox[{"1", "+", "\[ImaginaryI]"}], ",", "\[ImaginaryI]", ",", "0"}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Legacy", "@", "MediumBlue"}], ",", RowBox[{"PointSize", "[", "Large", "]"}], ",", "\[IndentingNewLine]", RowBox[{"ComplexPoint", "[", RowBox[{"1", "+", "\[ImaginaryI]"}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"Axes", "\[Rule]", "True"}], ",", "\[IndentingNewLine]", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1.5"}], ",", "1.5"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1.5"}], ",", "1.5"}], "}"}]}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"Background", "\[Rule]", RowBox[{"Legacy", "@", "HoneyDew"}]}], ",", "\[IndentingNewLine]", RowBox[{ "PlotLabel", "\[Rule]", "\"\\""}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", RowBox[{"3", " ", "72"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.490640240828125*^9, 3.490640380421875*^9}, { 3.490640424078125*^9, 3.490640546125*^9}, 3.490660244984375*^9, { 3.490660276359375*^9, 3.490660277265625*^9}, {3.490660449390625*^9, 3.490660508171875*^9}, {3.49066058084375*^9, 3.49066058159375*^9}, { 3.49066072190625*^9, 3.490660740015625*^9}, {3.49070350325*^9, 3.49070351478125*^9}, {3.49070427696875*^9, 3.490704296109375*^9}, 3.490709326203125*^9, {3.490721475140625*^9, 3.490721514296875*^9}, { 3.49072167609375*^9, 3.490721779375*^9}, {3.49072181403125*^9, 3.49072181496875*^9}, {3.4907218615625*^9, 3.490721925140625*^9}, { 3.4907220201875*^9, 3.49072202425*^9}, 3.490722130875*^9, { 3.49072236953125*^9, 3.49072237253125*^9}, 3.490793116046875*^9}], Cell["\<\ That looks better. It will be improved further in the next section.\ \>", "Text", ShowGroupOpener->True, CellChangeTimes->{{3.490722091265625*^9, 3.490722126359375*^9}, { 3.49078715321875*^9, 3.490787168140625*^9}}], Cell[TextData[{ "The ", StyleBox["PlotRange", FontFamily->"Courier"], " option, used above, specifies the \"window\" used for plotting. To specify \ a window consisting of points ", Cell[BoxData[ FormBox[ RowBox[{"z", "=", RowBox[{"x", "+", RowBox[{"y", " ", "\[ImaginaryI]"}]}]}], TraditionalForm]]], " with ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["x", "min"], "\[LessEqual]", "x", "\[LessEqual]", SubscriptBox["x", "max"]}], TraditionalForm]]], " and ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["y", "min"], "\[LessEqual]", "y", "\[LessEqual]", SubscriptBox["y", "max"]}], TraditionalForm]]], ", use the form ", StyleBox["PlotRange\[Rule]{{", FontFamily->"Courier"], Cell[BoxData[ FormBox[ SubscriptBox["x", "min"], TraditionalForm]], FontFamily->"Courier"], StyleBox[",", FontFamily->"Courier"], Cell[BoxData[ FormBox[ SubscriptBox["x", "max"], TraditionalForm]], FontFamily->"Courier"], StyleBox["},{", FontFamily->"Courier"], Cell[BoxData[ FormBox[ SubscriptBox["y", "min"], TraditionalForm]], FontFamily->"Courier"], StyleBox[",", FontFamily->"Courier"], Cell[BoxData[ FormBox[ SubscriptBox["y", "max"], TraditionalForm]], FontFamily->"Courier"], StyleBox["}}", FontFamily->"Courier"], "." }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.4907221519375*^9, 3.490722198234375*^9}, { 3.4907871768125*^9, 3.490787178796875*^9}}], Cell[TextData[{ StyleBox["Exercise ", FontWeight->"Bold"], StyleBox[ CounterBox["Exercise"], FontWeight->"Bold"], StyleBox[".", FontWeight->"Bold"], " Copy the preceding input cell. Then change it so as to use a different \ window, a different background color (", StyleBox["White", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], ", for example), and a different label for the plot. And make the drawing\ \[CloseCurlyQuote]s overall size much bigger, say 6 inches." }], "Exercise", CellChangeTimes->{ 3.48969559478125*^9, 3.48969563040625*^9, {3.49072221709375*^9, 3.490722351859375*^9}, {3.49078720784375*^9, 3.49078720834375*^9}}], Cell[TextData[{ StyleBox["Exercise ", FontWeight->"Bold"], StyleBox[ CounterBox["Exercise"], FontWeight->"Bold"], StyleBox[".", FontWeight->"Bold"], " For the same drawing, use a frame (with coordinates labeling its sides) \ instead of axes. (Hint: Look up ", StyleBox["Frame", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " in the Documentation Center.)" }], "Exercise", CellChangeTimes->{ 3.48969559478125*^9, 3.48969563040625*^9, {3.490735616859375*^9, 3.490735756640625*^9}}], Cell[TextData[{ "If you use the ", StyleBox["Axes\[Rule]True", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " option without a ", StyleBox["PlotRange", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " option, you may not get axes through the origin. For example:" }], "Text", CellChangeTimes->{{3.490799612140625*^9, 3.490799657078125*^9}, { 3.490799892109375*^9, 3.490799905734375*^9}}], Cell[BoxData[ RowBox[{"Draw2D", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{"Red", ",", "Thick", ",", "\[IndentingNewLine]", RowBox[{"ComplexLine", "[", RowBox[{"{", RowBox[{ RowBox[{"1", "+", RowBox[{"\[ImaginaryI]", "/", "2"}]}], ",", RowBox[{"2", "+", RowBox[{"\[ImaginaryI]", "/", "2"}]}], ",", RowBox[{"2", "+", "\[ImaginaryI]"}], ",", RowBox[{"1", "+", "\[ImaginaryI]"}], ",", RowBox[{"1", "+", RowBox[{"\[ImaginaryI]", "/", "2"}]}]}], "}"}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"Axes", "\[Rule]", "True"}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", RowBox[{"3", " ", "72"}]}]}], "]"}]], "Input"], Cell[TextData[{ "The remedy is to include an explicit ", StyleBox["AxesOrigin\[Rule]0", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " option:" }], "Text", CellChangeTimes->{{3.49079994696875*^9, 3.490799979640625*^9}}], Cell[BoxData[ RowBox[{"Draw2D", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{"Red", ",", "Thick", ",", "\[IndentingNewLine]", RowBox[{"ComplexLine", "[", RowBox[{"{", RowBox[{ RowBox[{"1", "+", RowBox[{"\[ImaginaryI]", "/", "2"}]}], ",", RowBox[{"2", "+", RowBox[{"\[ImaginaryI]", "/", "2"}]}], ",", RowBox[{"2", "+", "\[ImaginaryI]"}], ",", RowBox[{"1", "+", "\[ImaginaryI]"}], ",", RowBox[{"1", "+", RowBox[{"\[ImaginaryI]", "/", "2"}]}]}], "}"}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"Axes", "\[Rule]", "True"}], ",", RowBox[{"AxesOrigin", "\[Rule]", "0"}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", RowBox[{"3", " ", "72"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.490799990734375*^9, 3.490799996921875*^9}}], Cell[TextData[{ StyleBox["Exercise ", FontWeight->"Bold"], StyleBox[ CounterBox["Exercise"], FontWeight->"Bold"], StyleBox[".", FontWeight->"Bold"], " Redraw the rectangle from the preceding display but with the origin of \ axes at the center of the rectangle." }], "Exercise", CellChangeTimes->{ 3.48969559478125*^9, 3.48969563040625*^9, {3.490800107109375*^9, 3.490800164859375*^9}}] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Annotating ", StyleBox["Complex Graphics", FontSlant->"Italic"], " displays" }], "Section", ShowGroupOpener->True, CellChangeTimes->{{3.49073541478125*^9, 3.490735422734375*^9}, 3.49381282353125*^9}], Cell[TextData[{ "To further annotate a ", StyleBox["Complex Graphics", FontSlant->"Italic"], " drawing, you may want to include text within the drawing. ", StyleBox["To insert text at any location", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], ", invoke the ", StyleBox["Presentations", FontSlant->"Italic"], " function ", StyleBox["ComplexText", FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"], ". This function is used in the form\n\t", StyleBox["ComplexText[", FontFamily->"Courier"], StyleBox["txt", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], StyleBox[",", FontFamily->"Courier"], StyleBox["z", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], StyleBox["]", FontFamily->"Courier"], "\nwhere ", StyleBox["txt", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], " is the text you want to display and ", StyleBox["z", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], " is the complex number in the plane where (the center of) the text is to be \ displayed." }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.49073543975*^9, 3.490735484*^9}, 3.492292906265625*^9, { 3.49365921259375*^9, 3.49365923284375*^9}, 3.493812836359375*^9, { 3.493817778796875*^9, 3.493817779265625*^9}}, ParagraphSpacing->{0.5, 0}], Cell[TextData[{ "For example, enhance the same drawing as before but now also:\n\t\ \[FilledSmallCircle] use a ", StyleBox["ComplexText", FontFamily->"Courier"], " expression to label the plane as the complex plane;\n\t\ \[FilledSmallCircle] label the point." }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.490735519046875*^9, 3.49073555003125*^9}}, ParagraphSpacing->{0.5, 0}], Cell[BoxData[ RowBox[{"Draw2D", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"Legacy", "@", "IndianRed"}], ",", "Thick", ",", "\[IndentingNewLine]", RowBox[{"ComplexLine", "[", RowBox[{"{", RowBox[{"0", ",", "1", ",", RowBox[{"1", "+", "\[ImaginaryI]"}], ",", "\[ImaginaryI]", ",", "0"}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Legacy", "@", "MediumBlue"}], ",", RowBox[{"PointSize", "[", "Large", "]"}], ",", "\[IndentingNewLine]", RowBox[{"ComplexPoint", "[", RowBox[{"1", "+", "\[ImaginaryI]"}], "]"}], ",", "\[IndentingNewLine]", "Black", ",", "\[IndentingNewLine]", RowBox[{"ComplexText", "[", RowBox[{"\"\<1+\[ImaginaryI]\>\"", ",", RowBox[{"1.15", "\[InvisibleSpace]", "+", RowBox[{"1.15", "\[ImaginaryI]"}]}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Legacy", "@", "DimGray"}], ",", RowBox[{"ComplexText", "[", RowBox[{ RowBox[{"Style", "[", RowBox[{"\"\\"", ",", RowBox[{"FontFamily", "\[Rule]", "\"\\""}], ",", RowBox[{"FontSize", "\[Rule]", "10"}]}], "]"}], ",", RowBox[{ RowBox[{"-", "1"}], "-", "\[ImaginaryI]"}]}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"Axes", "\[Rule]", "True"}], ",", "\[IndentingNewLine]", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1.5"}], ",", "1.5"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1.5"}], ",", "1.5"}], "}"}]}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"Background", "\[Rule]", RowBox[{"Legacy", "@", "HoneyDew"}]}], ",", "\[IndentingNewLine]", RowBox[{"PlotLabel", "\[Rule]", RowBox[{"Style", "[", RowBox[{"\"\\"", ",", RowBox[{"FontWeight", "\[Rule]", "Bold"}]}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", RowBox[{"3", " ", "72"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.490640240828125*^9, 3.490640380421875*^9}, { 3.490640424078125*^9, 3.490640546125*^9}, 3.490660244984375*^9, { 3.490660276359375*^9, 3.490660277265625*^9}, {3.490660449390625*^9, 3.490660508171875*^9}, {3.49066058084375*^9, 3.49066058159375*^9}, { 3.49066072190625*^9, 3.490660740015625*^9}, {3.49070350325*^9, 3.49070351478125*^9}, {3.49070427696875*^9, 3.490704296109375*^9}, 3.490709326203125*^9, {3.490721475140625*^9, 3.490721514296875*^9}, { 3.49072167609375*^9, 3.490721779375*^9}, {3.49072181403125*^9, 3.49072181496875*^9}, {3.4907218615625*^9, 3.490721925140625*^9}, { 3.4907220201875*^9, 3.49072202425*^9}, 3.490722130875*^9, { 3.49072236953125*^9, 3.49072237253125*^9}, {3.49073556975*^9, 3.4907355876875*^9}, {3.490735805625*^9, 3.490735872734375*^9}, { 3.490735908515625*^9, 3.490735923359375*^9}, {3.490735962796875*^9, 3.490735997796875*^9}, {3.490736103703125*^9, 3.490736108609375*^9}, { 3.490736180828125*^9, 3.4907361834375*^9}, {3.49078753153125*^9, 3.490787558171875*^9}, 3.49078760571875*^9, {3.49078768865625*^9, 3.490787692546875*^9}, 3.490793079046875*^9}], Cell[TextData[{ "Notice that the ", Cell[BoxData[ FormBox[ RowBox[{"1", "+", "\[ImaginaryI]"}], TraditionalForm]]], " text labeling the point is automatically typeset in traditional \ mathematical format, since the text used for the input already includes the \ typeset form ", Cell[BoxData[ FormBox["\[ImaginaryI]", TraditionalForm]], FontFamily->"Courier"], " rather than ", StyleBox["I", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], ". This would ", StyleBox["not", FontSlant->"Italic"], " have happened had you used instead ", StyleBox["ComplexText[\[OpenCurlyDoubleQuote]1+I\[CloseCurlyDoubleQuote], \ 1.15\[InvisibleSpace]+ 1.15\[ImaginaryI]]", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], "." }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.490787436234375*^9, 3.490787673890625*^9}, { 3.490787707875*^9, 3.49078771040625*^9}, 3.4907880278125*^9, { 3.490788060046875*^9, 3.490788061984375*^9}, {3.492292913609375*^9, 3.49229291625*^9}}], Cell[TextData[{ StyleBox["Exercise ", FontWeight->"Bold"], StyleBox[ CounterBox["Exercise"], FontWeight->"Bold"], StyleBox[".", FontWeight->"Bold"], " Draw a square with vertices at ", Cell[BoxData[ FormBox["1", TraditionalForm]]], ", \[ImaginaryI], ", Cell[BoxData[ FormBox[ RowBox[{"-", "1"}], TraditionalForm]]], ", and ", Cell[BoxData[ FormBox[ RowBox[{"-", "\[ImaginaryI]"}], TraditionalForm]]], " and label its vertices in the drawing." }], "Exercise", CellChangeTimes->{ 3.48969559478125*^9, 3.48969563040625*^9, {3.490793158390625*^9, 3.490793161203125*^9}, {3.49079333996875*^9, 3.49079347071875*^9}}], Cell[TextData[{ "Sometimes you want to label a point or other object with an expression \ involving complex numbers but you want the ", StyleBox["form", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " of that expression to display, not its numerical value. For example, \ suppose you had calculated the point ", Cell[BoxData[ FormBox[ RowBox[{"1", "+", "\[ImaginaryI]"}], TraditionalForm]]], " from\[Ellipsis]" }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.4907881083125*^9, 3.490788114625*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"(", RowBox[{"1", " ", "+", " ", RowBox[{"3", "I"}]}], ")"}], "/", RowBox[{"(", RowBox[{"2", " ", "+", " ", "I"}], ")"}]}]], "Input", ShowGroupOpener->True], Cell[TextData[{ "\[Ellipsis]but you want to label the point with the actual expression ", Cell[BoxData[ FormBox[ FractionBox[ RowBox[{"1", " ", "+", " ", RowBox[{"3", "\[ImaginaryI]"}]}], RowBox[{"2", " ", "+", " ", "\[ImaginaryI]"}]], TraditionalForm]]], ". Try it:" }], "Text", ShowGroupOpener->True], Cell[BoxData[ RowBox[{"Draw2D", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"Legacy", "@", "MediumBlue"}], ",", RowBox[{"PointSize", "[", "Large", "]"}], ",", "\[IndentingNewLine]", RowBox[{"ComplexPoint", "[", RowBox[{"1", "+", "\[ImaginaryI]"}], "]"}], ",", "\[IndentingNewLine]", "Black", ",", "\[IndentingNewLine]", RowBox[{"ComplexText", "[", RowBox[{"\"\<(1 + 3I)/(2 + I)\>\"", ",", RowBox[{"1.15", "\[InvisibleSpace]", "+", RowBox[{"1.15", "\[ImaginaryI]"}]}]}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1.5"}], ",", "1.5"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1.5"}], ",", "1.5"}], "}"}]}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", RowBox[{"3", " ", "72"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.490640240828125*^9, 3.490640380421875*^9}, { 3.490640424078125*^9, 3.490640546125*^9}, 3.490660244984375*^9, { 3.490660276359375*^9, 3.490660277265625*^9}, {3.490660449390625*^9, 3.490660508171875*^9}, {3.49066058084375*^9, 3.49066058159375*^9}, { 3.49066072190625*^9, 3.490660740015625*^9}, {3.49070350325*^9, 3.49070351478125*^9}, {3.49070427696875*^9, 3.490704296109375*^9}, 3.490709326203125*^9, {3.490721475140625*^9, 3.490721514296875*^9}, { 3.49072167609375*^9, 3.490721779375*^9}, {3.49072181403125*^9, 3.49072181496875*^9}, {3.4907218615625*^9, 3.490721925140625*^9}, { 3.4907220201875*^9, 3.49072202425*^9}, 3.490722130875*^9, { 3.49072236953125*^9, 3.49072237253125*^9}, {3.49073556975*^9, 3.4907355876875*^9}, {3.490735805625*^9, 3.490735872734375*^9}, { 3.490735908515625*^9, 3.490735923359375*^9}, {3.490735962796875*^9, 3.490735997796875*^9}, {3.490736103703125*^9, 3.490736108609375*^9}, { 3.490736180828125*^9, 3.4907361834375*^9}, {3.49078753153125*^9, 3.490787558171875*^9}, 3.49078760571875*^9, {3.49078768865625*^9, 3.490787692546875*^9}, {3.49078816934375*^9, 3.490788220796875*^9}, 3.490788541703125*^9, 3.490793085484375*^9}], Cell[TextData[{ "It\[CloseCurlyQuote]s tempting to omit the quotations marks in the text ", StyleBox["\[OpenCurlyDoubleQuote](1 + 3I)/(2 + I)\[CloseCurlyDoubleQuote]", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], ". But see what happens if you do:" }], "Text", CellChangeTimes->{{3.49078824296875*^9, 3.49078828103125*^9}, 3.490788562296875*^9}], Cell[BoxData[ RowBox[{"Draw2D", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"Legacy", "@", "MediumBlue"}], ",", RowBox[{"PointSize", "[", "Large", "]"}], ",", "\[IndentingNewLine]", RowBox[{"ComplexPoint", "[", RowBox[{"1", "+", "\[ImaginaryI]"}], "]"}], ",", "\[IndentingNewLine]", "Black", ",", "\[IndentingNewLine]", RowBox[{"ComplexText", "[", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", " ", "+", " ", RowBox[{"3", "I"}]}], ")"}], "/", RowBox[{"(", RowBox[{"2", " ", "+", " ", "I"}], ")"}]}], ",", RowBox[{"1.15", "\[InvisibleSpace]", "+", RowBox[{"1.15", "\[ImaginaryI]"}]}]}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1.5"}], ",", "1.5"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1.5"}], ",", "1.5"}], "}"}]}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", RowBox[{"3", " ", "72"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.490640240828125*^9, 3.490640380421875*^9}, { 3.490640424078125*^9, 3.490640546125*^9}, 3.490660244984375*^9, { 3.490660276359375*^9, 3.490660277265625*^9}, {3.490660449390625*^9, 3.490660508171875*^9}, {3.49066058084375*^9, 3.49066058159375*^9}, { 3.49066072190625*^9, 3.490660740015625*^9}, {3.49070350325*^9, 3.49070351478125*^9}, {3.49070427696875*^9, 3.490704296109375*^9}, 3.490709326203125*^9, {3.490721475140625*^9, 3.490721514296875*^9}, { 3.49072167609375*^9, 3.490721779375*^9}, {3.49072181403125*^9, 3.49072181496875*^9}, {3.4907218615625*^9, 3.490721925140625*^9}, { 3.4907220201875*^9, 3.49072202425*^9}, 3.490722130875*^9, { 3.49072236953125*^9, 3.49072237253125*^9}, {3.49073556975*^9, 3.4907355876875*^9}, {3.490735805625*^9, 3.490735872734375*^9}, { 3.490735908515625*^9, 3.490735923359375*^9}, {3.490735962796875*^9, 3.490735997796875*^9}, {3.490736103703125*^9, 3.490736108609375*^9}, { 3.490736180828125*^9, 3.4907361834375*^9}, {3.49078753153125*^9, 3.490787558171875*^9}, 3.49078760571875*^9, {3.49078768865625*^9, 3.490787692546875*^9}, {3.49078816934375*^9, 3.490788220796875*^9}, { 3.49078829078125*^9, 3.49078829446875*^9}, 3.490788537625*^9, 3.490793088609375*^9}], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " evaluates the argument ", StyleBox["(1+3I)/(2+I)", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " inside ", StyleBox["ComplexText", FontFamily->"Courier"], " before forming the ", StyleBox["ComplexText", FontFamily->"Courier"], " graphics primitive object. 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Look first at this \ display:" }], "Text", ShowGroupOpener->True], Cell[BoxData[{ RowBox[{ RowBox[{ SubscriptBox["z", "0"], "=", " ", RowBox[{ RowBox[{"(", RowBox[{"1", "+", RowBox[{"3", "I"}]}], ")"}], "/", RowBox[{"(", RowBox[{"2", "+", "I"}], ")"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{"Draw2D", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"Legacy", "@", "MediumBlue"}], ",", RowBox[{"PointSize", "[", "Large", "]"}], ",", "\[IndentingNewLine]", RowBox[{"ComplexPoint", "[", RowBox[{"1", "+", " ", "\[ImaginaryI]"}], "]"}], ",", "\[IndentingNewLine]", "Black", ",", "\[IndentingNewLine]", RowBox[{"ComplexText", "[", RowBox[{ RowBox[{"z", "=", SubscriptBox["z", "0"]}], ",", RowBox[{"1.15", "+", RowBox[{"1.15", "I"}]}]}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"PlotRange", " ", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1.5"}], ",", "1.5"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1.5"}], ",", "1.5"}], "}"}]}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", " ", "\[Rule]", " ", RowBox[{"3", " ", "72"}]}]}], "]"}]}], "Input", ShowGroupOpener->True, CellChangeTimes->{{3.49078863859375*^9, 3.490788732875*^9}, { 3.49078882271875*^9, 3.49078882340625*^9}, {3.49078885965625*^9, 3.490788880203125*^9}, {3.49078913859375*^9, 3.490789141203125*^9}}], Cell[TextData[{ "Probably you had intended that the label for the point would be, literally, \ ", Cell[BoxData[ FormBox[ RowBox[{"z", "=", SubscriptBox["z", "0"]}], TraditionalForm]]], " rather than the value of ", Cell[BoxData[ FormBox[ StyleBox[ SubscriptBox["z", "0"], FontFamily->"Courier"], TraditionalForm]]], ". What\[CloseCurlyQuote]s worse, the ", StyleBox["Draw2D", FontFamily->"Courier"], " expression had a possibly unfortunate and unintended ", StyleBox["side-effect", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], ": it set ", StyleBox["z", FontFamily->"Courier"], " to be the value of ", Cell[BoxData[ FormBox[ SubscriptBox["z", "0"], TraditionalForm]], FontFamily->"Courier"], ":" }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.490788902296875*^9, 3.490788904015625*^9}, { 3.490789121625*^9, 3.490789129421875*^9}, {3.49078915959375*^9, 3.49078918646875*^9}, {3.49078923934375*^9, 3.490789294046875*^9}, { 3.4907896234375*^9, 3.49078962525*^9}}], Cell[BoxData["z"], "Input", ShowGroupOpener->True], Cell["So first clear that value z\[Ellipsis]", "Text", ShowGroupOpener->True], Cell[BoxData[ RowBox[{"Clear", "[", "z", "]"}]], "Input", ShowGroupOpener->True], Cell["\<\ \[Ellipsis] and then compare the following display:\ \>", "Text", ShowGroupOpener->True], Cell[BoxData[{ RowBox[{ RowBox[{ SubscriptBox["z", "0"], "=", " ", RowBox[{ RowBox[{"(", RowBox[{"1", "+", RowBox[{"3", "I"}]}], ")"}], "/", RowBox[{"(", RowBox[{"2", "+", "I"}], ")"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{"Draw2D", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"Legacy", "@", "MediumBlue"}], ",", RowBox[{"PointSize", "[", "Large", "]"}], ",", "\[IndentingNewLine]", RowBox[{"ComplexPoint", "[", SubscriptBox["z", "0"], "]"}], ",", "\[IndentingNewLine]", "Black", ",", "\[IndentingNewLine]", RowBox[{"ComplexText", "[", RowBox[{ RowBox[{"HoldForm", "[", RowBox[{"z", "=", SubscriptBox["z", "0"]}], "]"}], ",", RowBox[{"1.15", "+", RowBox[{"1.15", "I"}]}]}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"PlotRange", " ", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "1.5"}], ",", "1.5"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1.5"}], ",", "1.5"}], "}"}]}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", " ", "\[Rule]", " ", RowBox[{"3", " ", "72"}]}]}], "]"}]}], "Input", ShowGroupOpener->True, CellChangeTimes->{{3.49078863859375*^9, 3.490788732875*^9}, { 3.49078882271875*^9, 3.49078882340625*^9}, {3.49078885965625*^9, 3.490788880203125*^9}, {3.4907889695625*^9, 3.490788977*^9}, { 3.49078905803125*^9, 3.490789088515625*^9}, {3.49078920609375*^9, 3.490789209234375*^9}}], Cell[TextData[{ "Now not only is the point labeled as intended, but the side-effect of \ setting a value for ", StyleBox["z", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " has been avoided:" }], "Text", CellChangeTimes->{{3.490789011109375*^9, 3.490789036328125*^9}, { 3.49079949071875*^9, 3.490799497671875*^9}}], Cell[CellGroupData[{ Cell[TextData[{ "Using ", StyleBox["Mathematica", FontSlant->"Italic"], "'s ", StyleBox["Drawing Tools", FontFamily->"Helvetica", FontSlant->"Plain"], " to annotate drawings" }], "Subsection", CellChangeTimes->{{3.492560843921875*^9, 3.4925608519375*^9}, { 3.492560923328125*^9, 3.492560929453125*^9}, {3.492561137265625*^9, 3.492561139984375*^9}}], Cell[TextData[{ "A \"quick-and-dirty\" way to annotate and otherwise edit \ drawings\[LongDash]for example, to add text, insert arrows to point to \ particular things, and insert other curves and shapes\[LongDash]is to use ", StyleBox["Mathematica", FontSlant->"Italic"], "'s ", StyleBox["Drawing Tools", FontFamily->"Helvetica", FontWeight->"Plain", FontSlant->"Plain"], " palette. This palette works much the same way that similar palettes or \ buttons do in various drawing and paint programs.\nFor help about using those \ tools, see the Documentation Center ", ButtonBox["Drawing Tools Tutorial", BaseStyle->"Link", ButtonData->"paclet:tutorial/InteractiveGraphicsPalette"], "." }], "Text", CellChangeTimes->{{3.492560933671875*^9, 3.492561121421875*^9}, { 3.492561186703125*^9, 3.492561218640625*^9}, {3.49256161809375*^9, 3.4925616281875*^9}, {3.492561685046875*^9, 3.492561685046875*^9}}], Cell[TextData[{ "It is often much quicker to use ", StyleBox["Drawing Tools", FontFamily->"Helvetica", FontWeight->"Plain", FontSlant->"Plain"], " than to construct ", StyleBox["Presentations", FontSlant->"Italic"], " code to accomplish the same thing, especially when you can visually place \ objects in the drawing without having to figure out what the objects \ locations are in terms of coordinates." }], "Text", CellChangeTimes->{{3.49256117059375*^9, 3.492561177421875*^9}, { 3.492561233953125*^9, 3.492561321859375*^9}}], Cell[TextData[{ "On the other hand, if you alter the code that produced the drawing and \ evaluate the new code, you will have to go about applying the ", StyleBox["Drawing Tools", FontFamily->"Helvetica", FontWeight->"Plain", FontSlant->"Plain"], " modifications all over again." }], "Text", CellChangeTimes->{{3.492561327703125*^9, 3.49256138953125*^9}}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Drawing arrows: ", StyleBox["ComplexArrow", FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"] }], "Section", CellChangeTimes->{{3.49228774575*^9, 3.49228774928125*^9}, { 3.493813622375*^9, 3.49381362565625*^9}, {3.493813823390625*^9, 3.493813829625*^9}, {3.49381388625*^9, 3.493813887421875*^9}, { 3.493813965796875*^9, 3.49381397009375*^9}}], Cell[TextData[{ StyleBox["To construct an arrow", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], " with specified complex numbers as its tail and head, use the ", StyleBox["Presentations", FontSlant->"Italic"], " function ", StyleBox["ComplexArrow", FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"], ". The syntax, as you can discover from inserting a template for it from ", StyleBox["PresentationsPalette", FontFamily->"Helvetica", FontWeight->"Plain", FontSlant->"Plain"], ", is:\n\t", Cell[BoxData[ FormBox[ RowBox[{ StyleBox["ComplexArrow", FontFamily->"Courier"], StyleBox["[", FontFamily->"Courier"], RowBox[{ StyleBox["{", FontFamily->"Courier"], RowBox[{ StyleBox[ TagBox[ FrameBox["z1"], "Placeholder"], FontFamily->"Courier"], StyleBox[",", FontFamily->"Courier"], TagBox[ FrameBox["z2"], "Placeholder"]}], "}"}], StyleBox["]", FontFamily->"Courier"]}], TraditionalForm]]], "\nThere ", StyleBox["z1", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], " is the tail and ", StyleBox["z2", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], " the head of the arrow." }], "Text", CellChangeTimes->{{3.492287792671875*^9, 3.4922878294375*^9}, { 3.492291885953125*^9, 3.49229195384375*^9}, {3.492291993296875*^9, 3.49229200909375*^9}, {3.49365928359375*^9, 3.49365928825*^9}}, ParagraphSpacing->{0.5, 0}], Cell[BoxData[ RowBox[{"Draw2D", "[", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{"Blue", ",", "\[IndentingNewLine]", RowBox[{"ComplexArrow", "[", RowBox[{"{", RowBox[{"0", ",", RowBox[{"1", "+", "\[ImaginaryI]"}]}], "}"}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"Axes", "\[Rule]", "True"}], ",", RowBox[{"Ticks", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}]}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", RowBox[{"2", " ", "72"}]}]}], "\[IndentingNewLine]", "]"}]], "Input", CellChangeTimes->{{3.492292016015625*^9, 3.492292055234375*^9}, { 3.492292165421875*^9, 3.492292213390625*^9}, 3.492292279765625*^9, 3.49229237546875*^9}], Cell[TextData[{ "As you can see, the arrow head is rather small and hard to \ see\[LongDash]especially if, as below, you specify a non-default thickness. \ So you may want to change the dimensions of the arrow head with the ", StyleBox["Mathematica", FontSlant->"Italic"], " directive ", StyleBox["Arrowheads", FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"], "." }], "Text", CellChangeTimes->{{3.492292063921875*^9, 3.492292102328125*^9}, { 3.492292222171875*^9, 3.492292271890625*^9}, {3.492292381515625*^9, 3.4922923955*^9}}], Cell[BoxData[ RowBox[{"Draw2D", "[", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{"Thick", ",", "Blue", ",", RowBox[{"Arrowheads", "[", "Large", "]"}], ",", "\[IndentingNewLine]", RowBox[{"ComplexArrow", "[", RowBox[{"{", RowBox[{"0", ",", RowBox[{"1", "+", "\[ImaginaryI]"}]}], "}"}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"Axes", "\[Rule]", "True"}], ",", RowBox[{"Ticks", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}]}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", RowBox[{"2", " ", "72"}]}]}], "\[IndentingNewLine]", "]"}]], "Input", CellChangeTimes->{{3.492292016015625*^9, 3.492292055234375*^9}, { 3.492292165421875*^9, 3.492292213390625*^9}, {3.492292291125*^9, 3.492292326859375*^9}}], Cell[TextData[{ StyleBox["Exercise ", FontWeight->"Bold"], StyleBox[ CounterBox["Exercise"], FontWeight->"Bold"], StyleBox[".", FontWeight->"Bold"], " Pick two non-real complex numbers ", Cell[BoxData[ FormBox["z", TraditionalForm]]], " and ", Cell[BoxData[ FormBox["w", TraditionalForm]]], ". Make a drawing that shows the points ", Cell[BoxData[ FormBox["z", TraditionalForm]]], ", ", Cell[BoxData[ FormBox["w", TraditionalForm]]], ", and ", Cell[BoxData[ FormBox[ RowBox[{"z", "+", "w"}], TraditionalForm]]], " as well as arrows from the origin to each of these points. Include some \ lines to illustrate that, as vectors, complex numbers add by the \ parallelogram rule." }], "Exercise", CellChangeTimes->{ 3.48969559478125*^9, 3.48969563040625*^9, {3.4922923553125*^9, 3.4922923575*^9}, {3.492292409515625*^9, 3.49229265971875*^9}, { 3.492292746*^9, 3.492292760296875*^9}, 3.49381781121875*^9}, ParagraphSpacing->{0.5, 0}, CellTags->"SumDrawing"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Making dynamic drawings: ", StyleBox["Manipulate", FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"] }], "Section", CellChangeTimes->{{3.493217015078125*^9, 3.493217024359375*^9}, { 3.49322361384375*^9, 3.49322362690625*^9}, {3.493231564171875*^9, 3.493231570671875*^9}, 3.493813975421875*^9}], Cell[TextData[{ StyleBox["To move graphics objects around interactively", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], ", change constants appearing in the complex graphics objects to variables\ \[LongDash]parameters\[LongDash]and wrap the entire ", StyleBox["Draw2D", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " expression in a ", StyleBox["Mathematica", FontSlant->"Italic"], " ", StyleBox["Manipulate", FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"], " expression." }], "Text", CellChangeTimes->{{3.49321705596875*^9, 3.493217173171875*^9}}], Cell["\<\ For example, here again is a drawing of a point and a square.\ \>", "Text", CellChangeTimes->{{3.493217181171875*^9, 3.493217213109375*^9}}], Cell[BoxData[ RowBox[{"Draw2D", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{"Blue", ",", RowBox[{"PointSize", "[", "Large", "]"}], ",", RowBox[{"ComplexPoint", "[", RowBox[{"1", "+", "\[ImaginaryI]"}], "]"}], ",", "\[IndentingNewLine]", "Red", ",", "Thick", ",", RowBox[{"ComplexLine", "[", RowBox[{"{", RowBox[{"0", ",", "1", ",", RowBox[{"1", "+", "\[ImaginaryI]"}], ",", "\[ImaginaryI]", ",", "0"}], "}"}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"Axes", "\[Rule]", "True"}], ",", RowBox[{"ImageSize", "\[Rule]", RowBox[{"3", " ", "72"}]}], ","}], "\[IndentingNewLine]", "]"}]], "Input", CellChangeTimes->{{3.493217235734375*^9, 3.493217271734375*^9}, { 3.493217629375*^9, 3.493217634296875*^9}, {3.493304020234375*^9, 3.493304023390625*^9}}], Cell[TextData[{ "Let's first interactively scale of the square, so that it keeps its vertex \ at the origin and two of its sides on the axes. So change the fixed list ", StyleBox["{0,1,1+\[ImaginaryI],\[ImaginaryI],0}", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " of points to the variable list ", StyleBox["c{0,1,1+\[ImaginaryI],\[ImaginaryI],0}", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " and let the value of the parameter ", StyleBox["c", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " vary between 0.1 and 2." }], "Text", CellChangeTimes->{{3.49321728671875*^9, 3.4932174815*^9}, { 3.493217543234375*^9, 3.493217562*^9}, {3.493218506625*^9, 3.49321856396875*^9}, {3.493219132640625*^9, 3.493219145578125*^9}}], Cell[BoxData[ RowBox[{"Manipulate", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"Draw2D", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"Blue", ",", RowBox[{"PointSize", "[", "Large", "]"}], ",", RowBox[{"ComplexPoint", "[", RowBox[{"1", "+", "\[ImaginaryI]"}], "]"}], ",", "\[IndentingNewLine]", "Red", ",", "Thick", ",", RowBox[{"ComplexLine", "[", RowBox[{"c", RowBox[{"{", RowBox[{"0", ",", "1", ",", RowBox[{"1", "+", "\[ImaginaryI]"}], ",", "\[ImaginaryI]", ",", "0"}], "}"}]}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"Axes", "\[Rule]", "True"}], ",", RowBox[{"ImageSize", "\[Rule]", RowBox[{"3", " ", "72"}]}]}], "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"c", ",", "0.1", ",", "2"}], "}"}]}], "\[IndentingNewLine]", "]"}]], "Input", CellChangeTimes->{{3.493162028078125*^9, 3.49316217990625*^9}, { 3.4931622134375*^9, 3.493162288578125*^9}, {3.4931623320625*^9, 3.493162340609375*^9}, {3.493162371828125*^9, 3.493162435375*^9}, { 3.493162494203125*^9, 3.493162504703125*^9}, {3.49321751778125*^9, 3.4932175349375*^9}, {3.49321757053125*^9, 3.493217668140625*^9}, { 3.493218549515625*^9, 3.493218549953125*^9}, {3.49330402671875*^9, 3.493304035640625*^9}, {3.493304074*^9, 3.49330407915625*^9}, { 3.49330411465625*^9, 3.493304142453125*^9}}], Cell[TextData[{ "Move the slider at the top of the display to change the size of the square. \ Or click the little ", StyleBox["+", FontWeight->"Bold", FontColor->GrayLevel[1], Background->GrayLevel[0.5]], " sign at the end of the slider to open the \"video controls\" and then use \ the ", StyleBox["\[RightPointer]", FontSize->18], " button to move the slider automatically." }], "Text", CellChangeTimes->{{3.49321728671875*^9, 3.4932174815*^9}, { 3.493217683140625*^9, 3.493217768015625*^9}, {3.493217837953125*^9, 3.49321786028125*^9}, {3.49321793203125*^9, 3.493217944109375*^9}}], Cell[TextData[{ "The results are probably not what you expect: while the range along the \ axes changes, the square keeps the same physical size on-screen. 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As things stand \ now, its position is fixed at the constant ", StyleBox["1+\[ImaginaryI]", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], ". Change that constant to a variable, say ", StyleBox["pt", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], ". The control expression {", StyleBox["pt,", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], StyleBox["start", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], StyleBox[",", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], StyleBox["end", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], StyleBox["}", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " will specify the lower-left corner start and upper-right corner of where ", StyleBox["pt", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " can vary; let's use ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"-", "2"}], "-", RowBox[{"2", "\[ImaginaryI]"}]}], TraditionalForm]]], " and ", Cell[BoxData[ FormBox[ RowBox[{"2", "+", RowBox[{"2", "\[ImaginaryI]"}]}], TraditionalForm]]], ". But since ", StyleBox["Manipulate", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " expects the values of start and end to be Cartesian coordinates for the \ points, you must convert them. You may do that manually yourself or let ", StyleBox["Presentations", FontSlant->"Italic"], " do it for you by means of ", StyleBox["ToCoordinates", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], "." }], "Text", CellChangeTimes->{{3.4932182015625*^9, 3.49321828184375*^9}, { 3.49321833203125*^9, 3.493218498796875*^9}, 3.493219478125*^9, { 3.493219595609375*^9, 3.493219739109375*^9}, {3.4932228478125*^9, 3.493222871328125*^9}, {3.4932232624375*^9, 3.4932232686875*^9}}], Cell[BoxData[ RowBox[{"Manipulate", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"Draw2D", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{"Blue", ",", RowBox[{"PointSize", "[", "Large", "]"}], ",", "\[IndentingNewLine]", RowBox[{"ComplexPoint", "[", RowBox[{"ToComplex", "[", "pt", "]"}], "]"}], ",", "\[IndentingNewLine]", "Red", ",", "Thick", ",", "\[IndentingNewLine]", RowBox[{"ComplexLine", "[", RowBox[{"{", RowBox[{"0", ",", "1", ",", RowBox[{"1", "+", "\[ImaginaryI]"}], ",", "\[ImaginaryI]", ",", "0"}], "}"}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"Axes", "\[Rule]", "True"}], ",", "\[IndentingNewLine]", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"ToCoordinates", "[", RowBox[{ RowBox[{"-", "2"}], "+", RowBox[{"2", "\[ImaginaryI]"}]}], "]"}], ",", RowBox[{"ToCoordinates", "[", RowBox[{ RowBox[{"-", "2"}], "+", RowBox[{"2", "\[ImaginaryI]"}]}], "]"}]}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", RowBox[{"3", " ", "72"}]}]}], "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"pt", ",", RowBox[{"ToCoordinates", "[", RowBox[{ RowBox[{"-", "2"}], "-", RowBox[{"2", "\[ImaginaryI]"}]}], "]"}], ",", RowBox[{"ToCoordinates", "[", RowBox[{"2", "+", RowBox[{"2", "\[ImaginaryI]"}]}], "]"}]}], "}"}]}], "\[IndentingNewLine]", "]"}]], "Input", CellChangeTimes->{{3.493162028078125*^9, 3.49316217990625*^9}, { 3.4931622134375*^9, 3.493162288578125*^9}, {3.4931623320625*^9, 3.493162340609375*^9}, {3.493162371828125*^9, 3.493162435375*^9}, { 3.493162494203125*^9, 3.493162504703125*^9}, {3.49321831846875*^9, 3.49321832603125*^9}}], Cell[TextData[{ "You obtain a ", StyleBox["2D slider", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], " control. Move around the little point in the control at the top to move \ the point displayed in the drawing." }], "Text", CellChangeTimes->{{3.49321975978125*^9, 3.49321981890625*^9}}], Cell[TextData[{ "Instead of using ", StyleBox["ComplexPoint[ToComplex[pt]]", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], ", you could substitute simply ", StyleBox["Point[pt]", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], ". And instead of ", StyleBox["ToCoordinates[-2+2\[ImaginaryI]]", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " you could substitute ", StyleBox["{-2,2}", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], ", etc. I chose to keep everything possible in terms of complex numbers." }], "SmallText", CellChangeTimes->{{3.493296968453125*^9, 3.493297037484375*^9}, { 3.49329708803125*^9, 3.493297104078125*^9}}], Cell[CellGroupData[{ Cell["Locators", "Subsubsection", CellChangeTimes->{{3.4934624555625*^9, 3.493462459046875*^9}}], Cell[TextData[{ "It may seem silly to move a point around in a square region at the top just \ in order to move a corresponding point around in the drawing at the bottom. \ There is a another way of moving the point directly within the drawing, by \ changing the default 2D slider control to a ", StyleBox["Locator", FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"], " control." }], "Text", CellChangeTimes->{{3.4932198481875*^9, 3.49321992671875*^9}}], Cell[BoxData[ RowBox[{"Manipulate", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"Draw2D", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{"Blue", ",", RowBox[{"PointSize", "[", "Large", "]"}], ",", "\[IndentingNewLine]", RowBox[{"ComplexPoint", "[", RowBox[{"ToComplex", "[", "pt", "]"}], "]"}], ",", "\[IndentingNewLine]", "Red", ",", "Thick", ",", "\[IndentingNewLine]", RowBox[{"ComplexLine", "[", RowBox[{"{", RowBox[{"0", ",", "1", ",", RowBox[{"1", "+", "\[ImaginaryI]"}], ",", "\[ImaginaryI]", ",", "0"}], "}"}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"Axes", "\[Rule]", "True"}], ",", "\[IndentingNewLine]", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"ToCoordinates", "[", RowBox[{ RowBox[{"-", "2"}], "+", RowBox[{"2", "\[ImaginaryI]"}]}], "]"}], ",", RowBox[{"ToCoordinates", "[", RowBox[{ RowBox[{"-", "2"}], "+", RowBox[{"2", "\[ImaginaryI]"}]}], "]"}]}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", RowBox[{"3", " ", "72"}]}]}], "\[IndentingNewLine]", "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"pt", ",", RowBox[{"ToCoordinates", "[", RowBox[{ RowBox[{"-", "2"}], "-", RowBox[{"2", "\[ImaginaryI]"}]}], "]"}], ",", RowBox[{"ToCoordinates", "[", RowBox[{"2", "+", RowBox[{"2", "\[ImaginaryI]"}]}], "]"}], ",", "Locator"}], "}"}]}], "\[IndentingNewLine]", "]"}]], "Input", CellChangeTimes->{{3.493162028078125*^9, 3.49316217990625*^9}, { 3.4931622134375*^9, 3.493162288578125*^9}, {3.4931623320625*^9, 3.493162340609375*^9}, {3.493162371828125*^9, 3.493162435375*^9}, { 3.493162494203125*^9, 3.493162504703125*^9}, {3.49321831846875*^9, 3.49321832603125*^9}, {3.493219946640625*^9, 3.493219947875*^9}, { 3.493220319515625*^9, 3.49322033565625*^9}}], Cell["\<\ Now just move the point at the \"cross-hairs\" around directly with the \ mouse. 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It's hard to fix that directly. 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Control the whole drawing by putting a locator at ", Cell[BoxData[ FormBox["z", TraditionalForm]]], "." }], "Exercise", CellChangeTimes->{{3.49346267921875*^9, 3.493462847203125*^9}}, CellTags->"drawMultiplyByInoArc"], Cell[TextData[{ StyleBox["Exercise ", FontWeight->"Bold"], StyleBox[ CounterBox["Exercise"], FontWeight->"Bold"], StyleBox[".", FontWeight->"Bold"], " (a) Repeat Exercise ", CounterBox["Exercise", "drawMultiplyByInoArc"], " but instead of the multiple ", Cell[BoxData[ FormBox[ RowBox[{"\[ImaginaryI]", " ", "z"}], TraditionalForm]], FormatType->"TraditionalForm"], " of ", Cell[BoxData[ FormBox["z", TraditionalForm]], FormatType->"TraditionalForm"], ", use the sum ", Cell[BoxData[ FormBox[ RowBox[{"z", "+", "1"}], TraditionalForm]], FormatType->"TraditionalForm"], ".\n(b) Repeat Exercise ", CounterBox["Exercise", "drawMultiplyByInoArc"], " but instead of the multiple ", Cell[BoxData[ FormBox[ RowBox[{"\[ImaginaryI]", " ", "z"}], TraditionalForm]], FormatType->"TraditionalForm"], " of ", Cell[BoxData[ FormBox["z", TraditionalForm]], FormatType->"TraditionalForm"], ", use the sum ", Cell[BoxData[ FormBox[ RowBox[{"z", "+", "\[ImaginaryI]"}], TraditionalForm]], FormatType->"TraditionalForm"], "." }], "Exercise", CellChangeTimes->{{3.49346267921875*^9, 3.493462847203125*^9}, { 3.493463019484375*^9, 3.49346315421875*^9}}, ParagraphSpacing->{0.5, 0}], Cell[TextData[{ StyleBox["Exercise ", FontWeight->"Bold"], StyleBox[ CounterBox["Exercise"], FontWeight->"Bold"], StyleBox[".", FontWeight->"Bold"], " Repeat Exercise ", CounterBox["Exercise", "drawMultiplyByInoArc"], " but instead of the multiple ", Cell[BoxData[ FormBox[ RowBox[{"\[ImaginaryI]", " ", "z"}], TraditionalForm]], FormatType->"TraditionalForm"], " of ", Cell[BoxData[ FormBox["z", TraditionalForm]], FormatType->"TraditionalForm"], ", use the square ", Cell[BoxData[ FormBox[ SuperscriptBox["z", "2"], TraditionalForm]], FormatType->"TraditionalForm"], " of ", Cell[BoxData[ FormBox["z", TraditionalForm]], FormatType->"TraditionalForm"], "." }], "Exercise", CellChangeTimes->{{3.49346267921875*^9, 3.493462847203125*^9}, { 3.493463019484375*^9, 3.493463088671875*^9}}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Multiple controls", "Subsection", CellChangeTimes->{{3.493462396125*^9, 3.493462410484375*^9}, { 3.493462742046875*^9, 3.493462748703125*^9}, 3.493463214734375*^9}], Cell[TextData[{ "Next, scale the square ", StyleBox["and", FontSlant->"Italic"], " move the point around. Just use two controls. 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Include points at the vertices that \ move with the triangle as the latter is scaled." }], "Exercise", CellChangeTimes->{ 3.48969559478125*^9, 3.48969563040625*^9, {3.49322335240625*^9, 3.49322348190625*^9}}], Cell[TextData[{ StyleBox["Exercise ", FontWeight->"Bold"], StyleBox[ CounterBox["Exercise"], FontWeight->"Bold"], StyleBox[".", FontWeight->"Bold"], " Make a new ", StyleBox["Manipulate", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " expression that combines a slider control for the scale of the square and \ a locator for the point. Label both the scale and the point somehow (with \ names to indicate their meaning). Include a legend on the entire drawing." }], "Exercise", CellChangeTimes->{ 3.48969559478125*^9, 3.48969563040625*^9, {3.493222236734375*^9, 3.49322235715625*^9}, {3.49322308071875*^9, 3.493223082734375*^9}}], Cell[TextData[{ StyleBox["To use several locators", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], " in ", StyleBox["Manipulate", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " output, you could just add additional control variables for locators. A \ neater way is to use a single control variable that is a list of points. For \ example:" }], "Text", CellChangeTimes->{{3.4932181185625*^9, 3.493218193703125*^9}, { 3.493218237796875*^9, 3.4932182385625*^9}, {3.493221159640625*^9, 3.49322120271875*^9}, {3.4932235190625*^9, 3.49322356946875*^9}, { 3.493223666046875*^9, 3.493223700859375*^9}, 3.493223803421875*^9, { 3.4932238659375*^9, 3.493223866984375*^9}, {3.4938148305625*^9, 3.493814887140625*^9}, 3.493817281875*^9, {3.493817315234375*^9, 3.493817389265625*^9}, 3.49381784440625*^9}], Cell[BoxData[ RowBox[{"Manipulate", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"Draw2D", "[", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{"Red", ",", RowBox[{"PointSize", "[", "Large", "]"}], ",", RowBox[{"ComplexPoint", "/@", RowBox[{"ToComplex", "/@", "pts"}]}], ",", "\[IndentingNewLine]", "Blue", ",", "Thick", ",", RowBox[{"ComplexLine", "[", RowBox[{"ToComplex", "/@", "pts"}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"Axes", "\[Rule]", "True"}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", RowBox[{"3", " ", "72"}]}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"pts", ",", RowBox[{"{", RowBox[{ RowBox[{"ToCoordinates", "[", RowBox[{"1", "+", "\[ImaginaryI]"}], "]"}], ",", RowBox[{"ToCoordinates", "[", RowBox[{ RowBox[{"-", "1"}], "-", "\[ImaginaryI]"}], "]"}]}], "}"}]}], "}"}], ",", "Locator"}], "}"}]}], "\[IndentingNewLine]", "]"}]], "Input", CellChangeTimes->{{3.493297406140625*^9, 3.493297454828125*^9}, { 3.49329748884375*^9, 3.493297621421875*^9}, {3.49329794540625*^9, 3.493297962984375*^9}, {3.493298045375*^9, 3.493298099109375*^9}, { 3.49330431765625*^9, 3.493304395015625*^9}, {3.493461884296875*^9, 3.49346190984375*^9}, {3.49381433*^9, 3.493814428296875*^9}, 3.49381452459375*^9, {3.493814560328125*^9, 3.493814571515625*^9}, { 3.4938146326875*^9, 3.49381463640625*^9}, {3.49381489815625*^9, 3.49381500378125*^9}}], Cell["\<\ In the preceding output, you may independently move either of the two \ locators; the line joining the two points will move correspondingly.\ \>", "Text", CellChangeTimes->{{3.49381501365625*^9, 3.49381505609375*^9}}], Cell[TextData[{ "Look carefully at the control expression in the preceding input:\n\t", StyleBox["{{pts,lis},\[ThinSpace]Locator}", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], "\nThe list ", StyleBox["lis", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " of locators is an initialization for ", StyleBox["pts", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], ", and so both ", StyleBox["pts", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " and ", StyleBox["lis", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " are enclosed in the list\n\t", StyleBox["{pts,lis}", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], "\nthat in turn is nested inside the overall control expression list." }], "Text", CellChangeTimes->{{3.493817400953125*^9, 3.493817432859375*^9}, { 3.493817472671875*^9, 3.49381756153125*^9}, {3.493817601265625*^9, 3.493817693671875*^9}}, ParagraphSpacing->{0.5, 0}], Cell[TextData[{ StyleBox["Exercise ", FontWeight->"Bold"], StyleBox[ CounterBox["Exercise"], FontWeight->"Bold"], StyleBox[".", FontWeight->"Bold"], " Make a dynamic drawing of a filled-in polygon whose vertices you can move \ around interactively." }], "Exercise", CellChangeTimes->{ 3.48969559478125*^9, 3.48969563040625*^9, {3.493232091453125*^9, 3.49323215709375*^9}}], Cell[TextData[{ StyleBox["Exercise ", FontWeight->"Bold"], StyleBox[ CounterBox["Exercise"], FontWeight->"Bold"], StyleBox[".", FontWeight->"Bold"], " Make your drawing from Exercise ", CounterBox["Exercise", "SumDrawing"], " dynamic, so that you can interactively move the two points ", Cell[BoxData[ FormBox["z", TraditionalForm]]], " and ", Cell[BoxData[ FormBox["w", TraditionalForm]]], ". and so that, as you move them, their sum ", Cell[BoxData[ FormBox[ RowBox[{"z", "+", "w"}], TraditionalForm]]], " and the rest of the drawing correspondingly moves with ", Cell[BoxData[ FormBox["z", TraditionalForm]]], ", ", Cell[BoxData[ FormBox["w", TraditionalForm]]], ", and ", Cell[BoxData[ FormBox[ RowBox[{"z", "+", "w"}], TraditionalForm]]], "." }], "Exercise", CellChangeTimes->{ 3.48969559478125*^9, 3.48969563040625*^9, {3.4922923553125*^9, 3.4922923575*^9}, {3.492292409515625*^9, 3.49229265971875*^9}, { 3.492292746*^9, 3.492292760296875*^9}, {3.493231684625*^9, 3.4932317999375*^9}}, ParagraphSpacing->{0.5, 0}, CellTags->"dynamicSumDrawings"], Cell[CellGroupData[{ Cell[TextData[{ "Interactively creating and destroying locators: the ", StyleBox["LocatorAutoCreate", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " option" }], "Subsubsection", CellChangeTimes->{{3.49346259675*^9, 3.493462623953125*^9}}], Cell[TextData[{ "An intriguing possibility is to allow additional locators to be created and \ destroyed interactively. To do so, be sure that the initial value of the \ control variable for the locator is a list of one or more points, and then \ include the ", StyleBox["LocatorAutoCreate\[Rule]True", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " option for the locator control." }], "Text", CellChangeTimes->{{3.4932181185625*^9, 3.493218193703125*^9}, { 3.493218237796875*^9, 3.4932182385625*^9}, {3.493221159640625*^9, 3.49322120271875*^9}, {3.4932235190625*^9, 3.49322356946875*^9}, { 3.493223666046875*^9, 3.493223700859375*^9}, 3.493223803421875*^9, { 3.4932238659375*^9, 3.493223936765625*^9}, {3.493224055171875*^9, 3.49322407003125*^9}, {3.493817889796875*^9, 3.4938178919375*^9}}], Cell["\<\ For example, begin with a line segment each of whose ends can be \ independently varied by means of a locator:\ \>", "Text", CellChangeTimes->{{3.4932249186875*^9, 3.493224945484375*^9}}], Cell[BoxData[ RowBox[{"Manipulate", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"Draw2D", "[", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{"Thick", ",", "Red", ",", RowBox[{"ComplexLine", "[", RowBox[{"ToComplex", "/@", "pts"}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"Axes", "\[Rule]", "True"}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"ToCoordinates", "/@", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "2"}], "+", RowBox[{"2", "\[ImaginaryI]"}]}], ",", RowBox[{ RowBox[{"-", "2"}], "+", RowBox[{"2", "\[ImaginaryI]"}]}]}], "}"}]}]}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", RowBox[{"3", " ", "72"}]}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"pts", ",", RowBox[{"ToCoordinates", "/@", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "1"}], "-", "\[ImaginaryI]"}], ",", RowBox[{"1", "+", "\[ImaginaryI]"}]}], "}"}]}]}], "}"}], ",", "Locator"}], "}"}]}], "\[IndentingNewLine]", "]"}]], "Input", CellChangeTimes->{{3.493224572921875*^9, 3.4932247660625*^9}, { 3.4932248068125*^9, 3.493224888984375*^9}}, CellID->673259641], Cell["\<\ (Move one or another of the locators in the preceding output to see what \ happens.)\ \>", "Text", CellChangeTimes->{{3.493224966421875*^9, 3.493224987671875*^9}}], Cell[TextData[{ "Now add the ", StyleBox["LocatorAutoCreate\[Rule]True", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " option for the locator control." }], "Text", CellChangeTimes->{{3.493224992703125*^9, 3.493225013265625*^9}}], Cell[BoxData[ RowBox[{"Manipulate", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"Draw2D", "[", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{"Thick", ",", "Red", ",", RowBox[{"ComplexLine", "[", RowBox[{"ToComplex", "/@", "pts"}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"Axes", "\[Rule]", "True"}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"ToCoordinates", "/@", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "2"}], "+", RowBox[{"2", "\[ImaginaryI]"}]}], ",", RowBox[{ RowBox[{"-", "2"}], "+", RowBox[{"2", "\[ImaginaryI]"}]}]}], "}"}]}]}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", RowBox[{"3", " ", "72"}]}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"pts", ",", RowBox[{"ToCoordinates", "/@", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"-", "1"}], "-", "\[ImaginaryI]"}], ",", RowBox[{"1", "+", "\[ImaginaryI]"}]}], "}"}]}]}], "}"}], ",", "Locator", ",", RowBox[{"LocatorAutoCreate", "\[Rule]", "True"}]}], "}"}]}], "\[IndentingNewLine]", "]"}]], "Input", CellChangeTimes->{{3.493224572921875*^9, 3.4932247660625*^9}, { 3.4932248068125*^9, 3.4932249049375*^9}}, CellID->148008479], Cell["\<\ In the preceding output, each time you \[AltKey]-click (or \ \[ControlKey]-click) somewhere in the drawing, a new locator will be created \ there and that new point will be included in the polygonal line. To destroy a \ locator, put the cursor on it and \[AltKey]-click (or \[ControlKey]-click) \ it.\ \>", "Text", CellChangeTimes->{{3.493225060765625*^9, 3.493225084015625*^9}, { 3.493225167171875*^9, 3.493225351984375*^9}}], Cell[TextData[{ StyleBox["Exercise ", FontWeight->"Bold"], StyleBox[ CounterBox["Exercise"], FontWeight->"Bold"], StyleBox[".", FontWeight->"Bold"], " Make a dynamic drawing of a filled-in polygon whose vertices you can move \ interactively and in which you can interactively include or remove additional \ vertices." }], "Exercise", CellChangeTimes->{ 3.48969559478125*^9, 3.48969563040625*^9, {3.493232192375*^9, 3.493232251609375*^9}}] }, Closed]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Drawing circles and disks: ", StyleBox["ComplexCircle", FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"], " and ", StyleBox["ComplexDisk", FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"] }], "Section", ShowGroupOpener->True, CellChangeTimes->{{3.49381363459375*^9, 3.493813640390625*^9}, { 3.493813838734375*^9, 3.49381389471875*^9}, 3.493813980171875*^9}, CellTags->"circleAnddisk"], Cell[TextData[{ StyleBox["To draw a circle", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], "\n\t", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ SubscriptBox["C", "r"], "(", SubscriptBox["z", "0"], ")"}], "=", RowBox[{"{", RowBox[{"z", "\[Element]", RowBox[{"\[DoubleStruckCapitalC]", ":", RowBox[{"|", RowBox[{"z", "-", SubscriptBox["z", "0"]}], "|", RowBox[{"=", "r"}]}]}]}], "}"}]}], TraditionalForm]]], " \nwith specified center ", Cell[BoxData[ FormBox[ SubscriptBox["z", "0"], TraditionalForm]]], " (as a complex number) and radius ", Cell[BoxData[ FormBox[ RowBox[{"r", ">", "0"}], TraditionalForm]]], ", use the ", StyleBox["Presentations", FontSlant->"Italic"], " function ", StyleBox["ComplexCircle", FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"], ". For example:" }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.490789683953125*^9, 3.490789704171875*^9}, { 3.493658898484375*^9, 3.4936589246875*^9}}, ParagraphSpacing->{0.5, 0}], Cell[BoxData[ RowBox[{"Draw2D", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{"Red", ",", "Thick", ",", "\[IndentingNewLine]", RowBox[{"ComplexCircle", "[", RowBox[{ RowBox[{"\[ImaginaryI]", "/", "2"}], ",", "1"}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"Axes", "\[Rule]", "True"}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "}"}]}], ",", RowBox[{"ImageSize", "\[Rule]", RowBox[{"3", " ", "72"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.49078977278125*^9, 3.4907898671875*^9}, { 3.49079023771875*^9, 3.490790238796875*^9}, 3.4907930445*^9}], Cell[TextData[{ StyleBox["Exercise ", FontWeight->"Bold"], StyleBox[ CounterBox["Exercise"], FontWeight->"Bold"], StyleBox[".", FontWeight->"Bold"], " Let ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["z", "0"], "=", Cell["1+\[ThinSpace]\[ImaginaryI]"]}], TraditionalForm]]], " and ", Cell[BoxData[ FormBox[ RowBox[{"r", "=", RowBox[{"1", "/", "2"}]}], TraditionalForm]]], ". Draw the circle of radius ", Cell[BoxData[ FormBox["r", TraditionalForm]]], " centered at ", Cell[BoxData[ FormBox[ SubscriptBox["z", "0"], TraditionalForm]]], ". In your drawing, label its center and its circumference, the latter in \ the form ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"|", RowBox[{"z", "-", SubscriptBox["z", "0"]}], "|"}], "=", "r"}], TraditionalForm]]], "." }], "Exercise", CellChangeTimes->{ 3.48969559478125*^9, 3.48969563040625*^9, {3.490793158390625*^9, 3.490793161203125*^9}, {3.49079333996875*^9, 3.49079347071875*^9}, { 3.4907935299375*^9, 3.490793558078125*^9}, {3.490793637375*^9, 3.490793819453125*^9}, {3.493658185984375*^9, 3.493658191078125*^9}}], Cell[TextData[{ "And ", StyleBox["to draw an ", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], StyleBox["open disk", FontWeight->"Bold", FontSlant->"Plain", FontColor->RGBColor[0, 0, 1]], " \n\t", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ SubscriptBox["D", "r"], "(", SubscriptBox["z", "0"], ")"}], "=", RowBox[{"{", RowBox[{"z", "\[Element]", RowBox[{"\[DoubleStruckCapitalC]", ":", RowBox[{"|", RowBox[{"z", "-", SubscriptBox["z", "0"]}], "|", RowBox[{"<", "r"}]}]}]}], "}"}]}], TraditionalForm]]], "\n\[LongDash]", StyleBox["without ", FontSlant->"Italic"], "the boundary circle\[LongDash]use the ", StyleBox["Presentations", FontSlant->"Italic"], " function ", StyleBox["ComplexDisk", FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"], ". For example:" }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.490789880890625*^9, 3.49078989509375*^9}, { 3.4936589356875*^9, 3.49365893915625*^9}}, ParagraphSpacing->{0.5, 0}], Cell[BoxData[ RowBox[{"Draw2D", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{"Pink", ",", RowBox[{"ComplexDisk", "[", RowBox[{ RowBox[{"\[ImaginaryI]", "/", "2"}], ",", "1"}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"Axes", "\[Rule]", "True"}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "}"}]}], ",", RowBox[{"ImageSize", "\[Rule]", RowBox[{"3", " ", "72"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.4907899196875*^9, 3.49078995815625*^9}, { 3.49079023221875*^9, 3.490790257546875*^9}, {3.490793054296875*^9, 3.4907930661875*^9}}], Cell["\<\ To indicate that an open disk is really open, you could superimpose on it, \ dashed, its bounding circle:\ \>", "Text", CellChangeTimes->{{3.49365590415625*^9, 3.49365594175*^9}}], Cell[BoxData[ RowBox[{"Draw2D", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"Lighter", "@", "Pink"}], ",", RowBox[{"ComplexDisk", "[", RowBox[{ RowBox[{"\[ImaginaryI]", "/", "2"}], ",", "1"}], "]"}], ",", "\[IndentingNewLine]", "Red", ",", "Thick", ",", "Dashed", ",", RowBox[{"ComplexCircle", "[", RowBox[{ RowBox[{"\[ImaginaryI]", "/", "2"}], ",", "1"}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"Axes", "\[Rule]", "True"}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "}"}]}], ",", RowBox[{"ImageSize", "\[Rule]", RowBox[{"3", " ", "72"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.4907899196875*^9, 3.49078995815625*^9}, { 3.49079023221875*^9, 3.490790257546875*^9}, {3.490793054296875*^9, 3.4907930661875*^9}, {3.49365594896875*^9, 3.49365598934375*^9}}], Cell[TextData[{ "To represent a ", StyleBox["closed disk", FontWeight->"Bold", FontSlant->"Plain", FontColor->RGBColor[0, 0, 1]], " \n\t", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ SubscriptBox[ OverscriptBox["D", "_"], "r"], "(", SubscriptBox["z", "0"], ")"}], "=", RowBox[{"{", RowBox[{"z", "\[Element]", RowBox[{"\[DoubleStruckCapitalC]", ":", RowBox[{"|", RowBox[{"z", "-", SubscriptBox["z", "0"]}], "|", RowBox[{"\[LessEqual]", " ", "r"}]}]}]}], "}"}]}], TraditionalForm]]], "\n(including its bounding circle), you could use both a ", StyleBox["ComplexDisk", FontFamily->"Courier"], " and a ", StyleBox["ComplexCircle", FontFamily->"Courier"], " object. See the next paragraph for a simpler way." }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.490790007953125*^9, 3.490790041671875*^9}, { 3.493659381484375*^9, 3.493659405125*^9}}, ParagraphSpacing->{0.5, 0}], Cell[TextData[{ StyleBox["To indicate whether a disk is open or closed", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], ", a more direct way is to include an ", StyleBox["EdgeForm", FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"], " graphics directive:" }], "Text", CellChangeTimes->{{3.493658013984375*^9, 3.49365806525*^9}}], Cell[BoxData[ RowBox[{"Draw2D", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"Lighter", "@", "Pink"}], ",", "\[IndentingNewLine]", RowBox[{"EdgeForm", "[", RowBox[{"{", RowBox[{"Thick", ",", "Dashed", ",", RowBox[{"Legacy", "@", "IndianRed"}]}], "}"}], "]"}], ",", RowBox[{"ComplexDisk", "[", RowBox[{ RowBox[{"\[ImaginaryI]", "/", "2"}], ",", "1"}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"Axes", "\[Rule]", "True"}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "}"}]}], ",", RowBox[{"ImageSize", "\[Rule]", RowBox[{"3", " ", "72"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.4907899196875*^9, 3.49078995815625*^9}, { 3.49079023221875*^9, 3.490790257546875*^9}, {3.490793054296875*^9, 3.4907930661875*^9}, {3.49365594896875*^9, 3.49365598934375*^9}, { 3.4936580865*^9, 3.49365812190625*^9}}], Cell[TextData[{ "Notice that when the ", StyleBox["EdgeForm", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " argument includes more than one graphics directive, as above, that \ argument must be a list. 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Draw the closed disk of radius 1 centered at ", Cell[BoxData[ FormBox[ SubscriptBox["z", "0"], TraditionalForm]]], " along with an arrow from its center to some point of the bounding circle. \ Label the center and that arrow." }], "Exercise", CellChangeTimes->{ 3.48969559478125*^9, 3.48969563040625*^9, {3.490793158390625*^9, 3.490793161203125*^9}, {3.49079333996875*^9, 3.49079347071875*^9}, { 3.4907935299375*^9, 3.490793558078125*^9}, {3.490793637375*^9, 3.490793819453125*^9}, {3.49079403415625*^9, 3.4907941965625*^9}, { 3.490794257390625*^9, 3.49079431*^9}, 3.492292699640625*^9}], Cell[TextData[{ StyleBox["Exercise ", FontWeight->"Bold"], StyleBox[ CounterBox["Exercise"], FontWeight->"Bold"], StyleBox[".", FontWeight->"Bold"], " Pick a non-real complex number ", Cell[BoxData[ FormBox["z", TraditionalForm]]], ". Make a drawing that shows the points ", Cell[BoxData[ FormBox["z", TraditionalForm]]], " and \[ImaginaryI] z as well as arrows from the origin to each of these \ points. 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All you need to know about this function here is that, for real ", Cell[BoxData[ FormBox["a", TraditionalForm]], FormatType->"TraditionalForm"], " and ", Cell[BoxData[ FormBox["b", TraditionalForm]], FormatType->"TraditionalForm"], ":\n\t", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"exp", "(", RowBox[{"a", "+", RowBox[{"b", " ", "\[ImaginaryI]"}]}], ")"}], "=", RowBox[{ SuperscriptBox["\[ExponentialE]", "a"], "(", RowBox[{ RowBox[{"cos", " ", "b"}], "+", RowBox[{"\[ImaginaryI]", " ", "sin", " ", "b"}]}], ")"}]}], TraditionalForm]]] }], "Text", CellChangeTimes->{{3.49079481021875*^9, 3.4907948836875*^9}, { 3.49079491453125*^9, 3.49079497175*^9}, {3.490821854976466*^9, 3.490821857085841*^9}, {3.49221474484375*^9, 3.492214755*^9}}, ParagraphSpacing->{0.5, 0.}], Cell[TextData[{ "A ", StyleBox["curve", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], " in the complex plane is a continuous function\n\t", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"\[Gamma]", ":", " ", RowBox[{"[", RowBox[{"a", ",", "b"}], "]"}]}], "\[Rule]", "\[DoubleStruckCapitalC]"}], TraditionalForm]]], "\nwith domain some closed interval ", Cell[BoxData[ FormBox[ RowBox[{"[", RowBox[{"a", ",", "b"}], "]"}], TraditionalForm]]], ". For each ", Cell[BoxData[ FormBox[ RowBox[{"t", "\[Element]", RowBox[{"[", RowBox[{"a", ",", "b"}], "]"}]}], TraditionalForm]]], ", the complex number ", Cell[BoxData[ FormBox[ RowBox[{"\[Gamma]", "(", "t", ")"}], TraditionalForm]]], " has the form\n\t", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"\[Gamma]", "(", "t", ")"}], "=", RowBox[{ RowBox[{"z", "(", "t", ")"}], "=", RowBox[{ RowBox[{"x", "(", "t", ")"}], "+", RowBox[{"\[ImaginaryI]", " ", RowBox[{"y", "(", "t", ")"}]}]}]}]}], TraditionalForm]]], "\nwhere the functions\n\t", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"x", ":", RowBox[{"[", RowBox[{"a", ",", " ", "b"}], "]"}]}], "\[Rule]", "\[DoubleStruckCapitalR]"}], TraditionalForm]]], ", ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"y", ":", RowBox[{"[", RowBox[{"a", ",", "b"}], "]"}]}], "\[Rule]", "\[DoubleStruckCapitalR]"}], TraditionalForm]]], "\nare real-valued. Then the ", StyleBox["trace", FontWeight->"Bold", FontSlant->"Plain", FontColor->RGBColor[0, 0, 1]], " of the curve\[LongDash]its set of values\[LongDash]is the parametric plot \ of the pair of functions ", Cell[BoxData[ FormBox[ RowBox[{"(", RowBox[{ RowBox[{"x", "(", "t", ")"}], ",", RowBox[{"y", "(", "t", ")"}]}], ")"}], TraditionalForm]]], ".", Cell[BoxData[ FormBox[Cell[""], TraditionalForm]]] }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.490792694140625*^9, 3.490792821578125*^9}}, ParagraphSpacing->{0.5, 0}], Cell[TextData[{ "The ", StyleBox["Presentations", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], " function ", StyleBox["ComplexCurve", FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"], " facilitates drawing curves in the complex plane." }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.490792906984375*^9, 3.49079292490625*^9}, 3.492214877703125*^9, {3.49229279784375*^9, 3.492292801296875*^9}}], Cell[BoxData[ RowBox[{"?", "ComplexCurve"}]], "Input", ShowGroupOpener->True], Cell["\<\ Consider, for example, the upper semicircle of radius 2 with center the \ origin:\ \>", "Text", ShowGroupOpener->True], Cell[BoxData[ RowBox[{ RowBox[{"\[Gamma]", "[", "\[Theta]_", "]"}], ":=", RowBox[{"2", RowBox[{"Exp", "[", RowBox[{"\[ImaginaryI]", " ", "\[Theta]"}], "]"}]}]}]], "Input", ShowGroupOpener->True, CellChangeTimes->{{3.490792935640625*^9, 3.4907929425625*^9}, { 3.490795037296875*^9, 3.4907950378125*^9}}], Cell[BoxData[ RowBox[{"Draw2D", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{"Blue", ",", "\[IndentingNewLine]", RowBox[{"ComplexCurve", "[", RowBox[{ RowBox[{"\[Gamma]", "[", "\[Theta]", "]"}], ",", RowBox[{"{", RowBox[{"\[Theta]", ",", "0", ",", "\[Pi]"}], "}"}]}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"Frame", "\[Rule]", "True"}], ",", RowBox[{"FrameTicks", "\[Rule]", "Automatic"}], ",", RowBox[{"ImageSize", "\[Rule]", RowBox[{"4", " ", "72"}]}]}], "]"}]], "Input", ShowGroupOpener->True, CellChangeTimes->{{3.49079295146875*^9, 3.49079302940625*^9}, { 3.490794461046875*^9, 3.490794489703125*^9}}], Cell["Another example is a spiral:", "Text", ShowGroupOpener->True], Cell[BoxData[ RowBox[{ RowBox[{"Draw2D", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{"Blue", ",", "\[IndentingNewLine]", RowBox[{"ComplexCurve", "[", RowBox[{ RowBox[{"Exp", "[", RowBox[{ RowBox[{"(", RowBox[{"1", "+", RowBox[{"2", "\[ImaginaryI]"}]}], ")"}], "t"}], "]"}], ",", RowBox[{"{", RowBox[{"t", ",", RowBox[{"-", "2"}], ",", "3"}], "}"}]}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", RowBox[{"Axes", "\[Rule]", "True"}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", RowBox[{"4", " ", "72"}]}]}], "]"}], " "}]], "Input", ShowGroupOpener->True, CellChangeTimes->{{3.490794503546875*^9, 3.4907945545625*^9}, { 3.490794657765625*^9, 3.490794669953125*^9}, {3.490795044453125*^9, 3.490795045140625*^9}}], Cell[TextData[{ "The option ", StyleBox["PlotRange\[Rule]All", FontFamily->"Courier"], " in the preceding input ensures that all points on the curve, from ", Cell[BoxData[ FormBox[ RowBox[{"t", "=", RowBox[{"-", "2", " "}]}], TraditionalForm]]], " to ", Cell[BoxData[ FormBox[ RowBox[{"t", "=", "3"}], TraditionalForm]]], " are actually displayed. Try the same drawing but without that option to \ see what happens." }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.49079456725*^9, 3.490794606703125*^9}}], Cell[TextData[{ "Of course ", StyleBox["ComplexCurve", FontFamily->"Courier"], " objects may be combined with other ", StyleBox["Complex Graphics", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], " primitive objects. For example:" }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.49079468615625*^9, 3.490794700453125*^9}, 3.49381284409375*^9}], Cell[BoxData[ RowBox[{ RowBox[{"Draw2D", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{"Blue", ",", "\[IndentingNewLine]", RowBox[{"ComplexCurve", "[", RowBox[{ RowBox[{"Exp", "[", RowBox[{ RowBox[{"(", RowBox[{"1", "+", RowBox[{"2", "\[ImaginaryI]"}]}], ")"}], "t"}], "]"}], ",", RowBox[{"{", RowBox[{"t", ",", RowBox[{"-", "2"}], ",", "3"}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", "Red", ",", "Dashed", ",", "\[IndentingNewLine]", RowBox[{"ComplexLine", "[", RowBox[{"{", RowBox[{ RowBox[{"Exp", "[", RowBox[{ RowBox[{"-", "2"}], "-", RowBox[{"4", "I"}]}], "]"}], ",", RowBox[{"Exp", "[", RowBox[{"3", "+", RowBox[{"6", "I"}]}], "]"}]}], "}"}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"PlotRange", "\[Rule]", "All"}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", RowBox[{"4", " ", "72"}]}]}], "]"}], " "}]], "Input", ShowGroupOpener->True, CellChangeTimes->{{3.490794702953125*^9, 3.490794752265625*^9}, { 3.490795056671875*^9, 3.4907950914375*^9}}, CellTags->"spiral"], Cell[TextData[{ StyleBox["Exercise ", FontWeight->"Bold"], StyleBox[ CounterBox["Exercise"], FontWeight->"Bold"], StyleBox[".", FontWeight->"Bold"], " Draw the line segment from 1 to ", Cell[BoxData[ FormBox[ RowBox[{"1", "+", "\[ImaginaryI]"}], TraditionalForm]]], " in two different ways:\n\t(a) By using ", StyleBox["ComplexLine", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], ".\n\t(b) By using ", StyleBox["ComplexCurve", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], ". (", StyleBox["Hint:", FontSlant->"Italic"], " How can you parameterize a line segment from a point ", Cell[BoxData[ FormBox["A", TraditionalForm]]], " to a point ", Cell[BoxData[ FormBox["B", TraditionalForm]]], "?)\nThen evaluate just your ", StyleBox["ComplexLine", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " and then your ", StyleBox["ComplexCurve", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " expression alone\[LongDash]without the enclosing ", StyleBox["Draw2D", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " function\[LongDash]so as to see what each gives to ", StyleBox["Mathematica", FontSlant->"Italic"], " to display." }], "Exercise", CellChangeTimes->{ 3.48969559478125*^9, 3.48969563040625*^9, {3.49080021759375*^9, 3.490800351671875*^9}, {3.4908004831875*^9, 3.490800532421875*^9}}, ParagraphSpacing->{0.5, 0.}], Cell[TextData[{ "What you see in the displays produced from (a) and (b) in the preceding \ exercise should be the same. However, there is a critical difference in \ what's actually happening \"behind the scenes\":\n\t\[FilledSmallCircle] your \ ", StyleBox["ComplexLine", FontFamily->"Courier"], " expression gives ", StyleBox["Mathematica", FontSlant->"Italic"], " just the two endpoints ", Cell[BoxData[ FormBox[ RowBox[{"1", "=", RowBox[{"(", RowBox[{"1", ",", "0"}], ")"}]}], TraditionalForm]]], " and ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"1", "+", "\[ImaginaryI]"}], "=", RowBox[{"(", RowBox[{"1", ",", "1"}], ")"}]}], TraditionalForm]]], " of the line segment, and then the ", StyleBox["Draw2D", FontFamily->"Courier"], " expression causes ", StyleBox["Mathematica", FontSlant->"Italic"], " to draw the line segment connecting those two points; however,\n\t\ \[FilledSmallCircle] your ", StyleBox["ComplexCurve", FontFamily->"Courier"], " expression gives ", StyleBox["Mathematica", FontSlant->"Italic"], " a whole bunch of points along that line segment, and then the ", StyleBox["Draw2D", FontFamily->"Courier"], " expression causes ", StyleBox["Mathematica", FontSlant->"Italic"], " to \"connect the dots\", each one to the next, with very short line \ segments, to obtain the entire line segment.\nTo see that this is so, look \ again at the result you obtained in the preceding exercise when you evaluated \ your ", StyleBox["ComplexCurve[", FontFamily->"Courier"], StyleBox["\[Ellipsis]", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], StyleBox["]", FontFamily->"Courier"], " expression by itself." }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.49079512084375*^9, 3.490795199390625*^9}, { 3.4908005593125*^9, 3.490800560546875*^9}, {3.490821771288966*^9, 3.490821794976466*^9}}, ParagraphSpacing->{0.5, 0}], Cell[TextData[{ "This little discussion may seem pointless right now. But later, when you \ try to visualize what happens to a line segment when it is transformed by a \ function ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"f", ":", "\[DoubleStruckCapitalC]"}], "\[Rule]", "\[DoubleStruckCapitalC]"}], TraditionalForm]]], ", it will be crucial to use ", StyleBox["ComplexCurve", FontFamily->"Courier"], " rather than ", StyleBox["ComplexLine", FontFamily->"Courier"], " to form the segment." }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.4907952305625*^9, 3.490795250859375*^9}, { 3.490800590375*^9, 3.49080061765625*^9}}], Cell[TextData[{ StyleBox["Exercise ", FontWeight->"Bold"], StyleBox[ CounterBox["Exercise"], FontWeight->"Bold"], StyleBox[".", FontWeight->"Bold"], " Draw the circle with center ", Cell[BoxData[ FormBox[ RowBox[{"1", "+", "\[ImaginaryI]"}], TraditionalForm]]], " and radius 2 in two different ways:\n\t(a) By using ", StyleBox["ComplexCircle", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], ".\n\t(b) By using ", StyleBox["ComplexCurve", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], ". (", StyleBox["Hint:", FontSlant->"Italic"], " How can you parameterize a circle with given center and radius?)\nThen \ evaluate just your ", StyleBox["ComplexCircle", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " and then your ", StyleBox["ComplexCurve", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " expression alone\[LongDash]without the enclosing ", StyleBox["Draw2D", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " function\[LongDash]so as to see what each gives to ", StyleBox["Mathematica", FontSlant->"Italic"], " to display." }], "Exercise", CellChangeTimes->{ 3.48969559478125*^9, 3.48969563040625*^9, {3.49080021759375*^9, 3.490800351671875*^9}, {3.4908004831875*^9, 3.490800532421875*^9}, { 3.49080063615625*^9, 3.490800704890625*^9}}, ParagraphSpacing->{0.5, 0.}], Cell[TextData[{ StyleBox["Exercise ", FontWeight->"Bold"], StyleBox[ CounterBox["Exercise"], FontWeight->"Bold"], StyleBox[".", FontWeight->"Bold"], " Make a dynamic drawing of the same spiral as in a previous example but \ whose terminal end (the one not the origin) can be changed interactively, and \ the dashed line from the origin to the terminal end correspondingly changes \ too. In other words, as you move the slider forward, you see the spiral \ \"unroll\", getting longer and longer.\n(", StyleBox["Hint:", FontSlant->"Italic"], " You do not want a locator or 2D slider control. Rather, you want to vary \ how high the parameter values in the ComplexCurve can go.)" }], "Exercise", CellChangeTimes->{ 3.48969559478125*^9, 3.48969563040625*^9, {3.49323250078125*^9, 3.493232578734375*^9}, {3.493238061625*^9, 3.49323820259375*^9}, { 3.4932968576875*^9, 3.49329690946875*^9}, 3.493465035671875*^9}, ParagraphSpacing->{0.5, 0}] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Syntax of the ", StyleBox["Draw2D", FontFamily->"Courier"], " function" }], "Section", ShowGroupOpener->True, CellChangeTimes->{{3.49080073575*^9, 3.49080074021875*^9}, 3.490818863820216*^9}], Cell[TextData[{ "The template for ", StyleBox["Draw2D", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " that you can insert from the ", StyleBox["PresentationsPalette", FontFamily->"Helvetica", FontWeight->"Plain", FontSlant->"Plain"], " is\n\t", Cell[BoxData[ FormBox[ RowBox[{"Draw2D", "[", RowBox[{ RowBox[{"{", TagBox[ FrameBox["primitives"], "Placeholder"], "}"}], ",", TagBox[ FrameBox["options"], "Placeholder"]}], "]"}], TraditionalForm]]] }], "Text", CellChangeTimes->{{3.492214925765625*^9, 3.492214984546875*^9}, 3.492215024828125*^9}, ParagraphSpacing->{0.5, 0}], Cell[TextData[{ "Thus the general form of a ", StyleBox["Draw2D", FontFamily->"Courier"], " expression is\n\t", StyleBox["Draw2D[{", FontFamily->"Courier"], StyleBox["primitives", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], StyleBox["},", FontFamily->"Courier"], StyleBox["opts", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], StyleBox["]", FontFamily->"Courier"], "\t\nwhere:\n\t\[FilledSmallCircle] the argument ", StyleBox["{", FontFamily->"Courier"], StyleBox["primitives", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], StyleBox["}", FontFamily->"Courier"], " is a ", StyleBox["list", FontWeight->"Bold", FontSlant->"Italic"], " consisting of one or more complex ", StyleBox["graphics objects", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], " (", StyleBox["ComplexPoint", FontFamily->"Courier"], ", ", StyleBox["ComplexLine", FontFamily->"Courier"], ", ", StyleBox["ComplexCircle", FontFamily->"Courier"], ", ", StyleBox["ComplexDisk", FontFamily->"Courier"], ", ", StyleBox["ComplexCurve", FontFamily->"Courier"], ", ", StyleBox["ComplexText", FontFamily->"Courier"], ", etc., expressions) together with zero or more ", StyleBox["graphics directives", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], " (", StyleBox["PointSize", FontFamily->"Courier"], " and ", StyleBox["Thickness", FontFamily->"Courier"], " expressions, color specifications, etc.), in any order; and\n\t\ \[FilledSmallCircle] ", StyleBox["opts", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], ", if present, is a sequence of ", StyleBox["graphics options", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], " (", StyleBox["ImageSize\[Rule]", FontFamily->"Courier"], " ", StyleBox["\[Ellipsis]", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], StyleBox[", ", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Plain"], StyleBox["PlotRange\[Rule]", FontFamily->"Courier"], StyleBox["\[Ellipsis]", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], ", ", StyleBox["Background\[Rule]", FontFamily->"Courier"], StyleBox["\[Ellipsis]", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], ", ", StyleBox["PlotLabel\[Rule]", FontFamily->"Courier"], " ", StyleBox["\[Ellipsis]", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], ", ", StyleBox["Axes\[Rule]True", FontFamily->"Courier"], " , etc., options)." }], "Text", ShowGroupOpener->True, CellChangeTimes->{{3.490800745875*^9, 3.490800926109375*^9}, 3.490809367015625*^9, 3.490818863820216*^9, {3.492215042140625*^9, 3.492215044109375*^9}}, ParagraphSpacing->{0.5, 0}], Cell[TextData[{ "As usual, you may find out what options are available for Draw2D by looking \ at the function's reference page in the Documentation Center. And to get a \ quick list of the options and their default values, in your notebook \ evaluate:\n\t", StyleBox["Options[Draw2D]", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"] }], "Text", CellChangeTimes->{{3.493463338484375*^9, 3.49346341384375*^9}}, ParagraphSpacing->{0.5, 0}], Cell[TextData[{ "Another, handy way to find out the options for ", StyleBox["Draw2D", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], "\[LongDash]indeed, for ", StyleBox["any", FontSlant->"Italic"], " function\[LongDash]is to use the ", StyleBox["Presentations", FontSlant->"Italic"], " ", StyleBox["OptionsFinder", FontFamily->"Helvetica", FontWeight->"Plain", FontSlant->"Plain"], ". See notebook ", StyleBox["AboutPresentations.nb", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " for details." }], "Text", CellChangeTimes->{{3.493463418625*^9, 3.4934634291875*^9}, { 3.493463636703125*^9, 3.493463760453125*^9}, {3.49346385034375*^9, 3.493463857765625*^9}, {3.493463907625*^9, 3.4934640576875*^9}, { 3.49346409053125*^9, 3.493464211546875*^9}, {3.49346426653125*^9, 3.4934643188125*^9}, {3.49346436528125*^9, 3.493464521359375*^9}, { 3.493464572703125*^9, 3.49346462715625*^9}, {3.493466823640625*^9, 3.493466882203125*^9}, {3.493466915921875*^9, 3.493466917046875*^9}}, ParagraphSpacing->{0.5, 0}], Cell[CellGroupData[{ Cell["Lists of graphics objects", "Subsection", CellChangeTimes->{{3.490820405445216*^9, 3.490820414226466*^9}, { 3.490822070132716*^9, 3.490822073351466*^9}}], Cell[TextData[{ "Instead of individual ", StyleBox["Complex Graphics", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], " objects, you can use lists of such objects, too. For example:" }], "Text", CellChangeTimes->{{3.49081009690625*^9, 3.490810157796875*^9}, 3.490817899320216*^9, 3.490818863820216*^9, 3.493812850703125*^9}], Cell[BoxData[ RowBox[{"Draw2D", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{"Red", ",", "\[IndentingNewLine]", RowBox[{"ComplexLine", "[", RowBox[{"{", RowBox[{"0", ",", "1", ",", RowBox[{"1", "+", "\[ImaginaryI]"}], ",", "\[ImaginaryI]", ",", "0"}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"PointSize", "[", "Large", "]"}], ",", "Blue", ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"ComplexPoint", "[", "0", "]"}], ",", RowBox[{"ComplexPoint", "[", "1", "]"}], ",", RowBox[{"ComplexPoint", "[", RowBox[{"1", "+", "\[ImaginaryI]"}], "]"}], ",", RowBox[{"ComplexPoint", "[", "\[ImaginaryI]", "]"}], ",", RowBox[{"ComplexPoint", "[", "0", "]"}]}], "}"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", RowBox[{"3", " ", "72"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.4908095975625*^9, 3.49080972153125*^9}, { 3.49080975678125*^9, 3.490809930953125*^9}, 3.490810049046875*^9, { 3.490810259953125*^9, 3.49081035965625*^9}, {3.4908104083125*^9, 3.4908104091875*^9}, {3.490813737835841*^9, 3.490813769320216*^9}, 3.490818863820216*^9, {3.49227727290625*^9, 3.492277276890625*^9}}], Cell[TextData[{ "Of course in a situation like that, it\[CloseCurlyQuote]s easier to ", StyleBox["Map", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " the primitive ", StyleBox["ComplexPoint", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], " onto the list of complex numbers:" }], "Text", CellChangeTimes->{{3.4908103666875*^9, 3.49081040265625*^9}, 3.490818863820216*^9}], Cell[BoxData[ RowBox[{"Draw2D", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{"Red", ",", "\[IndentingNewLine]", RowBox[{"ComplexLine", "[", RowBox[{"{", RowBox[{"0", ",", "1", ",", RowBox[{"1", "+", "\[ImaginaryI]"}], ",", "\[ImaginaryI]", ",", "0"}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"PointSize", "[", "Large", "]"}], ",", "Blue", ",", "\[IndentingNewLine]", RowBox[{"ComplexPoint", "/@", RowBox[{"{", RowBox[{"0", ",", "1", ",", RowBox[{"1", "+", "\[ImaginaryI]"}], ",", "\[ImaginaryI]", ",", "0"}], "}"}]}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", RowBox[{"3", " ", "72"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.4908095975625*^9, 3.49080972153125*^9}, { 3.49080975678125*^9, 3.490809930953125*^9}, 3.490810049046875*^9, { 3.490810259953125*^9, 3.49081035965625*^9}, {3.4908104083125*^9, 3.490810440078125*^9}, 3.490813779523341*^9, 3.490818863820216*^9, { 3.49227728740625*^9, 3.492277299046875*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["Using names in place of graphics primitives", "Subsection", CellChangeTimes->{{3.490820533929591*^9, 3.490820564038966*^9}, { 3.490820776929591*^9, 3.490820781773341*^9}}], Cell[TextData[{ "In the final example of the preceding subsection, the list ", StyleBox["{0,1,1+\[ImaginaryI],\[ImaginaryI],0}", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " of complex numbers is used twice. In such a case, it\[CloseCurlyQuote]s \ often a good idea to assign a name to the list and then use that name within \ the ", StyleBox["Draw2D", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " expression:" }], "Text", CellChangeTimes->{{3.49081044671875*^9, 3.4908105215625*^9}, { 3.4908110818125*^9, 3.490811100625*^9}, 3.490818863820216*^9, { 3.490820573038966*^9, 3.490820686804591*^9}, {3.49227732446875*^9, 3.492277327921875*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"vertices", "=", RowBox[{"{", RowBox[{"0", ",", "1", ",", RowBox[{"1", "+", "\[ImaginaryI]"}], ",", "\[ImaginaryI]", ",", "0"}], "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Draw2D", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{"Red", ",", "\[IndentingNewLine]", RowBox[{"ComplexLine", "[", "vertices", "]"}], ",", "\[IndentingNewLine]", RowBox[{"PointSize", "[", "Large", "]"}], ",", "Blue", ",", "\[IndentingNewLine]", RowBox[{"ComplexPoint", "/@", "vertices"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", RowBox[{"3", " ", "72"}]}]}], "]"}]}], "Input", CellChangeTimes->{{3.4908095975625*^9, 3.49080972153125*^9}, { 3.49080975678125*^9, 3.490809930953125*^9}, 3.490810049046875*^9, { 3.490810259953125*^9, 3.49081035965625*^9}, {3.4908104083125*^9, 3.490810440078125*^9}, {3.490810537*^9, 3.49081054884375*^9}, { 3.490810641796875*^9, 3.490810654015625*^9}, 3.490818010117091*^9, 3.490818863820216*^9, {3.4922773089375*^9, 3.492277312015625*^9}}], Cell[TextData[{ "Other situations where you may want to use names as above, instead of using \ their values directly, are: (1) you are going to need the same ", StyleBox["Complex Graphics", FontSlant->"Italic"], " object in several drawings; or (2) you merely want to shorten the code \ within the ", StyleBox["Draw2D", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " expression. For example:" }], "Text", CellChangeTimes->{{3.490809375859375*^9, 3.49080958459375*^9}, { 3.490809742421875*^9, 3.490809743046875*^9}, {3.490810697375*^9, 3.49081071725*^9}, {3.490818032945216*^9, 3.490818107820216*^9}, 3.490818863820216*^9, {3.490820002101466*^9, 3.490820009585841*^9}, 3.493812856*^9}], Cell[BoxData[{ RowBox[{ RowBox[{"vertices", "=", RowBox[{"{", RowBox[{"0", ",", "1", ",", RowBox[{"1", "+", "\[ImaginaryI]"}], ",", "\[ImaginaryI]", ",", "0"}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"pts", "=", RowBox[{"ComplexPoint", "/@", "vertices"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"square", "=", RowBox[{"ComplexLine", "[", "vertices", "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"labels", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"ComplexText", "[", RowBox[{ RowBox[{"Style", "[", RowBox[{"0", ",", "16", ",", RowBox[{"FontWeight", "\[Rule]", "Bold"}]}], "]"}], ",", RowBox[{"0.05", "+", RowBox[{"0.05", "\[ImaginaryI]"}]}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"ComplexText", "[", RowBox[{ RowBox[{"Style", "[", RowBox[{"1", ",", "16", ",", RowBox[{"FontWeight", "\[Rule]", "Bold"}]}], "]"}], ",", RowBox[{"0.95", "+", RowBox[{"0.05", "\[ImaginaryI]"}]}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"ComplexText", "[", RowBox[{ RowBox[{"Style", "[", RowBox[{ RowBox[{"1", "+", "\[ImaginaryI]"}], ",", "14", ",", RowBox[{"FontWeight", "\[Rule]", "Bold"}]}], "]"}], ",", RowBox[{"0.95", "+", RowBox[{"1.05", "\[ImaginaryI]"}]}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"ComplexText", "[", RowBox[{ RowBox[{"Style", "[", RowBox[{"\[ImaginaryI]", ",", "16", ",", RowBox[{"FontWeight", "\[Rule]", "Bold"}]}], "]"}], ",", RowBox[{"0.05", "+", RowBox[{"1.05", "\[ImaginaryI]"}]}]}], "]"}]}], "\[IndentingNewLine]", "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Draw2D", "[", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{"Red", ",", "square", ",", "\[IndentingNewLine]", RowBox[{"PointSize", "[", "Large", "]"}], ",", "Blue", ",", "pts", ",", "\[IndentingNewLine]", "Black", ",", "labels"}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"PlotLabel", "\[Rule]", RowBox[{"Style", "[", "\"\\"", "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"Axes", "\[Rule]", "True"}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", RowBox[{"3.5", " ", "72"}]}]}], "]"}]}], "Input", CellChangeTimes->{{3.4908095975625*^9, 3.49080972153125*^9}, { 3.49080975678125*^9, 3.490809930953125*^9}, 3.490810049046875*^9, { 3.4908107821875*^9, 3.49081082*^9}, {3.49081085115625*^9, 3.490810918578125*^9}, {3.490810956640625*^9, 3.49081105253125*^9}, { 3.490813833413966*^9, 3.490813917335841*^9}, {3.490818119695216*^9, 3.490818287335841*^9}, {3.490818563663966*^9, 3.490818601679591*^9}, 3.490818863820216*^9, {3.490818907007716*^9, 3.490818984445216*^9}, { 3.492277337359375*^9, 3.492277391296875*^9}}], Cell[TextData[{ "Actually, there\[CloseCurlyQuote]s no reason to use a ", StyleBox["Style", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " argument to each separate ", StyleBox["ComplexText", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " object above. If you want to use the same style for ", StyleBox["all", FontSlant->"Italic"], " text appearing in the drawing\[LongDash]including plot labels, axes \ labels, etc.\[LongDash]then you may use a single ", StyleBox["BaseStyle", FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"], " graphics option for ", StyleBox["Draw2D", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], ". For example:" }], "Text", CellChangeTimes->{{3.490818406742091*^9, 3.490818539007716*^9}, 3.490818863835841*^9, {3.490819023585841*^9, 3.490819042117091*^9}, { 3.490820021820216*^9, 3.490820024757716*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"vertices", "=", RowBox[{"{", RowBox[{"0", ",", "1", ",", RowBox[{"1", "+", "\[ImaginaryI]"}], ",", "\[ImaginaryI]", ",", "0"}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"pts", "=", RowBox[{"ComplexPoint", "/@", "vertices"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"square", "=", RowBox[{"ComplexLine", "[", "vertices", "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"labels", "=", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"ComplexText", "[", RowBox[{"0", ",", RowBox[{"0.05", "+", RowBox[{"0.05", "\[ImaginaryI]"}]}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"ComplexText", "[", RowBox[{"1", ",", RowBox[{"0.95", "+", RowBox[{"0.05", "\[ImaginaryI]"}]}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"ComplexText", "[", RowBox[{ RowBox[{"1", "+", "\[ImaginaryI]"}], ",", RowBox[{"0.95", "+", RowBox[{"1.05", "\[ImaginaryI]"}]}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"ComplexText", "[", RowBox[{"\[ImaginaryI]", ",", RowBox[{"0.05", "+", RowBox[{"1.05", "\[ImaginaryI]"}]}]}], "]"}]}], "\[IndentingNewLine]", "}"}]}], ";"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Draw2D", "[", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{"Red", ",", "square", ",", "\[IndentingNewLine]", RowBox[{"PointSize", "[", "Large", "]"}], ",", "Blue", ",", "pts", ",", "\[IndentingNewLine]", "Black", ",", "labels"}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"PlotLabel", "\[Rule]", RowBox[{"Style", "[", "\"\\"", "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"Axes", "\[Rule]", "True"}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"BaseStyle", "\[Rule]", RowBox[{"{", RowBox[{"16", ",", RowBox[{"FontWeight", "\[Rule]", "Bold"}]}], "}"}]}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", RowBox[{"3.5", " ", "72"}]}]}], "]"}]}], "Input", CellChangeTimes->{{3.4908095975625*^9, 3.49080972153125*^9}, { 3.49080975678125*^9, 3.490809930953125*^9}, 3.490810049046875*^9, { 3.4908107821875*^9, 3.49081082*^9}, {3.49081085115625*^9, 3.490810918578125*^9}, {3.490810956640625*^9, 3.49081105253125*^9}, { 3.490813833413966*^9, 3.490813917335841*^9}, {3.490818119695216*^9, 3.490818287335841*^9}, {3.490818317992091*^9, 3.490818386867091*^9}, { 3.490818626304591*^9, 3.490818656742091*^9}, 3.490818863835841*^9, { 3.490819073179591*^9, 3.490819084929591*^9}, {3.49227740215625*^9, 3.49227742290625*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["Isolating the scope of a graphics directive", "Subsection", CellChangeTimes->{{3.490820449460841*^9, 3.490820481148341*^9}, { 3.490820719726466*^9, 3.490820734273341*^9}, {3.490822055788966*^9, 3.490822057007716*^9}}], Cell[TextData[{ "Just as you may use a list defined names of ", StyleBox["Complex Graphics", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], " objects, instead of individual objects, within the first (list) argument ", StyleBox["{", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], StyleBox["\[Ellipsis]", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], StyleBox["}", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " of ", StyleBox["Draw2D", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " , so you may use a list consisting of both graphics directives and ", StyleBox["Complex Graphics", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], " objects. This is another way to make the meaning of code more apparent. \ For example:" }], "Text", CellChangeTimes->{{3.49081009690625*^9, 3.490810157796875*^9}, { 3.490811141390625*^9, 3.490811227125*^9}, 3.490818863851466*^9, { 3.490819196351466*^9, 3.490819236929591*^9}, {3.490819334913966*^9, 3.490819365460841*^9}, {3.490820753273341*^9, 3.490820754351466*^9}, { 3.492277457953125*^9, 3.492277460046875*^9}, {3.493812860859375*^9, 3.49381286603125*^9}}], Cell[BoxData[ RowBox[{"Draw2D", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"Red", ",", "Thick", ",", RowBox[{"ComplexLine", "[", RowBox[{"{", RowBox[{"0", ",", "1", ",", RowBox[{"1", "+", "\[ImaginaryI]"}], ",", "\[ImaginaryI]", ",", "0"}], "}"}], "]"}], ",", RowBox[{"ComplexLine", "[", RowBox[{"{", RowBox[{"0", ",", RowBox[{"1", "+", "\[ImaginaryI]"}]}], "}"}], "]"}], ",", RowBox[{"ComplexText", "[", RowBox[{"\"\\"", ",", RowBox[{"0.55", "+", RowBox[{"0.7", "\[ImaginaryI]"}]}]}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{"Blue", ",", RowBox[{"PointSize", "[", "Large", "]"}], ",", RowBox[{"ComplexPoint", "[", RowBox[{ RowBox[{"1", "/", "2"}], RowBox[{"(", RowBox[{"1", "+", "\[ImaginaryI]"}], ")"}]}], "]"}]}], "}"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", RowBox[{"3", " ", "72"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.4908095975625*^9, 3.49080972153125*^9}, { 3.49080975678125*^9, 3.490809930953125*^9}, 3.490810049046875*^9, { 3.490810259953125*^9, 3.49081035965625*^9}, {3.4908104083125*^9, 3.4908104091875*^9}, {3.490813737835841*^9, 3.490813769320216*^9}, 3.490818863820216*^9, {3.490819158101466*^9, 3.490819181757716*^9}, { 3.490819242648341*^9, 3.490819324476466*^9}, {3.490819388804591*^9, 3.490819466757716*^9}, {3.4922774726875*^9, 3.492277483828125*^9}}], Cell[TextData[{ "It is important to understand the ", StyleBox["scope of graphics directives", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], ". A graphics directives within a ", StyleBox["Draw2D", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " expression will affect all subsequent ", StyleBox["Complex Graphics", FontSlant->"Italic"], " objects formed within that expression and to which it is relevant\ \[LongDash]", StyleBox["unless", FontSlant->"Italic"], " the directive is: \n\t\[FilledSmallCircle] overridden by a subsequent \ directive; or \n\t\[FilledSmallCircle] buried within a list nested inside \ the ", StyleBox["{", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], StyleBox["\[Ellipsis]", FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], StyleBox["}", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " list argument to ", StyleBox["Draw2D", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], ".\nThus, compare the two drawings below:" }], "Text", CellChangeTimes->{{3.49080110740625*^9, 3.490801180015625*^9}, 3.490818863851466*^9, {3.490819561976466*^9, 3.490819593788966*^9}, { 3.490819635492091*^9, 3.490819645867091*^9}, {3.490819715023341*^9, 3.490819731976466*^9}, {3.490819809554591*^9, 3.490819851570216*^9}, { 3.490820057538966*^9, 3.490820089242091*^9}, {3.490820246179591*^9, 3.490820320007716*^9}, {3.490821875273341*^9, 3.490821883913966*^9}, 3.493812873*^9}, ParagraphSpacing->{0.5, 0.}], Cell[BoxData[{ RowBox[{ RowBox[{"unnested", "=", RowBox[{"Draw2D", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{"Red", ",", "Thick", ",", RowBox[{"ComplexLine", "[", RowBox[{"{", RowBox[{"0", ",", "1", ",", RowBox[{"1", "+", "\[ImaginaryI]"}], ",", "\[ImaginaryI]", ",", "0"}], "}"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"PointSize", "[", "Large", "]"}], ",", RowBox[{"ComplexPoint", "[", RowBox[{ RowBox[{"1", "/", "2"}], RowBox[{"(", RowBox[{"1", "+", "\[ImaginaryI]"}], ")"}]}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", RowBox[{"3", " ", "72"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"nested", "=", RowBox[{"Draw2D", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"{", RowBox[{"Red", ",", "Thick", ",", RowBox[{"ComplexLine", "[", RowBox[{"{", RowBox[{"0", ",", "1", ",", RowBox[{"1", "+", "\[ImaginaryI]"}], ",", "\[ImaginaryI]", ",", "0"}], "}"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"PointSize", "[", "Large", "]"}], ",", RowBox[{"ComplexPoint", "[", RowBox[{ RowBox[{"1", "/", "2"}], RowBox[{"(", RowBox[{"1", "+", "\[ImaginaryI]"}], ")"}]}], "]"}]}], "\[IndentingNewLine]", "}"}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", RowBox[{"3", " ", "72"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"Row", "[", RowBox[{"{", RowBox[{"unnested", ",", RowBox[{"Spacer", "[", "5", "]"}], ",", "nested"}], "}"}], "]"}]}], "Input", CellChangeTimes->{{3.490819745398341*^9, 3.490819787976466*^9}, { 3.490820128492091*^9, 3.490820135023341*^9}, {3.4922774973125*^9, 3.492277513953125*^9}}], Cell[TextData[{ "Look again at input for the last output. As the code for the drawing at the \ right illustrates, you may isolate the effects of a graphics directive by \ using nested lists, as in the definition of ", StyleBox["nested", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " above." }], "Text", CellChangeTimes->{{3.490819882429591*^9, 3.490819954257716*^9}, { 3.490820826226466*^9, 3.490820859742091*^9}, {3.492286780015625*^9, 3.4922868450625*^9}, {3.492292956171875*^9, 3.492292957640625*^9}}], Cell[TextData[{ StyleBox["Exercise ", FontWeight->"Bold"], StyleBox[ CounterBox["Exercise"], FontWeight->"Bold"], StyleBox[".", FontWeight->"Bold"], " Copy and suitably edit the code for the last output in order to put a \ frame around the entire row of drawings and to give the whole thing a \ different background color." }], "Exercise", CellChangeTimes->{{3.4922869045*^9, 3.492286962921875*^9}, { 3.4922870188125*^9, 3.49228706821875*^9}}, CellTags->"frame2drawings"], Cell[TextData[{ "When you have several graphics directives in a row that are to effect \ subsequent graphics objects, you can sometimes make the code easier to read \ or write by combining the directives into arguments of a ", StyleBox["Directive", FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"], " expression. (In itself, this does nothing to alter the scope of the \ directives.) 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You could also use ", StyleBox["GraphicsRow", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " instead of ", StyleBox["Row", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], "; that would automatically take care of the intermediate spacing for you. \ Similarly you could use ", StyleBox["Column", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " or ", StyleBox["GraphicsColumn", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " to display two outputs stacked vertically. And you could use ", StyleBox["Grid", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " or ", StyleBox["GraphicsGrid", FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], " if you want to create a multi-row, multi-column display. 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