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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 62871, 1218]*) (*NotebookOutlinePosition[ 63847, 1251]*) (* CellTagsIndexPosition[ 63768, 1245]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Sierpinksi's Monster Made Palette-able", "Title"], Cell[TextData[{ "Buttons and palettes simplify the work of writing with ", StyleBox["Mathematica", FontSlant->"Italic"], " 3.0." }], "Subsubtitle"], Cell[CellGroupData[{ Cell["by David Fowler and Robert Dickau", "Subtitle"], Cell[TextData[{ "In ", StyleBox["Writing Mathematics Well", FontSlant->"Italic"], ", Leonard Gillman [Gillman 1987] presents the following example of \ terrible mathematical notation:" }], "Text"], Cell[BoxData[ \(TraditionalForm \`t\_\(n\_\[Kappa]\%\(\[Xi]\_\[Kappa]\%\[Alpha]\)\)\%\(\[Xi]\_\[Kappa]\%\ \[Alpha]\)\)], "Input"], Cell[TextData[{ "This symbol is the work of the great Polish topologist Wac\[LSlash]aw \ Sierpi", Cell[BoxData[ \(TraditionalForm\`n\&\[ReversePrime]\[Prime]\)]], "ski, (*Joe, can't find the correct Polish symbol*) perhaps better known to \ readers of this journal for the Sierpinski ", ButtonBox["triangle", ButtonData:>"The Triangle", ButtonStyle->"Hyperlink"], " (*Footnote: The underlined term is a ", StyleBox["hyperlink", FontSlant->"Italic"], ", which takes readers of the electronic version of this article to a \ section at the end showing ", StyleBox["Mathematica ", FontSlant->"Italic"], "3.0 code for generating a version of the triangle. Hyperlinks and advanced \ notebook programming will be covered in future issues of ", StyleBox["Mathematica in Education and Research", FontSlant->"Italic"], ". *). \n\nIn an appendix showing how to simplify the notation, Gillman \ remarks \"Sierpinski had a pixyish quality and may have done all this partly \ because it was so much fun.\" [Gillman 1987, page 38]." }], "Text"], Cell[TextData[{ "In the spirit of fun, then, but also to demonstrate the power of ", StyleBox["Mathematica", FontSlant->"Italic"], " 3.0's new palette feature, we show that this \"monster,\" as Gillman \ labels it, presents no problems for the ", StyleBox["Mathematica", FontSlant->"Italic"], " 3.0 user.\n\nWe list the exact set of clicks and keystrokes needed to \ create the expression. The reader who does not wish to verify each stroke \ will still appreciate the ease with which the expression can be created." }], "Text"], Cell[CellGroupData[{ Cell["\<\ Creating a Sierpinski monster with the BasicTypesetting \ palette\ \>", "Section"], Cell[TextData[{ "This simple tutorial uses the ", StyleBox["BasicTypesetting", FontFamily->"Chicago", FontSize->10], " palette, located under \n", StyleBox["File: Palettes", FontFamily->"Chicago", FontSize->10], StyleBox["\[RightTriangle] ", FontWeight->"Bold"] }], "Text"], Cell[BoxData[GridBox[{ { StyleBox[GridBox[{ { ButtonBox["\[Alpha]", ButtonNote->"\[EscapeKey]a\[EscapeKey]"], ButtonBox["\[Beta]", ButtonNote->"\[EscapeKey]b\[EscapeKey]"], ButtonBox["\[Gamma]", ButtonNote->"\[EscapeKey]g\[EscapeKey]"], ButtonBox["\[Delta]", ButtonNote->"\[EscapeKey]d\[EscapeKey]"], ButtonBox["\[Epsilon]", ButtonNote->"\[EscapeKey]e\[EscapeKey]"], ButtonBox["\[CurlyEpsilon]", ButtonNote->"\[EscapeKey]ce\[EscapeKey]"], ButtonBox["\[Zeta]", ButtonNote->"\[EscapeKey]z\[EscapeKey]"], ButtonBox["\[Eta]", ButtonNote->"\[EscapeKey]et\[EscapeKey]"], ButtonBox["\[Theta]", ButtonNote->"\[EscapeKey]th\[EscapeKey]"], ButtonBox["\[CurlyTheta]", ButtonNote->"\[EscapeKey]cq\[EscapeKey]"]}, { ButtonBox["\[Iota]", ButtonNote->"\[EscapeKey]i\[EscapeKey]"], ButtonBox["\[Kappa]", ButtonNote->"\[EscapeKey]k\[EscapeKey]"], ButtonBox["\[CurlyKappa]", ButtonNote->"\[EscapeKey]ck\[EscapeKey]"], ButtonBox["\[Lambda]", ButtonNote->"\[EscapeKey]l\[EscapeKey]"], ButtonBox["\[Mu]", ButtonNote->"\[EscapeKey]m\[EscapeKey]"], ButtonBox["\[Nu]", ButtonNote->"\[EscapeKey]n\[EscapeKey]"], ButtonBox["\[Xi]", ButtonNote->"\[EscapeKey]x\[EscapeKey]"], ButtonBox["\[Pi]", ButtonNote->"\[EscapeKey]p\[EscapeKey]"], ButtonBox["\[CurlyPi]", ButtonNote->"\[EscapeKey]cp\[EscapeKey]"], ButtonBox["\[Rho]", ButtonNote->"\[EscapeKey]r\[EscapeKey]"]}, { ButtonBox["\[CurlyRho]", ButtonNote->"\[EscapeKey]cr\[EscapeKey]"], ButtonBox["\[Sigma]", ButtonNote->"\[EscapeKey]s\[EscapeKey]"], ButtonBox["\[Tau]", ButtonNote->"\[EscapeKey]t\[EscapeKey]"], ButtonBox["\[Upsilon]", ButtonNote->"\[EscapeKey]u\[EscapeKey]"], ButtonBox["\[Phi]", ButtonNote->"\[EscapeKey]ph\[EscapeKey]"], ButtonBox["\[CurlyPhi]", ButtonNote->"\[EscapeKey]j\[EscapeKey]"], ButtonBox["\[Chi]", ButtonNote->"\[EscapeKey]ch\[EscapeKey]"], ButtonBox["\[Psi]", ButtonNote->"\[EscapeKey]ps\[EscapeKey]"], ButtonBox["\[Omega]", ButtonNote->"\[EscapeKey]o\[EscapeKey]"], ButtonBox["\[Sampi]", ButtonNote->"\[EscapeKey]sa\[EscapeKey]"]}, { ButtonBox["\[CapitalGamma]", ButtonNote->"\[EscapeKey]G\[EscapeKey]"], ButtonBox["\[CapitalDelta]", ButtonNote->"\[EscapeKey]D\[EscapeKey]"], ButtonBox["\[CapitalTheta]", ButtonNote->"\[EscapeKey]Th\[EscapeKey]"], ButtonBox["\[CapitalLambda]", ButtonNote->"\[EscapeKey]L\[EscapeKey]"], ButtonBox["\[CapitalXi]", ButtonNote->"\[EscapeKey]X\[EscapeKey]"], ButtonBox["\[CapitalPi]", ButtonNote->"\[EscapeKey]P\[EscapeKey]"], ButtonBox["\[CapitalSigma]", ButtonNote->"\[EscapeKey]S\[EscapeKey]"], ButtonBox["\[CapitalUpsilon]", ButtonNote->"\[EscapeKey]U\[EscapeKey]"], ButtonBox["\[CapitalPhi]", ButtonNote->"\[EscapeKey]Ph\[EscapeKey]"], ButtonBox["\[CapitalPsi]", ButtonNote->"\[EscapeKey]Ps\[EscapeKey]"]}, { ButtonBox["\[CapitalOmega]", ButtonNote->"\[EscapeKey]O\[EscapeKey]"], ButtonBox["\[CapitalKoppa]", ButtonNote->"\[EscapeKey]Ko\[EscapeKey]"], ButtonBox["\[CapitalSampi]", ButtonNote->"\[EscapeKey]Sa\[EscapeKey]"], ButtonBox["\[EmptySet]", ButtonNote->"\[EscapeKey]es\[EscapeKey]"], ButtonBox["\[Mho]", ButtonNote->"\[EscapeKey]mho\[EscapeKey]"], ButtonBox["\[Product]", ButtonNote->"\[EscapeKey]prod\[EscapeKey]"], ButtonBox["\[Sum]", ButtonNote->"\[EscapeKey]sum\[EscapeKey]"], ButtonBox["\[Del]", ButtonNote->"\[EscapeKey]del\[EscapeKey]"], ButtonBox["\[PartialD]", ButtonNote->"\[EscapeKey]pd\[EscapeKey]"], ButtonBox["\[Micro]", ButtonNote->"\[EscapeKey]mi\[EscapeKey]"]}, { ButtonBox["\[Infinity]", ButtonNote->"\[EscapeKey]inf\[EscapeKey]"], ButtonBox["\[Degree]", ButtonNote->"\[EscapeKey]deg\[EscapeKey]"], ButtonBox["\[Angle]", ButtonNote->""], ButtonBox["\[MeasuredAngle]", ButtonNote->""], ButtonBox["\[DifferentialD]", ButtonNote->"\[EscapeKey]dd\[EscapeKey]"], ButtonBox["\[ExponentialE]", ButtonNote->"\[EscapeKey]ee\[EscapeKey]"], ButtonBox["\[ImaginaryI]", ButtonNote->"\[EscapeKey]ii\[EscapeKey]"], ButtonBox["\[HBar]", ButtonNote->"\[EscapeKey]hb\[EscapeKey]"], ButtonBox["\[Angstrom]", ButtonNote->"\[EscapeKey]Ang\[EscapeKey]"], ButtonBox["\[Aleph]", ButtonNote->"\[EscapeKey]al\[EscapeKey]"]}, { ButtonBox["\[ScriptL]", ButtonNote->"\[EscapeKey]scl\[EscapeKey]"], ButtonBox["\[ScriptCapitalH]", ButtonNote->"\[EscapeKey]scH\[EscapeKey]"], ButtonBox["\[ScriptCapitalL]", ButtonNote->"\[EscapeKey]scL\[EscapeKey]"], ButtonBox["\[GothicCapitalI]", ButtonNote->"\[EscapeKey]goI\[EscapeKey]"], ButtonBox["\[GothicCapitalR]", ButtonNote->"\[EscapeKey]goR\[EscapeKey]"], ButtonBox["\[DoubleStruckCapitalC]", ButtonNote->"\[EscapeKey]dsC\[EscapeKey]"], ButtonBox["\[DoubleStruckCapitalN]", ButtonNote->"\[EscapeKey]dsN\[EscapeKey]"], ButtonBox["\[DoubleStruckCapitalR]", ButtonNote->"\[EscapeKey]dsR\[EscapeKey]"], ButtonBox["\[DoubleStruckCapitalZ]", ButtonNote->"\[EscapeKey]dsZ\[EscapeKey]"], ButtonBox["\[WeierstrassP]", ButtonNote->"\[EscapeKey]wp\[EscapeKey]"]} }, RowSpacings->0, ColumnSpacings->0, GridDefaultElement:>ButtonBox[ "\\[Placeholder]"]], FontSize->12]}, {GridBox[{ { ButtonBox[\(\[SelectionPlaceholder]\^\[Placeholder]\)], ButtonBox[\(\[SelectionPlaceholder]\_\[Placeholder]\)], ButtonBox[ \(\[SelectionPlaceholder]\_\[Placeholder]\%\[Placeholder]\)]\ , ButtonBox[ \(\(\[InvisiblePrefixScriptBase]\^\[Placeholder]\)\ \[SelectionPlaceholder]\)], ButtonBox[ \(\(\[InvisiblePrefixScriptBase]\_\[Placeholder]\)\ \[SelectionPlaceholder]\)], ButtonBox[\(\[SelectionPlaceholder]\&\[Placeholder]\)], ButtonBox[\(\[SelectionPlaceholder]\+\[Placeholder]\)], ButtonBox[ \(\[SelectionPlaceholder]\+\[Placeholder]\%\[Placeholder]\)]\ }, { ButtonBox[\(\[SelectionPlaceholder]\^\[Dagger]\)], ButtonBox[\(\[SelectionPlaceholder]\_+\)], ButtonBox[\(\[SelectionPlaceholder]\^+\)], ButtonBox[\(\[SelectionPlaceholder]\_-\)], ButtonBox[\(\[SelectionPlaceholder]\^-\)], ButtonBox[\(\[SelectionPlaceholder]\+_\)], ButtonBox[\(\[SelectionPlaceholder]\&_\)], ButtonBox[\(\[SelectionPlaceholder]\&\[RightVector]\)]}, { ButtonBox[\(\[SelectionPlaceholder]\^*\)], ButtonBox[\(\[SelectionPlaceholder]\_*\)], ButtonBox[\(\[SelectionPlaceholder]\^\[Prime]\)], ButtonBox[\(\[SelectionPlaceholder]\^\[DoublePrime]\)], ButtonBox[\(\[SelectionPlaceholder]\&.\)], ButtonBox[\(\[SelectionPlaceholder]\&\[DoubleDot]\)], ButtonBox[\(\[SelectionPlaceholder]\&~\)], ButtonBox[\(\[SelectionPlaceholder]\&^\)]} }, RowSpacings->0, ColumnSpacings->0, GridDefaultElement:>ButtonBox[ "\\[Placeholder]"]]} }, RowSpacings->1, GridFrame->False, GridFrameMargins->{{0.4, 0.4}, {2.4, 1}}]], NotebookDefault, Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, PageBreakAbove->True, PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, CellFrameMargins->{{6, 6}, {15, 8}}, DefaultFormatType->DefaultInputFormatType, LineSpacing->{1.25, 0}, FormatType->InputForm, ScriptMinSize->9, ShowStringCharacters->True, NumberMarks->True, StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Plain", GridBoxOptions->{RowSpacings->0, ColumnSpacings->0}], Cell[TextData[{ "Begin by typing the character \"t\" into a text cell. Now select the \ character and click the subsuperscript button on the ", StyleBox["BasicTypesetting", FontFamily->"Chicago", FontSize->10], " palette (see illustration). ", StyleBox["Mathematica", FontSlant->"Italic"], " will add placeholders for subscript and superscript characters, leaving \ the cursor within the subscript placeholder ", Cell[BoxData[ \(TraditionalForm\`t\_\[FilledSmallSquare]\%\[Placeholder]\)]], ". Notice that ", StyleBox["Mathematica", FontSlant->"Italic"], " also italicizes the letter t. A second click on the subsuperscript button \ adds two additional placeholders to the subscript placeholder: ", Cell[BoxData[ \(TraditionalForm \`t\_\(\[FilledSmallSquare]\_\[Placeholder]\%\[Placeholder]\)\%\ \[Placeholder]\)]], ". The cursor is still located within the original subscript placeholder. \ Pressing the \[TabKey] key moves the cursor into different placeholder \ boxes.The sequence of moves progresses in a pattern such that pressing \ \[TabKey] twice will relocate the cursor to the superscript attached to the \ original subscript. Another click on the subsuperscript button adds a new \ set of placeholders: ", Cell[BoxData[ \(TraditionalForm \`t\_\(\[Placeholder]\_\[Placeholder]\%\(\[Placeholder]\_\[Placeholder]\ \%\[Placeholder]\)\)\%\[Placeholder]\)]], ". Three more presses of the \[TabKey] key and a final click on the \ sub-superscript button gives us the template we were seeking: ", Cell[BoxData[ \(TraditionalForm \`t\_\(\[Placeholder]\_\[Placeholder]\%\(\[Placeholder]\_\[Placeholder]\ \%\[Placeholder]\)\)\%\(\[Placeholder]\_\[Placeholder]\%\[Placeholder]\)\)]], "." }], "Text"], Cell[TextData[{ "To fill the boxes with the appropriate characters, position the cursor in \ the bottom-left box and enter the character \"n\". The remaining characters \ can be entered by combining \[TabKey] keystrokes to relocate the cursor and \ clicking the appropriate Greek character on the ", StyleBox["BasicTypesetting", FontFamily->"Chicago", FontSize->10], " palette. The keystroke sequence is \[TabKey] -\[Kappa]-\[TabKey] -\[Xi]-\ \[TabKey] -\[Kappa]-\[TabKey] -\[Alpha]-\[TabKey] -\[Xi]-\[TabKey] -\[Kappa]-\ \[TabKey] -\[Alpha]. ", StyleBox["Behold the monster!", FontSlant->"Italic"], " \n\nWhen the cursor is positioned over a Greek character on the palette, \ an alternate keystroke combination is shown at the base of the palette. For \ example, instead of clicking on the \[Alpha] button, the keystroke \ combination \[EscapeKey]a\[EscapeKey] can be used. Expression of the \ corresponding keystroke combination will be left to the reader." }], "Text"], Cell["\<\ It is simple to create a button to give at one stroke a template \ for the Sierpinski monster.\ \>", "Text"], Cell[BoxData[ RowBox[{"\n", ButtonBox[ SubsuperscriptBox[ StyleBox["t", FontSlant->"Italic"], \(\[Placeholder]\_\[Placeholder]\%\(\[Placeholder]\_\[Placeholder]\%\ \[Placeholder]\)\), \(\[Placeholder]\_\[Placeholder]\%\[Placeholder]\)], ButtonStyle->"Paste"]}]], "Input"], Cell[TextData[{ "Create an empty button by choosing ", StyleBox["Input \[RightTriangle] Create Button \[RightTriangle] Paste", FontWeight->"Bold"], ", and then paste the template for the Sierpinski monster into the button\ \[CloseCurlyQuote]s placeholder. To activate the button, select the entire \ button, and then choose ", StyleBox["File \[RightTriangle] Generate Palette", FontWeight->"Bold"], " from ", StyleBox["Selection", FontWeight->"Bold"], "." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Creating a useful button", "Section"], Cell[TextData[{ "We now show how to create a button that would be useful in a mathematical \ discussion on sequences. The idea is inspired by Gillman's \"deconstruction\" \ of the Sierpinski notation\[LongDash]a topic to which we will return at the \ conclusion of this article.\n\nThe button we have in mind will insert in a \ line of text the string\n\"{", Cell[BoxData[ \(TraditionalForm\`\[Placeholder]\_1\)]], ", ", Cell[BoxData[ \(TraditionalForm\`\[Placeholder]\_2\)]], ", ...}\" with the selection boxes filled with a symbol of the writer's \ choice. Thus a writer wishing to compare the sequences\n{", Cell[BoxData[ \(TraditionalForm\`a\_1\)]], ", ", Cell[BoxData[ \(TraditionalForm\`a\_2\)]], ", ...} and {", Cell[BoxData[ \(TraditionalForm\`b\_1\)]], ", ", Cell[BoxData[ \(TraditionalForm\`b\_2\)]], ", ...}, could simply select this button once for each sequence. \ Furthermore, we will configure this button so that the writer need only type \ the initial letter in a sequence, select it and click the button. The button \ will then add a second instance of the letter, italicize both characters and \ insert subscripts, ellipses and braces. In other words: \"consider the \ sequence z \" becomes \"consider the sequence ", Cell[BoxData[ FormBox[ RowBox[{"{", RowBox[{ SubscriptBox[ StyleBox["z", FontSlant->"Italic"], "1"], ",", SubscriptBox[ StyleBox["z", FontSlant->"Italic"], "2"], ",", "\[Ellipsis]"}], "}"}], TraditionalForm]], "Output"], "\" with a selection motion and a click." }], "Text"], Cell[TextData[{ "The key to creating a button that performs sophisticated actions on any \ currently selected text is use of the notebook-manipulation commands ", StyleBox["NotebookRead", "Input"], " and ", StyleBox["NotebookWrite", "Input"], ". ", StyleBox["NotebookRead[", "Input"], StyleBox["notebook", FontSlant->"Italic"], StyleBox["]", "Input"], " returns an expression that represents the current selection in ", StyleBox["notebook", FontSlant->"Italic"], ", and ", StyleBox["NotebookWrite[", "Input"], StyleBox["notebook", FontSlant->"Italic"], StyleBox[",", "Input"], " ", StyleBox["data", FontSlant->"Italic"], StyleBox["]", "Input"], " writes ", StyleBox["data", FontSlant->"Italic"], " into ", StyleBox["notebook", FontSlant->"Italic"], " at the current insertion point, writing over anything currently \ selected." }], "Text"], Cell[TextData[{ "To determine what sort of data to write into a notebook, it is instructive \ to create the desired expression by hand, and then display the expression \ form of the expression by choosing ", StyleBox["Show Expression", FontWeight->"Bold"], " from the ", StyleBox["Format", FontWeight->"Bold"], " menu. For example, here is a text cell that contains an expression \ similar to the one we wish our button to create." }], "Text"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`{a\_1, a\_2, \[Ellipsis]}\)]]], "Text"], Cell[TextData[{ "Here is the expression form of the cell containing the expression, found \ by selecting the cell containing the expression and choosing ", StyleBox["Format \[RightTriangle] Show Expression", FontWeight->"Bold"], "." }], "Text"], Cell[TextData[StyleBox[ "Cell[TextData[Cell[BoxData[\n FormBox[\n RowBox[{\"{\", \n \ RowBox[{\n SubscriptBox[\"a\", \"1\"], \",\", \n \ SubscriptBox[\"a\", \"2\"], \",\", \"\\\[InvisibleSpace][Ellipsis]\"}], \n \ \"}\"}], TraditionalForm]]]], \"Text\"]", "Output"]], "Text"], Cell["\<\ Here is a function that reads in any currently selected text, and \ then writes back the desired list.\ \>", "Text"], Cell[BoxData[ \(Sequencify := Module[{inputnb = InputNotebook[], sel}, sel = NotebookRead[inputnb]; NotebookWrite[inputnb, \n\t\t\t Cell[BoxData[\n\t\t\t\t\t FormBox[RowBox[{"\<{\>", \n\t\t\t\t\t\t\t\t RowBox[{\n\t\t\t\t\t\t\t\t\t\t SubscriptBox[\n\t\t\t\t\t\t\t\t\t\t\t StyleBox[sel, FontSlant \[Rule] "\"], "\<1\>"], "\<,\>", SubscriptBox[ StyleBox[sel, FontSlant \[Rule] "\"], "\<2\>"], "\<,\>", "\<\[Ellipsis]\>"}], "\<}\>"}], TradionalForm]], "\"]\n\t\t]]\)], "Input"], Cell[TextData[{ "To create a button that executes the function ", StyleBox["Sequencify", "Input"], ", we create a new button by choosing ", StyleBox[ "Input \[RightTriangle] Create Button \[RightTriangle] Custom\[Ellipsis]", FontWeight->"Bold"], ". In the ", StyleBox["Edit Button", FontWeight->"Bold"], " dialog box that appears, we type ", StyleBox["Sequencify", "Input"], " into the Button Function text field, and choose Local from the Button \ Evaluator pop-up menu. (*Joe, some questions about typsetting format*)" }], "Text"], Cell["(*Joe, should probably shrink this graphic*)", "Text"], Cell[GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggYjN[Vi^OShn03ooeGooj[ooonIgIfM[Fe]OCdm03oEEGoEJ[oE@L71dI6AXF5QLC4a000ZUD0ZZX0Z_l0Z/`c CXf=SLcCXV9RLS8b000oeD0ZZX0Z_l0ZQ/K6eYJFYVIVMSHf01EoeEEojYEoomEoa0000?o0000 F002o`0000?o00001P000ol000080003o`0000<000?o00000P001?l00?l30003o`0000?o0`03o`@0 0ol30004o`3oo`P00ol40005o`000?l00`001Ol0003o00<00ol30005o`000?l00`03o`P00ol400?o 0`03o`<00_l30005o`000?l00`03on<000?o0000F002o`0000?o00001P000ol000080003o`0000<0 00?o00000P000ol000080003o`0000<000?o000070000ol0000d0003o`000?D000?o0000F002o`00 00?o00001P000ol000080003o`0000<01Ol;0003o`0000<000?o00006`02ocH000?o00000`000ol0 003_0003o`0005P00_l00003o`0000H03?oo06X000?o0000F002o`0000?o0000o`1l0003o`0005P0 0_l00003o`000?l0O0000ol0001H00;o00000ol0003o07`000?o0000F002o`0000?o0000o`1l0003 o`0005P00_l00003o`0007`0>oo40003o`0005P00_l00003o`0007X0?Oo40003o`0005P00_l00003 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0Ol00003oi>C0?nCeY<15`7o0Ol00?oofol1f`00\ \>"], "Graphics", Evaluatable->False, ImageSize->{475, 350}, ImageMargins->{{26, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ "After clicking OK, we create the button contents by typing any desired \ text into the button\[CloseCurlyQuote]s placeholder. In this case, we enter \ the expression ", Cell[BoxData[ \(TraditionalForm \`{\[FilledSquare]\_1, \[FilledSquare]\_2, \[Ellipsis]}\)]], ", where \[FilledSquare] is the character \\\[InvisibleSpace][FilledSquare] \ and ", StyleBox["not", FontSlant->"Italic"], " the character \\\[InvisibleSpace][SelectionPlaceholder] usually used in \ palettes. The result is the following." }], "Text"], Cell[BoxData[ ButtonBox[\({\[FilledSquare]\_1, \[FilledSquare]\_2, \[Ellipsis]}\), ButtonFunction:>Sequencify, ButtonEvaluator->"Local", ButtonStyle->None]], "Input", FontWeight->"Plain"], Cell[TextData[{ "To activate the button, we select the button and choose ", StyleBox["File \[RightTriangle] Generate Palette", FontWeight->"Bold"], " from ", StyleBox["Selection", FontWeight->"Bold"], "." }], "Text"], Cell["\<\ To use the button, we create a text cell containing the following \ text.\ \>", "Text"], Cell["\tWe consider the sequences a and b.", "Text", CellFrame->1], Cell[TextData[{ "Next we select the letter \[OpenCurlyDoubleQuote]a\[CloseCurlyDoubleQuote] \ and click on the ", StyleBox["Sequencify", "Input"], " button. The following is the result." }], "Text"], Cell[TextData[{ "\tWe consider the sequences ", Cell[BoxData[ FormBox[ RowBox[{"{", RowBox[{ SubscriptBox[ StyleBox["a", FontSlant->"Italic"], "1"], ",", SubscriptBox[ StyleBox["a", FontSlant->"Italic"], "2"], ",", "\[Ellipsis]"}], "}"}], TradionalForm]], "Output"], " and b." }], "Text", CellFrame->1], Cell[TextData[ "Selecting the letter \[OpenCurlyDoubleQuote]b\[CloseCurlyDoubleQuote] and \ clicking the button again produces the desired result."], "Text"], Cell[TextData[{ "\tWe consider the sequences ", Cell[BoxData[ FormBox[ RowBox[{"{", RowBox[{ SubscriptBox[ StyleBox["a", FontSlant->"Italic"], "1"], ",", SubscriptBox[ StyleBox["a", FontSlant->"Italic"], "2"], ",", "\[Ellipsis]"}], "}"}], TradionalForm]], "Output"], " and ", Cell[BoxData[ FormBox[ RowBox[{"{", RowBox[{ SubscriptBox[ StyleBox["b", FontSlant->"Italic"], "1"], ",", SubscriptBox[ StyleBox["b", FontSlant->"Italic"], "2"], ",", "\[Ellipsis]"}], "}"}], TradionalForm]], "Output"], "." }], "Text", CellFrame->1], Cell[TextData[{ "Note that the button works properly only in text cells, section cells, and \ title cells. Note also that the button can be made faster using commands \ evaluated directly in the front end, such as ", StyleBox["FrontEndExecute", "Input"], "." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Conclusion: Writing ", StyleBox["Mathematica", FontSlant->"Italic"], " well" }], "Section"], Cell[TextData[{ "We have only hinted at the power of ", StyleBox["Mathematica", FontSlant->"Italic"], " 3.0's palette and button features. In particular, we have shown the \ typsetting side of the new features. Buttons can be programmed to perform \ evaluations of any expression defined by the user. Of course, these new tools \ should be used with established common sense to create understandable and \ simplified mathematics, rather than to bring new typographical monsters into \ the world.\n\nGillman provides three excellent steps to take toward \ simplifying mathematical notation [Gillman 1987, page 37]:\nI. Use an \ uncomplicated symbol in place of an elaborate one.\nII. Discard any symbol \ that is just plain unnecessary.\nIII. Simplify the mathematical argument \ itself." }], "Text"], Cell[TextData[{ "Applying his own rules in a fine example of mathematical writing, Gillman \ simultaneously shows how to simplify the Sierpinski notation and outlines the \ proof in which this notation is used. Under Gillman's rewriting, the monstor \ becomes \n\n", Cell[BoxData[ \(TraditionalForm\`t\_\[Kappa]\%\[Alpha]\_i\)]], "." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["The Triangle", "Section", CellTags->"The Triangle"], Cell[TextData[ "As a final example of programming in a button, here is the button code for \ generating the Sierpinski triangle. The reader is invited to experiment with \ the character \"\[Xi]\" and to replace the number 5 with the desired depth of \ calculation."], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Nest[SubsuperscriptBox[#, #, #]&, "\<\[Xi]\>", 5] // DisplayForm\) // TraditionalForm\)], "Input"], Cell[BoxData[ FormBox[ TagBox[ \(\(\(\(\(\[Xi]\_\[Xi]\%\[Xi]\)\_\(\[Xi]\_\[Xi]\%\[Xi]\)\%\(\[Xi]\_\ \[Xi]\%\[Xi]\)\)\_\(\(\[Xi]\_\[Xi]\%\[Xi]\)\_\(\[Xi]\_\[Xi]\%\[Xi]\)\%\(\[Xi]\ \_\[Xi]\%\[Xi]\)\)\%\(\(\[Xi]\_\[Xi]\%\[Xi]\)\_\(\[Xi]\_\[Xi]\%\[Xi]\)\%\(\ \[Xi]\_\[Xi]\%\[Xi]\)\)\)\_\(\(\(\[Xi]\_\[Xi]\%\[Xi]\)\_\(\[Xi]\_\[Xi]\%\[Xi]\ \)\%\(\[Xi]\_\[Xi]\%\[Xi]\)\)\_\(\(\[Xi]\_\[Xi]\%\[Xi]\)\_\(\[Xi]\_\[Xi]\%\ \[Xi]\)\%\(\[Xi]\_\[Xi]\%\[Xi]\)\)\%\(\(\[Xi]\_\[Xi]\%\[Xi]\)\_\(\[Xi]\_\[Xi]\ \%\[Xi]\)\%\(\[Xi]\_\[Xi]\%\[Xi]\)\)\)\%\(\(\(\[Xi]\_\[Xi]\%\[Xi]\)\_\(\[Xi]\_\ \[Xi]\%\[Xi]\)\%\(\[Xi]\_\[Xi]\%\[Xi]\)\)\_\(\(\[Xi]\_\[Xi]\%\[Xi]\)\_\(\[Xi]\ \_\[Xi]\%\[Xi]\)\%\(\[Xi]\_\[Xi]\%\[Xi]\)\)\%\(\(\[Xi]\_\[Xi]\%\[Xi]\)\_\(\ \[Xi]\_\[Xi]\%\[Xi]\)\%\(\[Xi]\_\[Xi]\%\[Xi]\)\)\)\)\_\(\(\(\(\[Xi]\_\[Xi]\%\ \[Xi]\)\_\(\[Xi]\_\[Xi]\%\[Xi]\)\%\(\[Xi]\_\[Xi]\%\[Xi]\)\)\_\(\(\[Xi]\_\[Xi]\ \%\[Xi]\)\_\(\[Xi]\_\[Xi]\%\[Xi]\)\%\(\[Xi]\_\[Xi]\%\[Xi]\)\)\%\(\(\[Xi]\_\ \[Xi]\%\[Xi]\)\_\(\[Xi]\_\[Xi]\%\[Xi]\)\%\(\[Xi]\_\[Xi]\%\[Xi]\)\)\)\_\(\(\(\ \[Xi]\_\[Xi]\%\[Xi]\)\_\(\[Xi]\_\[Xi]\%\[Xi]\)\%\(\[Xi]\_\[Xi]\%\[Xi]\)\)\_\(\ \(\[Xi]\_\[Xi]\%\[Xi]\)\_\(\[Xi]\_\[Xi]\%\[Xi]\)\%\(\[Xi]\_\[Xi]\%\[Xi]\)\)\%\ \(\(\[Xi]\_\[Xi]\%\[Xi]\)\_\(\[Xi]\_\[Xi]\%\[Xi]\)\%\(\[Xi]\_\[Xi]\%\[Xi]\)\)\ \)\%\(\(\(\[Xi]\_\[Xi]\%\[Xi]\)\_\(\[Xi]\_\[Xi]\%\[Xi]\)\%\(\[Xi]\_\[Xi]\%\ \[Xi]\)\)\_\(\(\[Xi]\_\[Xi]\%\[Xi]\)\_\(\[Xi]\_\[Xi]\%\[Xi]\)\%\(\[Xi]\_\[Xi]\ \%\[Xi]\)\)\%\(\(\[Xi]\_\[Xi]\%\[Xi]\)\_\(\[Xi]\_\[Xi]\%\[Xi]\)\%\(\[Xi]\_\ \[Xi]\%\[Xi]\)\)\)\)\%\(\(\(\(\[Xi]\_\[Xi]\%\[Xi]\)\_\(\[Xi]\_\[Xi]\%\[Xi]\)\%\ \(\[Xi]\_\[Xi]\%\[Xi]\)\)\_\(\(\[Xi]\_\[Xi]\%\[Xi]\)\_\(\[Xi]\_\[Xi]\%\[Xi]\)\ \%\(\[Xi]\_\[Xi]\%\[Xi]\)\)\%\(\(\[Xi]\_\[Xi]\%\[Xi]\)\_\(\[Xi]\_\[Xi]\%\[Xi]\ \)\%\(\[Xi]\_\[Xi]\%\[Xi]\)\)\)\_\(\(\(\[Xi]\_\[Xi]\%\[Xi]\)\_\(\[Xi]\_\[Xi]\%\ \[Xi]\)\%\(\[Xi]\_\[Xi]\%\[Xi]\)\)\_\(\(\[Xi]\_\[Xi]\%\[Xi]\)\_\(\[Xi]\_\[Xi]\ \%\[Xi]\)\%\(\[Xi]\_\[Xi]\%\[Xi]\)\)\%\(\(\[Xi]\_\[Xi]\%\[Xi]\)\_\(\[Xi]\_\ \[Xi]\%\[Xi]\)\%\(\[Xi]\_\[Xi]\%\[Xi]\)\)\)\%\(\(\(\[Xi]\_\[Xi]\%\[Xi]\)\_\(\ \[Xi]\_\[Xi]\%\[Xi]\)\%\(\[Xi]\_\[Xi]\%\[Xi]\)\)\_\(\(\[Xi]\_\[Xi]\%\[Xi]\)\_\ \(\[Xi]\_\[Xi]\%\[Xi]\)\%\(\[Xi]\_\[Xi]\%\[Xi]\)\)\%\(\(\[Xi]\_\[Xi]\%\[Xi]\)\ \_\(\[Xi]\_\[Xi]\%\[Xi]\)\%\(\[Xi]\_\[Xi]\%\[Xi]\)\)\)\)\), DisplayForm], TraditionalForm]], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["References", "Section"], Cell[TextData[{ "Gillman, L., ", StyleBox["Writing Mathematics Well", FontSlant->"Italic"], ". Mathematical Association of America Press. 1987.\n\nStewart, I. Four \ encounters with Sierpinski's Gasket. ", StyleBox["The Mathematical Intelligencer", FontSlant->"Italic"], ", 17, 1, (1995), 52-64" }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["About the authors", "Section"], Cell["", "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Electronic subscriptions", "Section"], Cell[TextData[{ "Included in the distribution for each electronic subscription is the file \ Monster.nb containing ", StyleBox["Mathematica", FontSlant->"Italic"], " code for the material described in this article." }], "Text"] }, Open ]] }, Open ]] }, Open ]] }, FrontEndVersion->"Macintosh 3.0", ScreenRectangle->{{0, 640}, {0, 460}}, WindowSize->{494, 438}, WindowMargins->{{51, Automatic}, {-11, Automatic}}, MacintoshSystemPageSetup->"\<\ 00D0001804P000000]/2@?oWonh2o`9B7`<5:0?l0040004/0B`000002nL9H04/ 02d5X5k/02H40@4101P00BL?00400@0000000000000000010000000000000000 00000000000000000000004000910000\>" ] (*********************************************************************** Cached data follows. 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