(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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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[ 113917, 2747]*) (*NotebookOutlinePosition[ 115000, 2784]*) (* CellTagsIndexPosition[ 114956, 2780]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{Cell[TextData[{ StyleBox["Symbolic Geometry, Golden Spiral and ", Evaluatable->False, AspectRatioFixed->True], StyleBox["Descartes-Geometry ", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" ", Evaluatable->False, AspectRatioFixed->True] }], "Title", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ StyleBox["Mathematica in Education\n", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox["Vol.2 No.3\nSpring 1993", Evaluatable->False, AspectRatioFixed->True] }], "Subtitle", Evaluatable->False, AspectRatioFixed->True], Cell[TextData["by\nDenis Monasse"], "Subsubtitle", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[StyleBox[ "Mathsoft Overseas, CP 641, 1211 Geneva 3 (Switzerland)", Evaluatable->False, AspectRatioFixed->True, FontSize->18]], "Subsubtitle", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{Cell[TextData["Introduction"], "Section", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ StyleBox[ "Symbolic algebra becomes familiar to a growing population of students and \ professional users but symbolic geometry is just emerging from the shade. 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", Evaluatable->False, AspectRatioFixed->True], StyleBox["geometric objects", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" : points, straight lines, circles, arcs of circle;\nii. ", Evaluatable->False, AspectRatioFixed->True], StyleBox["geometric transformations", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" : rotation and homothety;\niii.", Evaluatable->False, AspectRatioFixed->True], StyleBox["geometric functions", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" to define families of elements,\niv.", Evaluatable->False, AspectRatioFixed->True], StyleBox["geometric arrays", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" to construct the set of arcs of circle.", Evaluatable->False, AspectRatioFixed->True] }], "Text", Evaluatable->False, AspectRatioFixed->True]}, Open]], Cell[CellGroupData[{Cell[TextData["Getting started"], "Section", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ StyleBox["The program ", Evaluatable->False, AspectRatioFixed->True], StyleBox["Descartes-Geometry", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" is a package of the ", Evaluatable->False, AspectRatioFixed->True], StyleBox["Mathematica", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" library and is called by the command", Evaluatable->False, AspectRatioFixed->True] }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData["Get[\"Descartes`Geometry2D`\"]"], "Input", InitializationCell->True, AspectRatioFixed->True]}, Open]], Cell[CellGroupData[{Cell[TextData["Geometric objects"], "Section", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ StyleBox["There are seven basic geometric objects in ", Evaluatable->False, AspectRatioFixed->True], StyleBox["Descartes-Geometry", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[ ": ARC, CIRCLE, LINE, POINT, POLYGON, STRAIGHT and VECTOR. For the present \ exercise, we shall consider ARC, CIRCLE, POINT and STRAIGHT only.", Evaluatable->False, AspectRatioFixed->True] }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{Cell[TextData["Point"], "Subsection", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "A point in the plane is characterized by its two coordinates and the head \ POINT. 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This example gives just \ a sampling of the facilities provided by Descartes-Geometry which contains \ more than hundred functions. The program is actually the symbolic image of a \ course of analytic geometry taught in high schools and colleges and updated \ with various objects such as the splines which are so common in graphical \ applications.\n "], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "The program Descartes-Geometry is commercially available from: "], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "Mathsoft Overseas, cp 641, 1211 Geneva 3 (Switzerland). \nTel: 41 22 346 52 \ 60. 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