(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 1332379, 27102] NotebookOptionsPosition[ 1325697, 26889] NotebookOutlinePosition[ 1326829, 26927] CellTagsIndexPosition[ 1326740, 26922] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["\<\ Four Triangle Fractals using Bucky Numbers and Synergetics Coordinates\ \>", "Title", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Courier New", FontWeight->"Bold", Background->GrayLevel[0.500008]], Cell[" By Cliff Nelson", "Text", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Courier New", FontWeight->"Bold"], Cell[CellGroupData[{ Cell["Abstract", "Section", FontFamily->"Courier New"], Cell[TextData[{ Cell[BoxData[ FormBox[ SubscriptBox["B", "3"], TraditionalForm]]], " numbers and my version of \"Synergetics coordinates\" are used to make \ four fractals based on the same method: the Sierpinski triangle when the Mean \ is used; a trefoil I call the Harmonic Trinity when the HarmonicMean is used; \ half of a circle when the GeometricMean is used; and something else when the \ RootMeanSquare is used." }], "Text", CellChangeTimes->{{3.4642232697049723`*^9, 3.4642232717014627`*^9}}, FontFamily->"Courier", Background->GrayLevel[0.900008]] }, Open ]], Cell[CellGroupData[{ Cell["Reference", "Section", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Courier New"], Cell["\<\ Written by Clifford J. 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Nelson.", "Commentary", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Courier", Background->GrayLevel[0.900008]], Cell["\<\ The coordinate system used in this notebook is called \"the Synergetics \ coordinate system\" because it is based on the two books:\ \>", "Commentary", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Courier", Background->GrayLevel[0.900008]], Cell["\<\ Synergetics: explorations in the geometry of thinking. 1975 by R. Buckminster \ Fuller. ISBN 0-02-065320-4 Macmillan Publishing Company 866 Third Avenue, New York, N. Y. 10022 Collier Macmillan Canada, Inc.\ \>", "Commentary", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Courier", Background->GrayLevel[0.900008]], Cell["\<\ Synergetics 2, 1979 by R. Buckminster Fuller. ISBN 0-02-541870-X (v. 1) ISBN 0-02-541880-7 (v. 2) Macmillan Publishing Co., Inc. 806 Third Avenue, New York, N. 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