(* 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[ 8974219, 148815] NotebookOptionsPosition[ 8968433, 148642] NotebookOutlinePosition[ 8970049, 148706] CellTagsIndexPosition[ 8969745, 148692] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[TextData[{ "\n", StyleBox["Antizykloiden", FontFamily->"Verdana", FontSize->18], StyleBox["\[LineSeparator]\nMathematik als sozialer Prozess ", FontFamily->"Verdana", FontSize->14], "\[Dash]", StyleBox["\nund wie sich Technologie weiterentwickelt\n\nnebst einem \ Ausblick auf ", FontFamily->"Verdana", FontSize->14], StyleBox["Roads and Wheels", FontFamily->"Verdana", FontSize->14, FontSlant->"Italic"], StyleBox[".", FontFamily->"Verdana", FontSize->14], StyleBox["\n\n", FontFamily->"Verdana"], StyleBox["Ralf Schaper\n", FontFamily->"Verdana", FontSize->14] }], "Text", CellChangeTimes->{{3.493808949390625*^9, 3.493808967625*^9}, { 3.493809022234375*^9, 3.4938090788125*^9}, 3.4939611651455727`*^9, 3.4943068855*^9, {3.494306955453125*^9, 3.494307026359375*^9}, { 3.494307211265625*^9, 3.494307222125*^9}, {3.494477236765625*^9, 3.4944772656875*^9}, 3.4944773018125*^9, 3.49448043603125*^9, { 3.494483091859375*^9, 3.494483095640625*^9}, {3.494558273328125*^9, 3.49455827384375*^9}}], Cell[TextData[{ "1984 Klagenfurt: Wie bei fr\[UDoubleDot]heren Tagungen zur Visualisierung \ in der Mathematik an der Universit\[ADoubleDot]t trafen sich Einige am \ Vorabend, dem Sonntag dem 15. Juli, beim \[OpenCurlyDoubleQuote]Wadler\ \[CloseCurlyDoubleQuote] in der Villacher Stra\[SZ]e. Damals war es ein sch\ \[ODoubleDot]nes \[ODoubleDot]sterreichisches Lokal mit Biergarten unter \ Kastanien. Wie \[UDoubleDot]blich lernte man sich schon kennen und sprach \ beim Essen \[UDoubleDot]ber Arbeitsgruppen und Themen f\[UDoubleDot]r die \ kommende Tagung. Heute kann ich es ja offen formulieren: Nicht nur einige \ Themen passten mir nicht, sondern auch, wer die zugeh\[ODoubleDot]rigen AGs \ leiten sollte. Also: Was tun? Nun, der Abend wurde l\[ADoubleDot]nger, das \ Essen mundete und der ", StyleBox[ButtonBox["Gr\[UDoubleDot]ne Veltliner", BaseStyle->"Hyperlink", ButtonData->{ URL["http://de.wikipedia.org/wiki/Gr%C3%BCner_Veltliner"], None}, ButtonNote->"http://de.wikipedia.org/wiki/Gr%C3%BCner_Veltliner"], FontColor->RGBColor[0, 0, 1]], " regte an. \nUnd so entstand im Gespr\[ADoubleDot]ch mit Bernd Bornscheuer \ und Dietmar Hennig die Idee: Wir \[OpenCurlyDoubleQuote]drehen \ \[CloseCurlyQuote]mal \[CloseCurlyQuote]ne Beobachtung um\ \[CloseCurlyDoubleQuote]: Beobachtet man z.B. einen Reflektor in den Speichen \ eines Fahrrades und die Bahn dieses Reflektors, wenn das Rad auf einer \ geraden Stra\[SZ]e abrollt, so erh\[ADoubleDot]lt man als Bahn ", StyleBox[ButtonBox["Zykloiden", BaseStyle->"Hyperlink", ButtonData->{ URL["http://de.wikipedia.org/wiki/Zykloide"], None}, ButtonNote->"http://de.wikipedia.org/wiki/Zykloide"], FontColor->RGBColor[0, 0, 1]], ". Das sind bekannte Kurven, die beispielsweise auch bei der Beschreibung \ des ", StyleBox[ButtonBox["ptolem\[ADoubleDot]ischen Weltbildes", BaseStyle->"Hyperlink", ButtonData->{ URL["http://de.wikipedia.org/wiki/Ptolem%C3%A4isches_Weltbild"], None}, ButtonNote->"http://de.wikipedia.org/wiki/Ptolem%C3%A4isches_Weltbild"], FontColor->RGBColor[0, 0, 1]], " bei den Planetenbahnen eine Rolle spielen, also seit Jahrhunderten \ wohlbekannt.\n\nNun im \[UDoubleDot]bertragenen Sinne unsere \ \[OpenCurlyDoubleQuote]Schnapsidee\[CloseCurlyDoubleQuote]; der Zustand der \ sog. Weinseligkeit war allerdings nicht erreicht:\n\[LineSeparator]", StyleBox["Der frei gew\[ADoubleDot]hlte Punkt im Rad soll sich auf einer \ Geraden bewegen! \nWie \[OpenCurlyDoubleQuote]krumm\[CloseCurlyDoubleQuote] \ muss dazu die \[OpenCurlyDoubleQuote]Stra\[SZ]e\[CloseCurlyDoubleQuote] sein \ und wie sehen diese Stra\[SZ]en aus? ", FontFamily->"Verdana", FontSize->10], StyleBox["\n", FontFamily->"Verdana"], "\nDas ist \[Dash] wie wir sp\[ADoubleDot]ter lernten \[Dash] ein sog. ", StyleBox[ButtonBox["inverses Problem", BaseStyle->"Hyperlink", ButtonData->{ URL["http://de.wikipedia.org/wiki/Inverses_Problem"], None}, ButtonNote->"http://de.wikipedia.org/wiki/Inverses_Problem"], FontColor->RGBColor[0, 0, 1]], ": Gegeben ist ein Ziel, ein Resultat, wie kann es erreicht werden?" }], "Text", CellChangeTimes->{{3.49372659671875*^9, 3.493726765625*^9}, { 3.493727098546875*^9, 3.493727166453125*^9}, {3.493727231125*^9, 3.49372779434375*^9}, {3.493727834*^9, 3.493728015234375*^9}, { 3.493728065390625*^9, 3.493728071171875*^9}, {3.493728214375*^9, 3.493728276171875*^9}, {3.49372830878125*^9, 3.4937284524375*^9}, { 3.493728485046875*^9, 3.49372852859375*^9}, {3.493788644046875*^9, 3.493788644546875*^9}, {3.49378868565625*^9, 3.49378874190625*^9}, { 3.493809128671875*^9, 3.4938091475*^9}, {3.493809212546875*^9, 3.493809214625*^9}, {3.49381201325*^9, 3.49381208*^9}, {3.493953908125*^9, 3.493953916828125*^9}, {3.49395396990625*^9, 3.4939539740625*^9}, { 3.493954203046875*^9, 3.493954236640625*^9}, {3.4939602532236977`*^9, 3.4939602680986977`*^9}, 3.4939618148330727`*^9, {3.4939618615674477`*^9, 3.4939618936768227`*^9}, 3.4939619700830727`*^9, {3.4939620041768227`*^9, 3.4939620436143227`*^9}, {3.4939620739736977`*^9, 3.4939621275361977`*^9}, {3.494304067375*^9, 3.494304136109375*^9}, { 3.494307055328125*^9, 3.49430712490625*^9}, {3.4944805163125*^9, 3.4944805163125*^9}, {3.494480580328125*^9, 3.494480580328125*^9}, { 3.494480659015625*^9, 3.494480672203125*^9}, {3.494480769640625*^9, 3.494480769640625*^9}, {3.494482137796875*^9, 3.494482152859375*^9}, { 3.49448325715625*^9, 3.494483279984375*^9}, {3.494504438078125*^9, 3.494504445671875*^9}, {3.494504507515625*^9, 3.494504510328125*^9}, { 3.494558441359375*^9, 3.4945584421875*^9}, 3.49455953890625*^9}], Cell[TextData[{ "Die oben Genannten bildeten zusammen mit Alois Vilim aus Wien dann in der \ folgenden Woche eine AG. Die zu ergr\[UDoubleDot]ndenden Kurven nannten wir \ Antizykloiden.\n\[LineSeparator]Zitat aus dem Tagungsband ", StyleBox[ButtonBox["[1, S. 174]", BaseStyle->"Hyperlink", ButtonData->"1"], FontWeight->"Bold"], ":\n\n", StyleBox["W\[ADoubleDot]hrend des Workshops stand uns keine Literatur bzgl. \ Antizykloiden und derartiger inverser Probleme bei Kurven zur Verf\ \[UDoubleDot]gung. Die K\[UDoubleDot]rze des Workshops lie\[SZ] eine \ Simulation des Problems auf einem Rechner nicht zu. Wir entschieden uns daher \ daf\[UDoubleDot]r, mit Pappe, Zwirn, Stecknadeln und einer Pinwand reale \ Modelle zu erstellen.\nAuf einer Pappscheibe von ca. 6 cm Durchmesser \ konstruierten wir ein regul\[ADoubleDot]res 64-Eck. Eine Rei\[SZ]zwecke \ fixierte den Gleitpunkt ", FontFamily->"Verdana", FontSize->10], StyleBox["P", FontFamily->"Verdana", FontSize->10, FontSlant->"Italic"], StyleBox[". Die aus der Pappscheibe herausragende Spitze der Rei\[SZ]zwecke \ wurde durch zwei festgespannte Zwirnsf\[ADoubleDot]den auf der \"Geraden\" \ gef\[UDoubleDot]hrt und so mit Hilfe des 64-Ecks eine Approximation einer \ Antizykloide konstruiert. Wir fixierten dann die Kurve mit \"dick-k\ \[ODoubleDot]pfigen\" Stecknadeln und konnten auf ihnen die Pappscheibe \ abrollen lassen. Die hier gezeigten Bilder sind Fotografien der so erstellten \ Kurven f\[UDoubleDot]r 3 Lagen des Gleitpunktes ", FontFamily->"Verdana", FontSize->10], StyleBox["P ", FontFamily->"Verdana", FontSize->10, FontSlant->"Italic"], StyleBox[".", FontFamily->"Verdana", FontSize->10], "\n\nSoweit der Tagungsband." }], "Text", CellChangeTimes->{{3.49372851346875*^9, 3.493728580265625*^9}, { 3.493728629859375*^9, 3.49372929990625*^9}, {3.49372933053125*^9, 3.493729367703125*^9}, {3.49372941890625*^9, 3.49372944196875*^9}, { 3.49378877321875*^9, 3.4937888823125*^9}, {3.493789118796875*^9, 3.49378911984375*^9}, {3.493809255125*^9, 3.493809267984375*^9}, { 3.493809312875*^9, 3.49380932640625*^9}, {3.4938093635*^9, 3.4938093964375*^9}, 3.493812086859375*^9, {3.493954115625*^9, 3.49395411890625*^9}, {3.493954635859375*^9, 3.49395466071875*^9}, 3.4939602975986977`*^9, {3.494304189484375*^9, 3.494304253171875*^9}, { 3.494304293046875*^9, 3.494304330359375*^9}, 3.494480799515625*^9, 3.49448225065625*^9, 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und Dietmar bem Nachdenken. 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