(************** Content-type: application/mathematica ************** Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing 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[ 324786, 10291]*) (*NotebookOutlinePosition[ 325448, 10314]*) (* CellTagsIndexPosition[ 325404, 10310]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Die Schneeflockenkurven", "Section"], Cell[TextData[{ "Materialien zur Vorlesung ", StyleBox["Elementare Analysis", FontWeight->"Bold"], ", Wintersemester 2003 / 4" }], "SmallText"], Cell[TextData[{ StyleBox[ButtonBox["Niels Fabian Helge von Koch", ButtonData:>{ URL[ "http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Koch.html"], None}, ButtonStyle->"Hyperlink"], FontFamily->"Arial"], StyleBox[" (1870 \[Dash] 1924)", FontFamily->"Arial"] }], "Text"], Cell[TextData[{ StyleBox["Vor etwa hundert Jahren wurden mehrere merkw\[UDoubleDot]rdige \ \"Kurven\" entdeckt, die bis dahin g\[ADoubleDot]ngigen Vorstellungen von \ Kurven stark ersch\[UDoubleDot]tterten.\n1906 ver\[ODoubleDot]ffentlichte \ Helge von Koch in einer Arbeit die \"Kurve\", die heute nach ihm benannt \ wird. Wie k\[ODoubleDot]nnen Sie sich das Entstehen dieser \"Kurve\" \ vorstellen? \nEs f\[ADoubleDot]ngt mit einem gleichseitigen Dreieck an. Nun \ wird jede Seite des Dreiecks gedrittelt und jedes mittlere Drittel durch die \ den \"oberen Teil\" eines geeignet gro\[SZ]en gleichseitigen Dreiecks \ ersetzt. Die Anschauung vermittelt diesen Sachverhalt viel einfacher als jede \ Beschreibung. Dann wird das gleiche Verfahren wiederholt. Und weil es so sch\ \[ODoubleDot]n ist, die gleiche Prozedur gleich noch einmal.", FontFamily->"Arial", FontSize->14], "\n\n" }], "Text"], Cell[CellGroupData[{ Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .86603 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.0206197 0.952381 [ [ 0 0 0 0 ] [ 1 .86603 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 0 r 1 Mabswid [ ] 0 setdash .02381 .02062 m .5 .84541 L s .5 .84541 m .97619 .02062 L s .97619 .02062 m .02381 .02062 L s 0 0 m 1 0 L 1 .86603 L 0 .86603 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{78.75, 68.25}, ImageMargins->{{224.188, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, 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