File:Moebius strip.svg is a vector version of this file. It should be used in place of this PNG file when not inferior. File:Moebius Surface 1 Display Small.png → File:Moebius strip.svg For more information, see Help:SVG. In other languages Alemannisch ∙ العربية ∙ беларуская (тарашкевіца) ∙ български ∙ বাংলা ∙ català ∙ нохчийн ∙ čeština ∙ dansk ∙ Deutsch ∙ Ελληνικά ∙ English ∙ British English ∙ Esperanto ∙ español ∙ eesti ∙ euskara ∙ فارسی ∙ suomi ∙ français ∙ Frysk ∙ galego ∙ Alemannisch ∙ עברית ∙ हिन्दी ∙ hrvatski ∙ magyar ∙ հայերեն ∙ Bahasa Indonesia ∙ Ido ∙ italiano ∙ 日本語 ∙ ქართული ∙ 한국어 ∙ lietuvių ∙ македонски ∙ മലയാളം ∙ Bahasa Melayu ∙ norsk bokmål ∙ Plattdüütsch ∙ Nederlands ∙ norsk nynorsk ∙ norsk ∙ occitan ∙ polski ∙ prūsiskan ∙ português ∙ português do Brasil ∙ română ∙ русский ∙ sicilianu ∙ Scots ∙ slovenčina ∙ slovenščina ∙ српски / srpski ∙ svenska ∙ தமிழ் ∙ ไทย ∙ Türkçe ∙ татарча / tatarça ∙ українська ∙ vèneto ∙ Tiếng Việt ∙ 中文 ∙ 中文（中国大陆） ∙ 中文（简体） ∙ 中文（繁體） ∙ 中文（马来西亚） ∙ 中文（新加坡） ∙ 中文（臺灣） ∙

 

DescriptionMoebius Surface 1 Display Small.png	A moebius strip parametrized by the following equations: , where n=1. This plot is for display purposes by itself as a thumbnail. If you are looking for the image that is part of the sequence from n=0 to 1, see below for the other verison, along with a larger version (800px) of this image
Date	19 June 2007
Source	Self-made, with Mathematica 5.1   This diagram was created with Mathematica by n.
Author	Inductiveload
Permission (Reusing this file)	Public domainPublic domainfalsefalse I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.
Other versions	Image for use a part of a sequence of increasing n Larger version of this image

Mathematical Function Plot
Description	Moebius Strip, 1 half-turn (n=1)
Equation	:
Co-ordinate System	Cartesian (Parametric Plot)
u Range	0 .. 4π
v Range	0 .. 0.3

Please be aware that at the time of uploading (15:27, 19 June 2007 (UTC)), this code may take a significant amount of time to execute on a consumer-level computer.

This uses Chris Hill's antialiasing code to average pixels and produce a less jagged image. The original code can be found here.

This code requires the following packages:

<<Graphics`Graphics`

MoebiusStrip[r_:1] =
    Function[
      {u, v, n},
      r {Cos[u] + v Cos[n u/2]Cos[u],
          Sin[u] + v Cos[n u/2]Sin[u],
          v Sin[n u/2],
          {EdgeForm[AbsoluteThickness[4]]}}];

aa[gr_] := Module[{siz, kersiz, ker, dat, as, ave, is, ar},
    is = ImageSize /. Options[gr, ImageSize];
    ar = AspectRatio /. Options[gr, AspectRatio];
    If[! NumberQ[is], is = 288];
    kersiz = 4;
    img = ImportString[ExportString[gr, "PNG", ImageSize -> (
      is kersiz)], "PNG"];
    siz = Reverse@Dimensions[img[[1, 1]]][[{1, 2}]];
    ker = Table[N[1/kersiz^2], {kersiz}, {kersiz}];
    dat = N[img[[1, 1]]];
    as = Dimensions[dat];
    ave = Partition[Transpose[Flatten[ListConvolve[ker, dat[[All, All, #]]]] \
& /@ Range[as[[3]]]], as[[2]] - kersiz + 1];
    ave = Take[ave, Sequence @@ ({1, Dimensions[ave][[#]], 
    kersiz} & /@ Range[Length[Dimensions[ave]] - 1])];
    Show[Graphics[Raster[ave, {{0, 0}, siz/kersiz}, {0, 255}, ColorFunction ->
     RGBColor]], PlotRange -> {{0, siz[[1]]/kersiz}, {
  0, siz[[2]]/kersiz}}, ImageSize -> is, AspectRatio -> ar]
    ]

deg = 1;
gr = ParametricPlot3D[Evaluate[MoebiusStrip[][u, v, deg]],
      {u, 0, 4π},
      {v, 0, .3},
      PlotPoints -> {99, 3},
      PlotRange -> {{-1.3, 1.3}, {-1.3, 1.3}, {-0.7, 0.7}},
      Boxed -> False,
      Axes -> False,
      ImageSize -> 220,
      PlotRegion -> {{-0.22, 1.15}, {-0.5, 1.4}},
      DisplayFunction -> Identity
      ];
finalgraphic = aa[gr];

Export["Moebius Surface " <> ToString[deg] <> ".png", finalgraphic]