Image:Moebius Surface 1 Display Small.png

Description	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
Source	Self-made, with Mathematica 5.1 Template:Mathemetica
Date	19/06/2007
Author	Inductiveload
Permission (Reusing this image)	I, the copyright holder of this work, hereby release it into the public domain. This applies worldwide. In case this is not legally possible: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. Afrikaans | Alemannisch | Aragonés | العربية | Asturianu | Български | Català | Česky | Cymraeg | Dansk | Deutsch | Eʋegbe | Ελληνικά | English | Español | Esperanto | Euskara | Estremeñu | فارسی | Français | Galego | 한국어 | हिन्दी | Hrvatski | Ido | Bahasa Indonesia | Íslenska | Italiano | עברית | Kurdî / كوردی | Latina | Lietuvių | Latviešu | Magyar | Македонски | Bahasa Melayu | Nederlands | ‪Norsk (bokmål)‬ | ‪Norsk (nynorsk)‬ | 日本語 | Polski | Português | Ripoarisch | Română | Русский | Shqip | Slovenčina | Slovenščina | Српски / Srpski | Svenska | ไทย | Tagalog | Türkçe | Українська | Tiếng Việt | Walon | ‪中文(简体)‬ | ‪中文(繁體)‬ | zh-yue-hant | +/-
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

[edit] Mathematica Code

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]

• Möbius strip
• Fiber bundle