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 ∙ Bahasa Indonesia ∙ Bahasa Melayu ∙ British English ∙ català ∙ čeština ∙ dansk ∙ Deutsch ∙ eesti ∙ English ∙ español ∙ Esperanto ∙ euskara ∙ français ∙ Frysk ∙ galego ∙ hrvatski ∙ Ido ∙ italiano ∙ lietuvių ∙ magyar ∙ Nederlands ∙ norsk bokmål ∙ norsk nynorsk ∙ occitan ∙ Plattdüütsch ∙ polski ∙ português ∙ português do Brasil ∙ română ∙ Scots ∙ sicilianu ∙ slovenčina ∙ slovenščina ∙ suomi ∙ svenska ∙ Tiếng Việt ∙ Türkçe ∙ vèneto ∙ Ελληνικά ∙ беларуская (тарашкевіца) ∙ български ∙ македонски ∙ нохчийн ∙ русский ∙ српски / srpski ∙ татарча/tatarça ∙ українська ∙ ქართული ∙ հայերեն ∙ বাংলা ∙ தமிழ் ∙ മലയാളം ∙ ไทย ∙ 한국어 ∙ 日本語 ∙ 简体中文 ∙ 繁體中文 ∙ עברית ∙ العربية ∙ فارسی ∙ +/−

 

DescriptionMoebius Surface 1 Display Small.png	A moebius strip parametrized by the following equations: ${\displaystyle x=\cos u+v\cos {\frac {nu}{2}}\cos u}$ ${\displaystyle y=\sin u+v\cos {\frac {nu}{2}}\sin u}$ ${\displaystyle z=v\sin {\frac {nu}{2}}}$, 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.
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	:${\displaystyle x=\cos u+v\cos {\frac {nu}{2}}\cos u}$ ${\displaystyle y=\sin u+v\cos {\frac {nu}{2}}\sin u}$ ${\displaystyle z=v\sin {\frac {nu}{2}}}$
Co-ordinate System	Cartesian (Parametric Plot)
u Range	0 .. 4π
v Range	0 .. 0.3

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]