 # File:Moebius Surface 1 Display Small.png

Moebius_Surface_1_Display_Small.png(180 × 140 pixels, file size: 16 KB, MIME type: image/png) File:Moebius strip.svg is a vector version of this file. It should be used in place of this raster image when superior. File:Moebius Surface 1 Display Small.png File:Moebius strip.svg For more information about vector graphics, read about Commons transition to SVG. There is also information about MediaWiki's support of SVG images. Description A moebius strip parametrized by the following equations: $x = \cos u + v\cos\frac{nu}{2}\cos u$ $y = \sin u + v\cos\frac{nu}{2}\sin u$ $z = v\sin\frac{nu}{2}$,

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 This mathematical image was created with Mathematica.
Permission
( Reusing this file) 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. Mathematical Function Plot
Description Moebius Strip, 1 half-turn (n=1)
Equation : $x = \cos u + v\cos\frac{nu}{2}\cos u$ $y = \sin u + v\cos\frac{nu}{2}\sin u$ $z = v\sin\frac{nu}{2}$
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:

< 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]}}];

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[]]], as[] - 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[]/kersiz}, {
0, siz[]/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]


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