# 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 not inferior.

File:Moebius Surface 1 Display Small.png File:Moebius strip.svg

Templates:Vector version available/I18n

Description

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
 This diagram 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.
Other versions
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:

<<GraphicsGraphics

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]


## File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current15:31, 19 June 2007180 × 140 (16 KB)Inductiveload
15:30, 19 June 2007200 × 150 (18 KB)Inductiveload
15:27, 19 June 2007200 × 150 (18 KB)Inductiveload{{Information |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
The following pages on the English Wikipedia use this file (pages on other projects are not listed):

## Global file usage

The following other wikis use this file:

• Usage on el.wikipedia.org
• Usage on en.wikiversity.org
• Usage on eo.wikipedia.org
• Usage on es.wikipedia.org
• Usage on et.wikipedia.org
• Usage on fr.wikipedia.org
• Usage on it.wikipedia.org
• Usage on ja.wikipedia.org
• Usage on ru.wikipedia.org
• Usage on simple.wikipedia.org