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MAKE A MEME View Large Image $Moebius Surface 0.1.png A moebius strip parametrized by the following equations <math>x \cos u + v\cos\frac nu 2 \cos u</math> <math>y \sin u + v\cos\frac nu 2 \sin u</math> <math>z v\sin\frac nu 2 </math> where n 0 1 This plot is part of a ...$

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Keywords: Moebius Surface 0.1.png A moebius strip parametrized by the following equations <math>x \cos u + v\cos\frac nu 2 \cos u</math> <math>y \sin u + v\cos\frac nu 2 \sin u</math> <math>z v\sin\frac nu 2 </math> where n 0 1 This plot is part of a series depicting n for 0 to 1 See Möbius Strip for the rest of the series Self-made with Mathematica 5 1 Created with Mathematica 2007-06-24 Inductiveload Moebius Strip 1 half-turn n 0 1 - Equation <math>x \cos u + v\cos\frac nu 2 \cos u</math><br> <math>y \sin u + v\cos\frac nu 2 \sin u</math><br> <math>z v\sin\frac nu 2 </math> - Co-ordinate System Cartesian Parametric Plot - u Range 0 4 - v Range 0 0 3 Mathematica Code border solid 2px BF0C1D; ; valign top ; width 75 align center 50px Please be aware that at the time of uploading 15 15 19 June 2007 UTC this code may take a significant amount of time to execute on a consumer-level computer 50px border solid 2px D6D6FF; ; valign top ; width 75 align center 50px This uses Chris Hill's antialiasing code to average pixels and produce a less jagged image The original code can be found http //members wri com/jeffb/visualization/aa shtml here 50px This code requires the following packages <<Graphics`Graphics` <pre> MoebiusStripr_ 1 Function u v n r Cosu + v Cosn u/2Cosu Sinu + v Cosn u/2Sinu v Sinn u/2 EdgeFormAbsoluteThickness4 ; aagr_ Module siz kersiz ker dat as ave is ar is ImageSize / Optionsgr ImageSize; ar AspectRatio / Optionsgr AspectRatio; If NumberQis is 288; kersiz 4; img ImportStringExportStringgr PNG ImageSize -> is kersiz PNG ; siz Reverse Dimensionsimg1 1 1 2 ; ker TableN1/kersiz 2 kersiz kersiz ; dat Nimg1 1; as Dimensionsdat; ave PartitionTransposeFlattenListConvolveker datAll All \ / Rangeas3 as2 - kersiz + 1; ave Takeave Sequence 1 Dimensionsave kersiz / RangeLengthDimensionsave - 1 ; ShowGraphicsRasterave 0 0 siz/kersiz 0 255 ColorFunction -> RGBColor PlotRange -> 0 siz 1/kersiz 0 siz2/kersiz ImageSize -> is AspectRatio -> ar deg 0 1; gr ParametricPlot3DEvaluateMoebiusStripu v deg u 0 4� v 0 3 PlotPoints -> 249 5 PlotRange -> -1 3 1 3 -1 3 1 3 -0 7 0 7 Boxed -> False Axes -> False ImageSize -> 800 PlotRegion -> -0 22 1 15 -0 5 1 4 DisplayFunction -> Identity ; finalgraphic aagr; Export Moebius Surface <> ToStringdeg <> png finalgraphic </pre> Moebius strip plots