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MathGroup Archive 2000

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Re:what mathematical formula can generate a mobius strip?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg25059] Re:[mg25044] what mathematical formula can generate a mobius strip?
  • From: "Ingolf Dahl" <f9aid at fy.chalmers.se>
  • Date: Thu, 7 Sep 2000 22:28:02 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

VIKTORA6 at aol.com asked the following question:
"what mathematical formula can generate a mobius strip?"

If you only want to plot it, use

<< Graphics`Shapes`
Show[Graphics3D[MoebiusStrip[2, 1, 80]]]

If you want to play more, and have control over the parameters, use

r1 = 5; r2 = 2.5; theta0 = 6*Pi/2.;
ParametricPlot3D[{(r1 - r2*u*Sin[(theta - theta0)/2])*Cos[theta],
(r1 - r2*u*Sin[(theta - theta0)/2])*Sin[theta],
r2*u*Cos[(theta - theta0)/2]}, {theta, 0, 2*Pi}, {u, -1, 1}]

With the given values of r1, r2 and theta0, you get almost the same curve as
the curve from MoebiusStrip, but you can also experiment with other values.
If you only want the outer edge, use

r1 = 5; r2 = 2.5; theta0 = 6*Pi/2.;
ParametricPlot3D[{(r1 - r2*Sin[(theta - theta0)/2])*Cos[theta],
(r1 - r2*Sin[(theta - theta0)/2])*Sin[theta],
 r2*Cos[(theta - theta0)/2]}, {theta, 0, 4*Pi}]

Ingolf Dahl
Chalmers University
f9aid at fy.chalmers.se





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