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MathGroup Archive 1991

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How to plot a Klein bottle

  • To: mathgroup at yoda.ncsa.uiuc.edu
  • Subject: How to plot a Klein bottle
  • From: Ari Lehtonen <Ari.Lehtonen at jyu.fi>
  • Date: Tue, 26 Feb 91 15:26:57 +0200

Hint to David C. Royster about a model for the Klein bottle.
I sent this version of the Klein bottle to the
1990 Mathematica Graphics Competition.

The representation is from Jean Dieudonne, Treatise on Analysis,
vol. III, problem 15, Ch. XVI.25, p. 192  (see also Ch. XV.14.10, p. 98).

The coordinate functions are:
a= 2;
f= (a + Cos[u/2] Sin[t] - Sin[u/2] Sin[2 t]) Cos[u];
g= (a + Cos[u/2] Sin[t] - Sin[u/2] Sin[2 t]) Sin[u];
h= Sin[u/2] Sin[t] + Cos[u/2] Sin[2 t];

The plot:
Needs["Graphics`ParametricPlot3D`"];
ParametricPlot3D[{f,g,h}, {t,0,2Pi,Pi/16}, {u,0,2Pi,Pi/16}];

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|                   Ari Lehtonen                     |
| Dept. of Mathematics | BITnet   : LEHTONEN at FINJYU  |
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