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}];

/====================================================\
|                   Ari Lehtonen                     |
| Dept. of Mathematics | BITnet   : LEHTONEN at FINJYU  |
| Univ. of Jyvaskyla   | Internet : lehtonen at jyu.fi  |
| P.O Box 35           | Phone    : +358 41 602 718  |
| SF-40351  JYVASKYLA  | Fax      : +358 41 602 701  |
|                   FINLAND                          |
\====================================================/

```

• Prev by Date: gray levels
• Next by Date: List contour plots
• Previous by thread: gray levels
• Next by thread: Re: How to plot a Klein bottle