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Gluing Two Moebius Strips Into a Klein Bottle
Author

Srdjan Vukmirovic
Organization: Faculty of Mathematics, Belgrade
URL: http://alas.matf.bg.ac.yu/~vsrdjan/
Old MathSource #

0211-341
Revision date

2000-09-19
Description

Klein Bottle Klein bottle is after projective plane the "simplest" closed, non-orientable surface. It is well known fact that one can obtain it by gluing two Moebius strips over their common boundary. Although well known, that fact is not obvious.

In this notebook we made a continuous deformation of a Moebius strip into a half-Klein bottle. Having such a deformation it is easy to obtain a nice animation which deforms and glues two Moebius strips into a Klein bottle.

Besides deformation there is an interesting realization of a Klein bottle as a tube around certain curve.
Subject

*Mathematics > Topology
Keywords

topology, Klein bottle, Moebius strip
Downloads Download Wolfram CDF Player

Download
Moebius2Klein.nb (451.3 KB) - Mathematica notebook
Download
m2klein.gif (166.9 KB) - animated gif
Download
m2kleinBigger.gif (441.6 KB) - animated gif