







Title

Gluing Two Moebius Strips Into a Klein Bottle

Author

Srdjan Vukmirovic Organization: Faculty of Mathematics, Belgrade Old MathSource #

0211-341

Revision date

2000-09-19

Description

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

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