Chloe Chao

Spring 1997

The Klein bottle is a closed surface that has no interior. Perhaps its closest kin is the Mobius strip. Regardless, the basic principle of continuity is the same.

In the following images (which you can click on to make larger), I have used the parametric equations defined below to define a Klein bottle that is two Mobius strips joined together to make a closed surface.

Here is a quicktime movie of one of my klein examples.

To realize the Klein bottles in 3D requires the surface to intersect itself. What I would be interested in is to perhaps define the Klein bottle over time, thereby adding a "fourth" dimension.

Methods: The program that generates the points is written in C++ and uses the Inventor C++ graphics libraries to display the point/line sets to the screen.

Acknowledgements/References: The parametric equations for these forms can be found at Paul Bourke's site, which in general is an excellent computer graphics reference site.