Revealed

A blog about scientific and medical visualization and all that’s involved.

Visualizing Klein Bottles

Posted by Janet on February 17, 2008

The Klein bottle, a one-sided surface that exists in 4-dimensional space, is a subject of interest for many people. How do you represent a 4-D object when we live in a 3-D space? More importantly, how would you apply artistic freedom when visualizing this object?

Cliff Stoll’s business, Acme Klein Bottle, makes glass Klein bottles in many different shapes and sizes. I’m hoping to pay him a visit in late March when I visit the area. The Acme Klein Bottle also makes Klein hats and Mobius scarves.
http://www.kleinbottle.com/index.htm

Tim Hawkinson wove a Klein bottle out of bamboo. Although made out of a natural organic material, this woven effect mimics transparency and gives it a high tech feel almost like looking at a computer generated image. The video below shows this rotating Klein bottle at the Pace Wildenstein Gallery.

Konrad Polthier presents visual models of the Klein bottle and Mobius strip in this interesting article from “Plus” magazine.
http://plus.maths.org/issue26/features/mathart/index-gifd.html

Finally, here’s my own drawing of a Klein bottle:
klein-bottle.jpg

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