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Summary

The Klein bottle is a two-dimensional manifold which cannot be consistently oriented, meaning that a system for determining a normal vector cannot be defined for it.
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It is an example of a non-orientable surface.
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Summary
In topology , a branch of mathematics , the Klein bottle ( / ˈ k l aɪ n / ) is an example of a non-orientable surface ; it is a two-dimensional manifold against which a system for determining a normal vector cannot be consistently defined

Klein bottle - Wikipedia
wikipedia.org

Acme Klein Bottle makes and sells glass Klein Bottles. Come visit! ... bottle, I will compose a non-automated email, with the return address of kleinbottle ...

Acme Klein Bottle
kleinbottle.com

The Klein bottle is a closed nonorientable surface of Euler characteristic 0 (Dodson and ... Weisstein, Eric W. "Klein Bottle." From MathWorld --A Wolfram Web ...

Klein Bottle -- from Wolfram MathWorld
wolfram.com

The Klein bottle is a closed nonorientable surface of Euler characteristic 0 (Dodson and ... Weisstein, Eric W. "Klein Bottle." From MathWorld --A Wolfram Web ...

Handmade Glass Klein Bottle
amazon.com

Klein bottle, topological space, named for the German mathematician Felix Klein, obtained by identifying two ends of a cylindrical surface in the direction ...

Klein bottle | topology | Britannica
britannica.com

Klein Bottles They cannot be deformed into each other.

Klein Bottle
virtualmathmuseum.org

A Klein bottle is a surface with a very strange property. A surface is any object that is locally 2-dimensional; every part looks like a piece of the plane. A ...

Klein Bottle – Math Fun Facts
hmc.edu

The Klein bottle is another unorientable surface. It can be constructed by gluing together the two ends of a cylindrical tube with a twist. Unfortunately this ...

The Klein Bottle
osu.edu