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Klein Bottle
© Copyright 2001, Jim Loy
Here is a drawing of a Klein Bottle (named after its inventor
Felix Klein). Or at least it is a drawing of a three dimensional approximation
of a Klein Bottle. A true Klein Bottle does not intersect its own surface. The
little intersection between the thin neck and the side (the little darker green
ellipse) does not exist in a real Klein Bottle. The neck passes around the
side, through a fourth dimension. But the three dimensional version has many of
the properties of a real Klein Bottle. It is just a more complicated object in
three dimensions. The main feature is that the bottle has only one side. Inside
and outside are the same. A Klein Bottle can be cut into two
Mobius Strips.
Buy a real (3-dimensional, unfortunately) Klein Bottle (or a Klein Stein or
Klein Stocking Cap) at Acme Klein Bottles (http://www.kleinbottle.com/).
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