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Grand Illusions Ltd
Wine Klein
A Klein bottle is a non-orientable surface, where there is no distinction between inside and outside. So unlike a sphere, where you cannot pass from the outside to the inside without passing through the surface, in a Klein bottle you can do just that. If you were very small, an ant say, you could start at any point, and keep crawling until you reached the other side of the surface, without passing through any surfaces, and without needing to cross any edges.
It was first described by the German mathematician Felix Klein in 1882, and it is related to the Möbius strip. Essentially he combined two Möbius surfaces, a left and a right, to form a single surfaced 3 dimensional object. Although in fact a Klein Bottle is really a four dimensional object, that is immersed in three dimensions.
The Möbius strip is a surface with only one side (when embedded in 3-dimensional Euclidean space) and only one boundary. The Möbius strip has the mathematical property of being non-orientable. It can be realized as a ruled surface. It was discovered independently by the German mathematicians August Ferdinand Möbius and Johann Benedict Listing in 1858.
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