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Klein bottle

Klein Bottle

In mathematics, Klein Bottle is an example of certain non orientable surface without any distinction between the inside and outside surface. It was named after the German Mathematician Felix Klein in 1882.

This bottle is same like Mobius strip (continuous closed surface with only one layer). They differ only in the surface boundary. Mobius strip has surface boundary whereas Klein bottle doesn't have surface boundary. Mobius strip can be embedded in three dimensional Euclidean space while Klein can be embedded in two and four dimensional shape.

Klein thought the shape of the Mobius strip was divine, so he told,

"If you glue

The edges of two,

You'll get a weird bottle like mine."

It's a bottle with the hole in the bottom. The neck of the bottle was extended inside the bottle until it joins the hole in the bottom. A true Klein bottle in four dimensions does not intersect itself where it crosses the side. Unlike a drinking bottle, this object has no rim, so the surface area stops abruptly.

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