Question

What is Klein Bottle?
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Answer 1

Answer:

In topology, a branch of mathematics, the Klein bottle (/ˈklaɪn/) 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. Informally, it is a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down. Other related non-orientable objects include the Möbius strip and the real projective plane. While a Möbius strip is a surface with boundary, a Klein bottle has no boundary. For comparison, a sphere is an orientable surface with no boundary

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Answer 2

Answer:

A Klein bottle is a type of non-orientable surface, which is often depicted as looking like a long-necked flask with a bent neck passing within itself to open as its base. A Klein bottle's unique shape means that it has only one surface - its inside is the same as its outside. A Klein bottle cannot truly exist in 3-dimensional, Euclidean space, but blown glass representations can give us an interesting glimpse. This is not a true Klein bottle, but it helps one visualize what the German mathematician Felix Klein imagined when he came up with the idea of the Klein bottle

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