Klein bottle

American  

noun

Geometry.

1. a one-sided figure consisting of a tapered tube the narrow end of which is bent back, run through the side of the tube, and flared to join the wide end, thereby allowing any two points on the figure to be joined by an unbroken line.

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Klein bottle British  

/ klaɪn /

noun

1. maths a surface formed by inserting the smaller end of an open tapered tube through the surface of the tube and making this end contiguous with the other end

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Klein bottle Scientific  

/ klīn /

1. A smooth surface that has no inside or outside. It is often pictured in ordinary space as a tube that bends back upon itself, entering through the side and joining with the open end. A true Klein bottle, which cannot be constructed in ordinary three-dimensional space, would not actually intersect itself. The Klein bottle is named after the German mathematician Felix Klein (1849–1925).

2. Compare Möbius strip

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Etymology

Origin of Klein bottle

First recorded in 1940–45; named after F. Klein

Example Sentences

Mathematically, he explained, the design is inspired by the “mind-boggling” topology of a Klein bottle: a “non-orientable closed surface,” with no inside, outside, up or down.

From New York Times

The implication is that, in some strange sense, the outside of a black hole was the same as the inside, like a Klein bottle that has only one side.

From New York Times

I have more trouble with the Klein bottle than the Mobius strip, probably because it’s a bottle, and I can’t think of a bottle that isn’t intended to contain something.

From Literature

A diagram of a Klein bottle, one of the many mathematical objects named after German mathematician Felix Klein.

From Scientific American

Behind her was a display case full of Klein bottles.

From The Guardian