# Definitions for **klein bottle**klaɪn

### This page provides all possible meanings and translations of the word **klein bottle**

### Random House Webster's College Dictionary

Klein′ bot`tleklaɪn(n.)

a one-sided figure consisting of a tapered tube whose narrow end is bent back, run through the side of the tube, and flared to join the wide end.

**Category:**Math

#### Origin of **Klein bottle**:

1940–45; after Felix Klein (1849–1925), German mathematician

### Princeton's WordNet

Klein bottle(noun)

a closed surface with only one side; formed by passing one end of a tube through the side of the tube and joining it with the other end

### Wiktionary

Klein bottle(Noun)

The closed manifold obtained by identifying the boundary components of the annulus so that the resultant surface is nonorientable.

**Origin:** Named after German mathematician (1849-1925) who first described such a surface in 1882. bottle seems to have come from a misreading or mistranslation of Fläche as .

### Freebase

Klein bottle

In mathematics, the Klein bottle is an example of a non-orientable surface; informally, it is a surface in which notions of left and right cannot be consistently defined. Other related non-orientable objects include the Möbius strip and the real projective plane. Whereas a Möbius strip is a surface with boundary, a Klein bottle has no boundary. The Klein bottle was first described in 1882 by the German mathematician Felix Klein. It may have been originally named the Kleinsche Fläche and that this was incorrectly interpreted as Kleinsche Flasche, which ultimately led to the adoption of this term in the German language as well.

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