Definitions for klein bottle
klaɪnklein bot·tle

Princeton's WordNetRate this definition:0.0 / 0 votes

1. Klein bottlenoun

   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

WiktionaryRate this definition:0.0 / 0 votes

1. Klein bottlenoun

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

2. Etymology: 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.

WikipediaRate this definition:0.0 / 0 votes

1. Klein bottle

   In topology, a branch of mathematics, the Klein bottle () 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. The concept of a Klein bottle was first described in 1882 by the German mathematician Felix Klein.

ChatGPTRate this definition:0.0 / 0 votes

1. klein bottle

   A Klein bottle is a mathematical concept, a non-orientable surface with no distinguishable inside and outside, and only one surface or boundary. It is a two-dimensional manifold that cannot be embedded in three-dimensional Euclidean space without intersecting itself. The Klein bottle was first described in 1882 by the German mathematician Felix Klein. It is a topology concept in mathematics more than a viable physical object.

WikidataRate this definition:0.0 / 0 votes

1. 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.

Matched Categories

1. • Surface

How to pronounce klein bottle?

1. Alex

   US English

   David

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   Mark

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   Daniel

   British

   Libby

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   Mia

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   Karen

   Australian

   Hayley

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   Neerja

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   Zira

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   Oliver

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How to say klein bottle in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of klein bottle in Chaldean Numerology is: 5

2. Pythagorean Numerology

   The numerical value of klein bottle in Pythagorean Numerology is: 8

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=klein bottle
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Klein_Bottle
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Klein_Bottle
4. ^ ChatGPT
   https://chat.openai.com
5. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=klein bottle