Klein bottle

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Klein bottle

Klein bottle

n.
A one-sided topological surface having no inside or outside. It is depicted in ordinary space by inserting the small open end of a tapered tube through the side of the tube and making it contiguous with the larger open end, although a true Klein bottle would not intersect itself.

[After Felix Klein (1849-1925), German mathematician.]
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

Klein bottle

(klaɪn)
n
(Mathematics) 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
[named after Felix Klein (1849–1925), German mathematician]
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

Klein′ bot`tle

(klaɪn)
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.
[1940–45; after Felix Klein (1849–1925), German mathematician]
Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.
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Klein bottle

Klein bottle

(klīn)
A theoretical surface in topology that has no inside or outside. It can be 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 would not actually intersect itself. Compare Möbius strip.
The American Heritage® Student Science Dictionary, Second Edition. Copyright © 2014 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
ThesaurusAntonymsRelated WordsSynonymsLegend:
Noun1.Klein bottle - 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
surface - the outer boundary of an artifact or a material layer constituting or resembling such a boundary; "there is a special cleaner for these surfaces"; "the cloth had a pattern of red dots on a white surface"
Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.
References in periodicals archive ?
Klein bottles and Mobius strips are examples of the kinds of subjects a topologist might invest her energies in.
Assume also that all the boundary components of M are tori and Klein bottles. M is called [P.sub.2]-irreducible if any embedded 2-sphere bounds a 3-cell and there are no embedded 2-sided projective planes.
The conjecture holds that any closed, orientable, prime 3-manifold M contains a disjoint union of embedded incompressible 2-tori and Klein bottles such that each connected component of the complement admits a complete, locally homogeneous Riemannian metric of finite volume.
Highlights included scientific glass maker Alan Bennett''s Klein bottles; an exploration of the Mobius strip in three dimensions; Beryl Sokoloff''s film, My Mirrored Hope, which immortalised Clarence Schmidt''s House of Mirrors; notebooks from the National Science Museum, belonging to mathematician, inventor and mechanical engineer Charles Babbage; Attila Cs|rg|'s Magnet Spring which consisted of a series of aligned, but not touching, glass panes held in balance purely by magnectic force; and Michelangelo Pistolleto''s Cubic Metre of Infinity.
From planes they move to spheres, folded patterns, Escher-like patterns and Klein bottles. They add the dimension of symmetry of colors to the mix, as well.