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 ?
Non-Euclidean geometries, Mobius band and Klein bottle were not in the original syllabus, but we have included them in the course content, because Klein bottle is a well-known 4D object and mentioned in the discussion on dimension.
More generally, Kronk [3] showed that if S is a surface with Euler genus g, then a(S) = 3 and if S is the sphere or the Klein bottle, then a(S) = [(9 + [square root of 1 + 24g])/4].
Ultimately he arrives at the Klein bottle or Klein surface, a fully paradoxical entity in which inside flows continuously into outside.
Especially spun normal surfaces represent proper essential surfaces using ideal triangulations of 3-manifolds with tori and Klein bottle boundary components.
Galileo wine, served by the Sumalier in a Klein bottle
Introducing and making Mobius strip and Klein Bottle:
So there are only four possible surfaces on which fullerenes ((4,6)-fullerenes) can be embedded, namely, the sphere, the projective plane, the torus, and the Klein bottle. The fullerenes ((4,6)-fullerenes) on these surfaces are called spherical, projective, toroidal, and Klein-bottle fullerenes ((4,6)-fullerenes), respectively.
In one area of the gallery, a ceramic Klein bottle is suspended from two pieces of plywood.
[7] considered fullerene's extension to other closed surfaces and showed that only four surfaces are possible, namely sphere, torus, Klein bottle and pro jective plane.
For its part, the Klein bottle (which as Rosen observes, represents "swallowing the serpent") brings back the discontinuity, in that it cannot be constructed (in three dimensions) without the hole that lets it pass through itself--but the hole makes it topologically imperfect.
But Rosen takes us a step further and presents the Klein bottle as a more sophisticated model of his thesis.