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.]

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]

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]
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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.
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"
References in periodicals archive ?
Assume also that all the boundary components of M are tori and Klein bottles.
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.
From planes they move to spheres, folded patterns, Escher-like patterns and Klein bottles.
The high-level languages of these systems make it possible to visualize various conventional topological objects, such as Platonic solids, knots, Klein bottles, soap-bubble surfaces, and molecular models.
The Banach-Tarski paradox, string theory, Klein bottles, and universes where time runs in reverse are some subjects explored.