Klein bottle

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  • noun

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a closed surface with only one side

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A Klein bottle was mentioned as a famous 4-D object via related visual material from the internet.
Although the Klein bottle (or Mobius strip) can be used metaphorically to convey the mutual permeation of opposites or integration of what is "out there" with what is "in here," Rosen emphasizes that the Klein bottle is not simply an object in space--a different kind of uncontained container--nor simply a metaphor, symbol, or sign for the interpenetration of subject and object.
In [1], it was proved that the interior of a compact orientable 3-manifold M which is irreducible, atoroidal, anannular, with tori and Klein bottle boundary components has a 1-efficient ideal triangulation.
I've designed a simple form and the characteristics of the Klein bottle
His ensuing discussion of the reflection, self-reflection, and pre-reflection in the context of the Klein bottle has parallels with various creation myths.
Key words: Klein bottle, Clifford torus, projective spaces, minimal surfaces.
Rosen suggests that the 'fourth dimension needed to contemplate the formation of the Klein bottle engages the dimension of being'.
The Klein bottle has the same property of asymmetric one-sidedness as the two-dimensional Moebius surface, but embodies an added dimension (see Rosen 1994, 2004, 2006, 2008).
In addition to Taimina's hyperbolic planes and a Lorenz surface crocheted by Yackel, the exhibit featured Mobius strips, which are twisted rings that have only one side, and Klein bottles, which are closed surfaces that have no inside.
The topological property of the Klein bottle that is responsible for its peculiar nature is its one-sidedness.
Readers learn what monsters, moonshine, and 24-dimensional oranges have in common, how one infinity can be larger than another, and why you can't drink from a Klein bottle.
Both the cross-cap and the Klein bottle offer somewhat more complicated examples of nonorientable surfaces.
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.