Klein bottle


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Klein bottle

[′klīn ‚bäd·əl]
(mathematics)
The nonorientable surface having only one side with no inside or outside; it resembles a bottle pulled into itself.
References in periodicals archive ?
The material on non-Euclidean geometry and terms like Mobius band and Klein bottle were introduced in a short period of time (2 hours) and it was too much information for background this audience had.
As Rosen suggests, the Klein bottle offers a sign-vehicle for Kleinian (w)holeness, complexity, and dynamism.
Let M be a 3-manifold with a complete hyperbolic metric of finite volume with tori or Klein bottle cusps and let T be a 1-efficient ideal triangulation of M.
One of the properties of Klein Bottle as it is shown in the picture is that if a glass, the water won't pour out of the bottle.
Can we read the hole in the Klein bottle in such as way that we relax the compulsion to regard it as merely a hole .
In the first part of this paper we prove, in a constructive and simple way, that we cannot embed either the Klein bottle or a Klein bottle with a finite number of handles attached in [RP.
There is a different but mathematically equivalent way to describe the making of a Klein bottle that, for our purposes, will be instructive.
What the Klein bottle does for its part is help sharpen the intuition of depth by lending topological detail and precision to it.
Ferguson's dusty basement studio is filled with the results of his dialogues between materials and mathematical theorems -- sculpted geometrical forms that go by exotic names: Klein bottles, trefoil knots, cross-caps, horned spheres and tori.
Like the Etruscan Venus, Ida is also the shadow of a four-dimensional Klein bottle.
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.