Klein bottle


Also found in: Dictionary, Thesaurus, Wikipedia.

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.
I've designed a simple form and the characteristics of the Klein bottle
Thomassen, "Tilings of the torus and the Klein bottle and vertex-transitive graphs on a fixed surface," Transactions of the American Mathematical Society, vol.
Returning to the Klein bottle, Rosen proposes that it "...
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.
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.
Because Idaszak was the first to see it, this one came to be called "Ida.' Like the Etruscan Venus, Ida is also the shadow of a four-dimensional Klein bottle.