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Definition 2024

Klein_bottle

Klein bottle

English

A Klein bottle immersed in three-dimensional space.

Noun

Klein bottle ‎(plural Klein bottles)

  1. (mathematics) The closed manifold obtained by identifying the boundary components of the annulus so that the resultant surface is nonorientable.

Translations

Etymology

Named after German mathematician Felix Klein (1849-1925) who first described such a surface in 1882. Bottle seems to have come from a misreading or mistranslation of German Fläche ‎(“surface”) as Flasche ‎(“bottle”).

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