Klein bottle

English

A Klein bottle immersed in three-dimensional space.

Etymology

Calque of German Kleinsche Flasche, named after German mathematician Felix Klein (1849–1925), who first described such a surface in 1882.

Noun

Klein bottle (plural Klein bottles)

1. (topology) The closed manifold obtained by identifying the boundary components of the annulus so that the resultant surface is nonorientable.
   • 1981, William Irwin Thompson, The Time Falling Bodies Take to Light: Mythology, Sexuality and the Origins of Culture, London: Rider/Hutchinson & Co., page 222:

     At this level Atman and Brahman are like a Klein bottle or a Möbius strip: there is no edge where one can say that this is Atman, but this is Brahman.

2. A physical bottle, usually of blown glass, made to resemble the topological shape.

Translations

closed surface

• Czech: Kleinova láhev f
• Finnish: Kleinin pullo
• French: bouteille de Klein (fr) f
• German: Kleinsche Flasche f
• Hungarian: Klein kancsó
• Italian: bottiglia di Klein f, otre di Klein m
• Japanese: クラインの壺 (ja) (Kurain no tsubo)
• Korean: 클라인 병 (Keullain byeong)
• Portuguese: garrafa de Klein f
• Russian: буты́лка Клейна (ru) f (butýlka Klejna)
• Spanish: botella de Klein f