Klein bottle

noun

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

Meanings

nounKlein bottle (plural Klein bottles)

plural Klein bottles

  1. mathematicsThe closed manifold obtained by identifying the boundary components of the annulus so that the resultant surface is nonorientable.

    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.

    1981, William Irwin Thompson, The Time Falling Bodies Take to Light: Mythology, Sexuality and the Origins of Culture, London: Rider/Hutchinson & Co., page 222
  2. A physical bottle, usually of blown glass, made to resemble said shape.

Origin

  1. GermanKleinsche Flasche
  2. EnglishKlein bottle

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

Full word history & related roots →

Translations

Czech Kleinova láhev
  • Kleinova láhevclosed surface
Finnish Kleinin pullo
  • Kleinin pulloclosed surface
French bouteille de Klein
  • bouteille de Kleinclosed surface
German Kleinsche Flasche
  • Kleinsche Flascheclosed surface
Hungarian Klein kancsó
  • Klein kancsóclosed surface
Italian bottiglia di Klein, otre di Klein
  • bottiglia di Kleinclosed surface
  • otre di Kleinclosed surface
Japanese クラインの壺
  • クラインの壺 (Kurain no tsubo)closed surface
Korean 클라인 병
  • 클라인 병 (Keullain byeong)closed surface
Polish butelka Kleina
  • butelka Kleinaclosed surface
Portuguese garrafa de Klein
  • garrafa de Kleinclosed surface
Russian буты́лка Клейна
  • буты́лка Клейна (butýlka Klejna)closed surface
Spanish botella de Klein
  • botella de Kleinclosed surface
Cite this entry
APA

Klein bottle. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Klein%20bottle

MLA

“Klein bottle.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Klein%20bottle. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “Klein bottle,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Klein%20bottle.

Source: Klein bottle on Wiktionary, CC BY-SA 4.0.