Klein bottle

English

A Klein bottle immersed in three-dimensional space.

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 (deprecated template usage) [etyl] German Fläche (“surface”) as Flasche (“bottle”).

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

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
• (deprecated template usage) {{trans-mid}}
• 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