## Klein bottle

noun

A one-sided topological surface having no inside or outside. It is depicted in ordinary space by inserting the small open end of a tapered tube through the side of the tube and making it contiguous with the larger open end, although a true Klein bottle would not intersect itself.

Origin of Klein bottle

After Felix*Klein*,

*(1849–1925), German mathematician*.

**Klein bottle**

## klein-bottle

Noun

(*plural* Klein bottles)

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

Origin

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 *FlÃ¤che* (“surface") as *Flasche* (“bottle").