Klein bottlen.

Brit.

/ˈklʌɪn ˌbɒtl/, U.S.

/ˈklaɪn ˌbɑd(ə)l/

Etymology: < the name of Felix Klein (1849–1925), German mathematician.

A closed non-orientable surface that can be represented in three dimensions by passing the neck of a bottle through its side and joining its end to a hole in the base.

ΘΚΠ

the world > relative properties > number > geometry > surface > [noun] > generated by rotation or twisting

pseudosphere1884

Möbius surface1900

Möbius strip1904

Möbius band1932

Klein bottle1941

1941 R. Courant & H. E. Robbins What is Math.? v. 262 Another interesting one-sided surface is the ‘Klein bottle’.

1950 Astounding Sci. Fiction Dec. 75/2 ‘The Möbius band’, Turpelo said, ‘has unusual properties because it has a singularity. The Klein bottle, with two singularities, manages to be inside of itself.’

1965 H. Eves Surv. Geom. II. xv. 357 The surface is homeomorphic to a sphere with two crosscaps, and is called a Klein bottle, after Felix Klein who first called attention to it in 1882.

1965 H. Eves Surv. Geom. II. xv. 357 Show that a Klein bottle can, by one cut, be converted into a disc and a Möbius strip.

This entry has not yet been fully updated (first published 1976; most recently modified version published online March 2022).

单词	klein bottle
释义	Klein bottlen. Brit. /ˈklʌɪn ˌbɒtl/, U.S. /ˈklaɪn ˌbɑd(ə)l/ Etymology: < the name of Felix Klein (1849–1925), German mathematician. A closed non-orientable surface that can be represented in three dimensions by passing the neck of a bottle through its side and joining its end to a hole in the base. ΘΚΠ the world > relative properties > number > geometry > surface > [noun] > generated by rotation or twisting pseudosphere1884 Möbius surface1900 Möbius strip1904 Möbius band1932 Klein bottle1941 1941 R. Courant & H. E. Robbins What is Math.? v. 262 Another interesting one-sided surface is the ‘Klein bottle’. 1950 Astounding Sci. Fiction Dec. 75/2 ‘The Möbius band’, Turpelo said, ‘has unusual properties because it has a singularity. The Klein bottle, with two singularities, manages to be inside of itself.’ 1965 H. Eves Surv. Geom. II. xv. 357 The surface is homeomorphic to a sphere with two crosscaps, and is called a Klein bottle, after Felix Klein who first called attention to it in 1882. 1965 H. Eves Surv. Geom. II. xv. 357 Show that a Klein bottle can, by one cut, be converted into a disc and a Möbius strip. This entry has not yet been fully updated (first published 1976; most recently modified version published online March 2022). < n.1941
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