Möbius strip

See also: Mobius strip and Moebius strip

English

Möbius strip.

Alternative forms

• Mobius strip
• Moebius strip

Etymology

Named after August Ferdinand Möbius (1790–1868), one of two German mathematicians—the other being Johann Benedict Listing (1808–1882)—who independently discovered the strip at the same time (1858).

Pronunciation

• (UK) IPA^(key): /ˈmɜː.bi.əs stɹɪp/, IPA^(key): /ˈməʊ.bi.əs stɹɪp/
• (US) IPA^(key): /ˈmoʊ.bi.əs stɹɪp/

• Audio (US)

  (file)

Noun

Möbius strip (plural Möbius strips)

1. (topology) A one-sided surface formed by identifying two opposite edges of a square in opposite senses;
   a narrow strip given a half twist and joined at the ends, forming a three-dimensional embedding of said surface.
   • 1981, William Irwin Thompson, The Time Falling Bodies Take to Light: Mythology, Sexuality and the Origins of Culture, page 8:

     Like a mind moving on a Möbius strip of events, one's consciousness goes over the same territory again and again without ever becoming aware of the nature of awareness.

   • 1991, Theoni Pappas, More Joy of Mathematics, Wide World Publishing, page 117,

     B. F. Goodrich Co. has a patent for a Möbius strip conveyor belt. It lasts longer since the wear and tear is spread uniformly over the entire surface.

   • 1992, Speculations in Science and Technology, Volume 15, Elsevier Sequoia, page 221:

     A geometrical model of electron (positron) structure is presented based upon an object of two linked loops obtained by cutting a Möbius strip asymmetrically.

   • 2013 November 16, Patrick McGuinness, “Who's afraid of Marcel Proust?”, in The Daily Telegraph (Review)‎^[1], page R20:

     Proust's novel grew and deepened into over 3,000 pages of everything and nothing: a Möbius strip of profundity twisting into mundanity, mundanity twisting into profundity.

Synonyms

• Möbius band, Möbius loop
• twisted cylinder (rare)

Related terms

• Möbius group
• Möbius scarf

Translations

one-sided surface

• Bulgarian: лист на Мьобиус m (list na Mjobius)
• Catalan: cinta de Möbius f, banda de Möbius f
• Chinese:

  Mandarin: 莫比烏斯帶／莫比乌斯带 (mòbǐwūsī dài).

• Czech: Möbiova páska f
• Danish: möbiusbånd n
• Dutch: Möbiusband m
• Finnish: Möbiuksen nauha
• French: ruban de Möbius (fr) m
• Galician: banda de Möbius f
• German: Möbiusband n
• Hebrew: טבעת מביוס f
• Hungarian: Möbius-szalag (hu)
• Icelandic: Möbíusarræma f
• Ido: Mobius-strio
• Indonesian: pita Möbius
• Interlingua: banda de Möbius
• Irish: stiall Möbius f
• Italian: nastro di Möbius m
• Japanese: メビウスの帯 (ja) (mebiusu no obi)
• Korean: 뫼비우스의 띠 (ko) (moebiuseuui tti)
• Latin: moebii taenia f
• Luxembourgish: Möbiusschläif
• Norwegian: möbius’ bånd n
• Polish: wstęga Möbiusa f
• Portuguese: fita de Möbius f
• Russian: лист Мёбиуса m (list Mjóbiusa), ле́нта Мёбиуса f (lénta Mjóbiusa)
• Serbo-Croatian: мебијусова трака f
• Slovene: Möbiusov trak m
• Spanish: banda de Möbius f, cinta de Möbius f
• Swedish: Möbiusband (sv) n
• Ukrainian: стрічка Мебіуса f (strička Mebiusa)
• Vietnamese: mặt Mobius

narrow strip given a half twist

• Catalan: cinta de Möbius f, banda de Möbius f
• Danish: möbiusbånd n
• Finnish: Möbiuksen nauha
• German: Möbiusband n
• Polish: wstęga Möbiusa f
• Russian: лист Мёбиуса m (list Mjóbiusa), ле́нта Мёбиуса f (lénta Mjóbiusa)
• Swedish: Möbiusband (sv) n
• Turkish: Möbius şeridi
• Vietnamese: dải Mobius

The translations below need to be checked and inserted above into the appropriate translation tables. See instructions at Wiktionary:Entry layout § Translations.

Translations to be checked

• Arabic: ^{(please verify)} شَرِيط مُوبِيُوس m (šarīṭ mōbiyus)
• Esperanto: ^{(please verify)} rubando de Möbius
• Estonian: ^{(please verify)} möbiuse leht
• Slovak: Möbiova páska f, ^{(please verify)} Möbiov list
• Thai: ^{(please verify)} แถบโมเบียส (tàep mohbìat)
• Turkish: ^{(please verify)} möbius şeridi
• Welsh: ^{(please verify)} stribyn Möbius
• West Frisian: ^{(please verify)} möbiusbân

See also

• projective plane
• cross-cap
• ♻
• nonorientable

Further reading

• Mathworld article on the Möbius strip