Möbius strip

• Mobius strip
• Moebius strip

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).

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

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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)‎, 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.

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

• Möbius group
• Möbius scarf

• projective plane
• cross-cap
• ♻
• nonorientable

• Mathworld article on the Möbius strip