Editing Möbius strip (section)

==In popular culture==
[[File:Middelheim Max Bill Eindeloze kronkel 1956 03 Cropped.jpg|thumb|''Endless Twist'', [[Max Bill]], 1956, from the [[Middelheim Open Air Sculpture Museum]]]]
Two-dimensional artworks featuring the Möbius strip include an untitled 1947 painting by [[Corrado Cagli]] (memorialized in a poem by [[Charles Olson]]),{{r|emmer|olson}} and two prints by [[M. C. Escher]]: ''Möbius Band I'' (1961), depicting three folded [[flatfish]] biting each others' tails; and ''Möbius Band II'' (1963), depicting ants crawling around a [[lemniscate]]-shaped Möbius strip.{{r|escher1|escher2}} It is also a popular subject of [[mathematical sculpture]], including works by [[Max Bill]] (''Endless Ribbon'', 1953), [[José de Rivera]] (''[[Infinity (de Rivera)|Infinity]]'', 1967), and [[Sebastián (sculptor)|Sebastián]].{{r|emmer}} A [[trefoil knot|trefoil-knotted]] Möbius strip was used in [[John Robinson (sculptor)|John Robinson]]{{'}}s ''Immortality'' (1982).{{sfnp|Pickover|2005|p=13}} [[Charles O. Perry]]'s ''[[Continuum (sculpture)|Continuum]]'' (1976) is one of several pieces by Perry exploring variations of the Möbius strip.{{r|brecher}}

{{multiple image|total_width=400
|image1=Recycle001.svg|caption1=[[Recycling symbol]]
|image2=Logo of Google Drive (2012-2014).svg|caption2=[[Google Drive]] logo (2012–2014)
|image3=Stamp of Brazil - 1967 - Colnect 263101 - Mobius Symbol.jpeg|caption3=[[Instituto Nacional de Matemática Pura e Aplicada|IMPA]] logo on stamp}}

Because of their easily recognized form, Möbius strips are a common element of [[graphic design]].{{sfnp|Pickover|2005|page=13}} The familiar [[recycling symbol|three-arrow logo]] for [[recycling]], designed in 1970, is based on the smooth triangular form of the Möbius {{nowrap|strip,{{r|peterson}}}} as was the logo for the environmentally-themed [[Expo '74]].{{r|expo74}} Some variations of the recycling symbol use a different embedding with three half-twists instead of {{nowrap|one,{{r|peterson}}}} and the original version of the [[Google Drive]] logo used a flat-folded three-twist Möbius strip, as have other similar designs.{{r|gdrive}} The Brazilian [[Instituto Nacional de Matemática Pura e Aplicada]] (IMPA) uses a stylized smooth Möbius strip as its logo, and has a matching large sculpture of a Möbius strip on display in its building.{{r|impa}} The Möbius strip has also featured in the artwork for [[postage stamp]]s from countries including Brazil, Belgium, the Netherlands, and {{nowrap|Switzerland.{{sfnp|Pickover|2005|pp=156–157}}{{r|briefmarken}}}}

[[File:NASCAR Hall of Fame (7553589908).jpg|thumb|upright|[[NASCAR Hall of Fame]] entrance]]
Möbius strips have been a frequent inspiration for the architectural design of buildings and bridges. However, many of these are projects or conceptual designs rather than constructed objects, or stretch their interpretation of the Möbius strip beyond its recognizability as a mathematical form or a functional part of the architecture.{{r|architecture|bridges}} An example is the [[National Library of Kazakhstan]], for which a building was planned in the shape of a thickened Möbius strip but refinished with a different design after the original architects pulled out of the project.{{r|kazakh}} One notable building incorporating a Möbius strip is the [[NASCAR Hall of Fame]], which is surrounded by a large twisted ribbon of stainless steel acting as a façade and canopy, and evoking the curved shapes of racing tracks.{{r|nascar}} On a smaller scale, ''Moebius Chair'' (2006) by [[Pedro Reyes (artist)|Pedro Reyes]] is a [[courting bench]] whose base and sides have the form of a Möbius strip.{{r|reyes}} As a form of [[mathematics and fiber arts]], [[scarf|scarves]] have been [[knitting|knit]] into Möbius strips since the work of [[Elizabeth Zimmermann]] in the early 1980s.{{r|zimmermann}} In [[food styling]], Möbius strips have been used for slicing [[bagel]]s,{{r|bagel}} making loops out of [[bacon]],{{r|bacon}} and creating new shapes for [[pasta]].{{r|pasta}}

Although mathematically the Möbius strip and the fourth dimension are both purely spatial concepts, they have often been invoked in [[speculative fiction]] as the basis for a [[time loop]] into which unwary victims may become trapped. Examples of this trope include [[Martin Gardner]]{{'}}s "No-Sided Professor" (1946), [[Armin Joseph Deutsch]]{{'}}s "[[A Subway Named Mobius]]" (1950) and the film ''[[Moebius (1996 film)|Moebius]]'' (1996) based on it. An entire world shaped like a Möbius strip is the setting of [[Arthur C. Clarke]]'s "The Wall of Darkness" (1946), while conventional Möbius strips are used as clever inventions in multiple stories of [[William Hazlett Upson]] from the 1940s.{{sfnp|Pickover|2005|pp=174–177}} Other works of fiction have been analyzed as having a Möbius strip–like structure, in which elements of the plot repeat with a twist; these include [[Marcel Proust]]{{'s}} ''[[In Search of Lost Time]]'' (1913–1927), [[Luigi Pirandello]]{{'s}} ''[[Six Characters in Search of an Author]]'' (1921), [[Frank Capra]]{{'}}s ''[[It's a Wonderful Life]]'' (1946), [[John Barth]]{{'s}} ''[[Lost in the Funhouse]]'' (1968), [[Samuel R. Delany]]{{'}}s ''[[Dhalgren]]'' (1975) and the film ''[[Donnie Darko]]'' (2001).{{sfnp|Pickover|2005|pp=179–187}}

One of the [[Canon (music)|musical canons]] by [[J. S. Bach]], the fifth of 14 canons ([[BWV 1087]]) discovered in 1974 in Bach's copy of the ''[[Goldberg Variations]]'', features a [[Glide reflection|glide-reflect]] symmetry in which each voice in the canon repeats, with [[Inversion (music)|inverted notes]], the same motif from two measures earlier. Because of this symmetry, this canon can be thought of as having its score written on a Möbius strip.{{r|phillips}}{{efn|Möbius strips have also been used to analyze many other canons by Bach and others, but in most of these cases other looping surfaces such as a cylinder could have been used equally well.{{r|phillips}}}} In [[music theory]], tones that differ by an octave are generally considered to be equivalent notes, and the space of possible notes forms a circle, the [[chromatic circle]]. Because the Möbius strip is the [[configuration space (mathematics)|configuration space]] of two unordered points on a circle, the space of all [[Dyad (music)|two-note chords]] takes the shape of a Möbius strip. This conception, and generalizations to more points, is a significant [[Orbifold#Music theory|application of orbifolds to music theory]].{{r|music|chords}} Modern musical groups taking their name from the Möbius strip include American electronic rock trio [[Mobius Band (band)|Mobius Band]]{{r|bandband}} and Norwegian progressive rock band [[Ring Van Möbius]].{{r|ringvan}}

Möbius strips and their properties have been used in the design of [[Magic (illusion)|stage magic]]. One such trick, known as the Afghan bands, uses the fact that the Möbius strip remains in one piece as a single strip when cut lengthwise. It originated in the 1880s, and was very popular in the first half of the twentieth century. Many versions of this trick exist and have been performed by famous illusionists such as [[Harry Blackstone Sr.]] and [[Thomas Nelson Downs]].{{r|magic|gardner}}