quincunx

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The quincunx was originally a coin issued by the Roman Republic {{circa|211–200 BC}}, whose value was five twelfths (quinque and uncia) of an as, the Roman standard bronze coin. On the Roman quincunx coins, the value was sometimes indicated by a pattern of five dots or pellets. However, these dots were not always arranged in a quincunx pattern.

The Oxford English Dictionary (OED) dates the first appearances of the Latin word in English as 1545 and 1574 ("in the sense 'five-twelfths of a pound or as{{'"}}; i.e. 100 old pence). The first citation for a geometric meaning, as "a pattern used for planting trees", dates from 1606. The OED also cites a 1647 reference to the German astronomer Kepler for an astronomical/astrological meaning, an angle of 5/12 of a whole circle. When used to describe a tree-planting pattern, the same word can also refer to groups of more than five trees, arranged in a square grid but aligned diagonally to the dimensions of the surrounding plot of land; however, this article considers only five-point patterns and not their extension to larger square grids.

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Quincunx patterns occur in many contexts:

File:Flag of the Solomon Islands.svg features a quincunx of stars.]]

File:Peirce-quincuncial-projection.jpg]]

File:Décor mural de la Chapelle palatine (Palerme) (6880608996).jpg, Palermo, Sicily]]

• In heraldry, groups of five elements (charges) are often arranged in a quincunx pattern. This arrangement is called, in heraldic terminology, in saltire for its usual orientation with the sides of the square vertical or horizontal, or in cross when the square is diagonally oriented. The flag of Solomon Islands features this pattern, with its five stars representing the five main island groups in Solomon Islands. Another instance of this pattern occurred in the flag of the 19th-century Republic of Yucatán, where it signified the five departments into which the republic was divided. The coat of arms of Portugal includes both orientations of the same patterns, nested within each other.{{citation|title= The book of public arms : a complete encyclopædia of all royal, territorial, municipal, corporate, official, and impersonal arms|last=Fox-Davies|first= Arthur Charles|year=1915 |publisher=T.C. & E.C. Jack |page=624|url=https://archive.org/details/bookofpublicarms00foxd/page/624}}
• Quincunxes are used in modern computer graphics as a pattern for multisample anti-aliasing. Quincunx antialiasing samples scenes at the corners and centers of each pixel. These five sample points, in the shape of a quincunx, are combined to produce each displayed pixel. However, samples at the corner points are shared with adjacent pixels, so the number of samples needed is only twice the number of displayed pixels.{{citation|url=http://www.nvnews.net/previews/geforce3/quincunx.shtml|title=NVIDIA GeForce3 Preview|first=Mike|last=Chambers|journal=NV News|date=February 27, 2001|url-status=dead|archive-url=https://web.archive.org/web/20091113170739/http://www.nvnews.net/previews/geforce3/quincunx.shtml|archive-date=November 13, 2009}}.
• In numerical analysis, the quincunx pattern describes the two-dimensional five-point stencil, a sampling pattern used to derive finite difference approximations to derivatives. The five points of the five-point stencil are arranged directly above, below, and to the two sides of the center point, rather than (as in quincunx sampling) diagonally with respect to it.{{citation|contribution=1.2 The Finite Difference Method|pages=21–29|title=Numerical Methods for Elliptic and Parabolic Partial Differential Equations|volume=44|series=Texts in Applied Mathematics|first1=Peter|last1=Knabner|first2=Lutz|last2=Angermann|publisher=Springer-Verlag|year=2003|isbn=978-0-387-95449-3}}.
• In Khmer architecture, the towers of a temple, such as Angkor Wat, are sometimes arranged in a quincunx to represent the five peaks of Mount Meru.{{Cite web |date=2004-12-25 |title=Angkor Wat |url=https://earthobservatory.nasa.gov/images/5112/angkor-wat |access-date=2022-03-04 |website=earthobservatory.nasa.gov |language=en}}
• A quincunx is one of the quintessential designs of Cosmatesque inlay stonework.{{citation|title=Cosmatesque ornament: flat polychrome geometric patterns in architecture|first=Paloma|last=Pajares-Ayuela|publisher=W. W. Norton & Company|year=2001|isbn=978-0-393-73037-1|contribution=The Signification — The Cosmatesque Quincunx: A Double-Cross Motif|pages=196–246|url=https://books.google.com/books?id=LX2ooH1uFpsC&pg=PA196}}.
• A quincuncial map is a conformal map projection that maps the poles of the sphere to the centre and four corners of a square, thus forming a quincunx.
• The points on each face of a unit cell of a face-centred cubic lattice form a quincunx.
• The quincunx as a tattoo is known as the five dots tattoo. It has been variously interpreted as a fertility symbol,{{citation|title=Tattoo history: a source book : an anthology of historical records of tattooing throughout the world|first=Steve|last=Gilbert|publisher=Juno Books|year=2000|isbn=978-1-890451-06-6|page=[https://archive.org/details/tattoohistorysou0000gilb/page/153 153]|url=https://archive.org/details/tattoohistorysou0000gilb/page/153}}. a reminder of sayings on how to treat women or police, a recognition symbol among the Romani people,{{citation|title=Kishkindha|first=Robert|last=Turner|publisher=Osiris Press Ltd|year=2005|isbn=978-1-905315-05-5|page=53|url=https://books.google.com/books?id=cnxh8vR2HzQC&pg=PA53}}. a group of close friends,{{citation|title=A law enforcement sourcebook of Asian crime and cultures: tactics and mindsets|first=Douglas D.|last=Daye|publisher=CRC Press|year=1997|isbn=978-0-8493-8116-4|page=113|url=https://books.google.com/books?id=Z0k0kTGivP4C&pg=PA113}}. standing alone in the world,{{citation|title=A rainbow of gangs: street cultures in the mega-city|first=James Diego|last=Vigil|publisher=University of Texas Press|year=2002|isbn=978-0-292-78749-0|page=115|url=https://books.google.com/books?id=0qKcorWNve0C&pg=PA115}}. or time spent in prison (with the outer four dots representing the prison walls and the inner dot representing the prisoner).{{citation|title=Russian criminal tattoo encyclopedia, Volume 3|first=Danzig|last=Baldayev|publisher=FUEL Publishing|year=2006|page=214}}. Thomas Edison, whose many inventions included an electric pen which later became the basis of a tattooing machine created by Samuel O'Reilly, had this pattern tattooed on his forearm.{{citation|title=The Pocket Idiot's Guide to Not So Useless Facts|first1=Dane|last1=Sherwood|first2=Sandy|last2=Wood|first3=Kara|last3=Kovalchik|publisher=Penguin|year=2006|isbn=978-1-59257-567-1|page=48|url=https://books.google.com/books?id=9F6Xq8WtmeMC&pg=PT48}}.
• The first two stages of the Saturn V super heavy-lift rocket had engines in a quincunx arrangement.{{citation|title=Apollo in Perspective: Spaceflight Then and Now|first=Jonathan|last=Allday|publisher=CRC Press|year=2000|isbn=9780750306454|page=77|url=https://books.google.com/books?id=LqZcSAM3nrYC&pg=PA77|quote=The engines were arranged across the base of the stage in the same pattern as the dots on a number 5 domino}}.
• A baseball diamond forms a quincunx with the four bases and the pitcher's mound.{{citation|title=Pataphysica|editor-first=Cal|editor-last=Clements|year=2002|publisher=Writers Club Press|isbn=9780595236046|first=Brisbane|last=di Milo|contribution=Telepathic letter to Alfred Jarry|pages=60–68}}. See in particular [https://books.google.com/books?id=PlmXbgrvJFYC&pg=PA62 p. 62].

Various literary works use or refer to the quincunx pattern:

• Quincunx (1564) was the name of the political treatise by a Polish-Ruthenian writer Stanisław Orzechowski: here, the five points symbolized five pillars of Polish state, with the Church at the very top.Jerzy Ziomek: Renesans. Wyd. XI – 5 dodruk. Warszawa: Wydawnictwo Naukowe PWN, 2012, s. 201-204, seria: Wielka Historia Literatury Polskiej. ISBN 978-83-01-13843-1.
• The Garden of Cyrus, or The Quincuncial Lozenge, or Network Plantations of the Ancients, naturally, artificially, mystically considered, is an essay by Sir Thomas Browne, published in 1658. Browne elaborates upon evidence of the quincunx pattern in art, nature and mystically as evidence of "the wisdom of God". Although writing about the quincunx in its geometric meaning, he may have been influenced by English astrology, as the astrological meaning of "quincunx" (unrelated to the pattern) was introduced by the astronomer Kepler in 1604. The Victorian critic Edmund Gosse complained that "gathering his forces it is Quincunx, Quincunx, all the way until the very sky itself is darkened with revolving Chess-boards", while conceding that "this radically bad book contains some of the most lovely paragraphs which passed from an English pen during the seventeenth Century".[https://aquariumofvulcan.blogspot.com/2013/05/what-is-more-beautiful-than-quincunx.html "That Vulcan gave Arrows unto Apollo and Diana"] Aquarium of Vulcanblog; [https://books.google.com/books?id=5BZ8wzwllBEC&dq=Quincunx+Browne&pg=PA126 Sir Thomas Browne: A Study in Religious Philosophy], Dunn, William P., pp 126-129, 1950
• James Joyce uses the term in "Grace", a short story in Dubliners of 1914, to describe the seating arrangement of five men in a church service. Lobner{{citation|title=Equivocation As Stylistic Device: Joyce's 'Grace' and Dante|last=Lobner|first=Corinna del Greco|journal=Lectura Dantis|volume=4|year=1989|url=http://www.brown.edu/Departments/Italian_Studies/LD/numbers/04/lobner.html}}; for additional work on this instance of the quincunx pattern, see {{citation|last=Duffy|first=Charles F.|title=The Seating Arrangement in 'Grace'|journal=James Joyce Quarterly|volume=9|year=1972|pages=487–489}}. argues that in this context the pattern serves as a symbol both of the wounds of Christ and of the Greek cross.
• Lawrence Durrell's novel sequence The Avignon Quintet is arranged in the form of a quincunx, according to the author; the final novel in the sequence is called Quinx, the plot of which includes the discovery of a quincunx of stones.{{citation|journal=CLCWeb: Comparative Literature and Culture|title=Reading Orientalism and the Crisis of Epistemology in the Novels of Lawrence Durrell|first=James|last=Gifford|volume=1|issue=2|year=1999|doi=10.7771/1481-4374.1036|url=https://docs.lib.purdue.edu/clcweb/vol1/iss2/3/|quote=the most dominant formal element expressing this state of multiplicity in The Avignon Quintet is its quincunx structure|doi-access=free}}.
• The Quincunx is the title of a lengthy and elaborate novel by Charles Palliser set in 19th-century England, published in 1989; the pattern appears in the text as a heraldic device, and is also reflected in the structure of the book.{{citation|title=Theme Parks, Rainforests and Sprouting Wastelands: European Essays on Theory and Performance in Contemporary British Fiction|volume=123|series=Costerus New Series|editor1-first=Richard|editor1-last=Todd|editor2-first=Luisa|editor2-last=Flora|publisher=Rodopi|year=2000|isbn=9789042005020|url=https://books.google.com/books?id=B1amyMDNfmQC&pg=PA151|pages=151–163|contribution=Mirror games and hidden narratives in The Quincunx|first=Susana|last=Onega}}.
• In the first chapter of The Rings of Saturn, W. G. Sebald's narrator cites Browne's writing on the quincunx. The quincunx in turn becomes a model for the way in which the rest of the novel unfolds.{{citation|title=Narratology Beyond Literary Criticism: Mediality, Disciplinarity|volume=6|series=Narratologia : contributions to narrative theory|editor-first=Jan Christoph|editor-last=Meister|publisher=Walter de Gruyter|year=2005|isbn=9783110183528|first=Silke|last=Horstkotte|contribution=The double dynamics of focalization in W. G. Sebald's The Rings of Saturn|url=https://books.google.com/books?id=6-M4s5Hv3DkC&pg=PA25|pages=25–44}}.
• Séamus Heaney describes Ireland's historical provinces as together forming a quincunx, as the Irish word for province cúige (literally: "fifth part") also explicates. The five provinces of Ireland were Ulster (north), Leinster (east), Connacht (west), Munster (south) and Meath (center, and now a county within Leinster). More specifically, in his essay Frontiers of Writing, Heaney creates an image of five towers forming a quincunx pattern within Ireland, one tower for each of the five provinces, each having literary significance.{{citation|first=Séamus|last=Heaney|author-link=Séamus Heaney|contribution=Frontiers of Writing|title=The Redress of Poetry: Oxford Lectures|publisher=Faber and Faber|year=1995|pages=186–202}}.{{citation|title=Poets of Modern Ireland|first=Neil|last=Corcoran|publisher=SIU Press|year=1999|isbn=9780809322909|page=62|url=https://books.google.com/books?id=0p3x6JtsnLYC&pg=PA62}}.
• Early African American scientist Benjamin Banneker describes a dream in which he is asked to measure the shape of the soul after death. The answer is "quincunx". Research locates his ancestry in Senegal, where the quincunx is a common religious symbol.{{citation|last=Eglash|first=Ron|date=April 1997|issue=2|journal=Social Studies of Science|jstor=285472|pages=307–315|title=The African heritage of Benjamin Banneker|volume=27|doi=10.1177/030631297027002004|s2cid=143652183}}

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• {{commons category-inline|Quincunxes}}
• {{wiktionary-inline}}

Category:Dot patterns

Category:5 (number)