Quincunx
Encyclopedia
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
pattern consisting of five points arranged in a cross, that is five coplanar points
Point (geometry)
In geometry, topology and related branches of mathematics a spatial point is a primitive notion upon which other concepts may be defined. In geometry, points are zero-dimensional; i.e., they do not have volume, area, length, or any other higher-dimensional analogue. In branches of mathematics...
, four of them forming a square
Square (geometry)
In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles...
or rectangle
Rectangle
In Euclidean plane geometry, a rectangle is any quadrilateral with four right angles. The term "oblong" is occasionally used to refer to a non-square rectangle...
and a fifth at its center. It forms the arrangement of five units in the pattern corresponding to the five-spot on a six-sided die
Dice
A die is a small throwable object with multiple resting positions, used for generating random numbers...
, playing cards, or dominoes.
Historical origins of the name
The quincunxQuincunx (coin)
The quincunx was an Ancient Roman bronze coin produced during the Roman Republic. The word quincunx comes from Latin "quinque" which means "five" and "uncia" which means "one twelfth", because the coin was valued at five-twelfths of an as , or five unciae...
was originally a coin issued by the Roman Republic c. 211–200 BC, whose value was five twelfths (quinque + uncia) of an as
As (coin)
The , also assarius was a bronze, and later copper, coin used during the Roman Republic and Roman Empire.- Republican era coinage :...
, 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.
Examples
Quincunx patterns occur in many contexts:
- In heraldryHeraldryHeraldry is the profession, study, or art of creating, granting, and blazoning arms and ruling on questions of rank or protocol, as exercised by an officer of arms. Heraldry comes from Anglo-Norman herald, from the Germanic compound harja-waldaz, "army commander"...
, groups of five elements (charges) are often arranged in a quincunx pattern, called in saltireSaltireA saltire, or Saint Andrew's Cross, is a heraldic symbol in the form of a diagonal cross or letter ex . Saint Andrew is said to have been martyred on such a cross....
in heraldic terminology. The flag of the Solomon IslandsFlag of the Solomon IslandsThe national flag of the Solomon Islands was adopted officially on November 18, 1977. The five main island groups are represented by the five stars. The blue is supposed to represent the surrounding ocean, while the green represents the land...
features this pattern, with its five stars representing the five main island groups in the Solomon IslandsSolomon IslandsSolomon Islands is a sovereign state in Oceania, east of Papua New Guinea, consisting of nearly one thousand islands. It covers a land mass of . The capital, Honiara, is located on the island of Guadalcanal...
. Another instance of this pattern occurs in the flag of the Republic of YucatánRepublic of YucatánThe Republic of Yucatan was a nineteenth century sovereign state during two periods of the century. The first Republic of Yucatan, founded May 29, 1823, joined the Mexican federation as the Federated Republic of Yucatán on December 23, 1823, less than seven months later...
, where it symbolized the five departments into which the republic was divided. - A quincunx is a standard pattern for planting an orchardOrchardAn orchard is an intentional planting of trees or shrubs that is maintained for food production. Orchards comprise fruit or nut-producing trees which are grown for commercial production. Orchards are also sometimes a feature of large gardens, where they serve an aesthetic as well as a productive...
. - Quincunxes are used in modern computer graphicsComputer graphicsComputer graphics are graphics created using computers and, more generally, the representation and manipulation of image data by a computer with help from specialized software and hardware....
as a multisampling pattern for anti-aliasingAnti-aliasingIn digital signal processing, spatial anti-aliasing is the technique of minimizing the distortion artifacts known as aliasing when representing a high-resolution image at a lower resolution...
. 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. - In numerical analysisNumerical analysisNumerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
, the quincunx pattern describes the two-dimensional five-point stencilFive-point stencilIn numerical analysis, given a square grid in one or two dimensions, the five-point stencil of a point in the grid is made up of the point itself together with its four "neighbors"...
, a sampling pattern used to derive finite differenceFinite differenceA finite difference is a mathematical expression of the form f − f. If a finite difference is divided by b − a, one gets a difference quotient...
approximations to derivativeDerivativeIn calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...
s. - In architectureArchitectureArchitecture is both the process and product of planning, designing and construction. Architectural works, in the material form of buildings, are often perceived as cultural and political symbols and as works of art...
, a quincuncial plan, also defined as a "cross-in-squareCross-in-squareThe term cross-in-square or crossed-dome denotes the dominant architectural form of middle- and late-period Byzantine churches. The first cross-in-square churches were probably built in the late 8th century, and the form has remained in use throughout the Orthodox world until the present day...
", is the plan of an edifice composed of nine bays. The central and the four angular ones are covered with domeDomeA dome is a structural element of architecture that resembles the hollow upper half of a sphere. Dome structures made of various materials have a long architectural lineage extending into prehistory....
s or groin vaultGroin vaultA groin vault or groined vault is produced by the intersection at right angles of two barrel vaults. The word groin refers to the edge between the intersecting vaults; cf. ribbed vault. Sometimes the arches of groin vaults are pointed instead of round...
s so that the pattern of these domes forms a quincunx; the other four bays are surmounted by barrel vaultBarrel vaultA barrel vault, also known as a tunnel vault or a wagon vault, is an architectural element formed by the extrusion of a single curve along a given distance. The curves are typically circular in shape, lending a semi-cylindrical appearance to the total design...
s. - A quincunx is one of the quintessential designs of CosmatesqueCosmatesqueCosmatesque, or Cosmati, is a style of geometric decorative inlay stonework typical of Medieval Italy, and especially of Rome and its surroundings. It was used most extensively for the decoration of church floors, but was also used to decorate church walls, pulpits, and bishop's thrones...
inlay stonework. - 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 tattooTattooA tattoo is made by inserting indelible ink into the dermis layer of the skin to change the pigment. Tattoos on humans are a type of body modification, and tattoos on other animals are most commonly used for identification purposes...
is known as the five dots tattooFive Dots TattooThe five dots tattoo is a tattoo of five dots arranged in a quincunx, usually on the outer surface of the hand, between the thumb and the index finger...
. It has been variously interpreted as a fertility symbol, a reminder of sayings on how to treat women or police, a recognition symbol among the Romani people, a group of close friends, standing alone in the world, or time spent in prison (with the outer four dots representing the prison walls and the inner dot representing the prisoner). Thomas EdisonThomas EdisonThomas Alva Edison was an American inventor and businessman. He developed many devices that greatly influenced life around the world, including the phonograph, the motion picture camera, and a long-lasting, practical electric light bulb. In addition, he created the world’s first industrial...
, whose many inventions included a tattooing machine, had this pattern tattooed on his forearm.
Literary symbolism
Various literary works use or refer to the quincunx pattern for its symbolic valueSymbol
A symbol is something which represents an idea, a physical entity or a process but is distinct from it. The purpose of a symbol is to communicate meaning. For example, a red octagon may be a symbol for "STOP". On a map, a picture of a tent might represent a campsite. Numerals are symbols for...
:
- The English physician Sir Thomas BrowneThomas BrowneSir Thomas Browne was an English author of varied works which reveal his wide learning in diverse fields including medicine, religion, science and the esoteric....
in his philosophical discourse The Garden of CyrusThe Garden of CyrusThe Garden of Cyrus or The Quincunciall Lozenge, or Network Plantations of the Ancients, naturally, artificially, mystically considered is a Discourse written by Sir Thomas Browne. It was first published in 1658, along with its diptych companion, Urn-Burial...
(1658) elaborates upon evidence of the quincunx pattern in art, nature and mystically as evidence of "the wisdom of God". - In the first chapter The Rings of SaturnThe rings of saturnThe Rings of Saturn is a novel by W. G. Sebald and was published in English in 1998.The second novel of W. G. Sebald to be translated into English, The Rings of Saturn is the account of the narrator, also named W. G. Sebald, on a walking tour of Suffolk...
W.G. Sebald'sW. G. SebaldW. G. Maximilian Sebald was a German writer and academic. At the time of his death at the age of 57, he was being cited by many literary critics as one of the greatest living authors and had been tipped as a possible future winner of the Nobel Prize in Literature...
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. - James JoyceJames JoyceJames Augustine Aloysius Joyce was an Irish novelist and poet, considered to be one of the most influential writers in the modernist avant-garde of the early 20th century...
uses the term in GraceGrace (short story)"Grace" is a short story by James Joyce published in his 1914 collection Dubliners. According to Stanislaus Joyce, the story is based on Dante's Divine Comedy.-Plot summary:...
, a short story in The DublinersDublinersDubliners is a collection of 15 short stories by James Joyce, first published in 1914. They were meant to be a naturalistic depiction of Irish middle class life in and around Dublin in the early years of the 20th century....
of 1914, to describe the seating arrangement of five men in a church service. Lobner argues that in this context the pattern serves as a symbol both of the wounds of Christ and of the Greek cross. - Lawrence DurrellLawrence DurrellLawrence George Durrell was an expatriate British novelist, poet, dramatist, and travel writer, though he resisted affiliation with Britain and preferred to be considered cosmopolitan...
's novel-sequence The Avignon QuintetThe Avignon QuintetThe Avignon Quintet is a five-volume series of novels by British writer Lawrence Durrell, published between 1974 and 1985. The novels are openly metafictional and reflect the developments in experimental fiction following after Durrell's previous The Alexandria Quartet...
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. - The QuincunxThe QuincunxThe Quincunx is the epic first novel of Charles Palliser. It takes the form of a Dickensian mystery set in early 19th century England, but Palliser has added the modern attributes of an ambiguous ending and unreliable narrators...
(ISBN 0-345-37113-5) is the title of a lengthy and elaborate novel by Charles PalliserCharles PalliserCharles Palliser is a best-selling novelist, American-born but British-based. His most well-known novel, "The Quincunx", has sold over a million copies internationally. He is the elder brother of the late author and freelance journalist Marcus Palliser.-Life and career:Born in New England he is...
set in 19th-century England, published in 1989; the pattern appears in the text as a heraldicHeraldryHeraldry is the profession, study, or art of creating, granting, and blazoning arms and ruling on questions of rank or protocol, as exercised by an officer of arms. Heraldry comes from Anglo-Norman herald, from the Germanic compound harja-waldaz, "army commander"...
device, and is also reflected in the structure of the book. - Séamus HeaneySeamus HeaneySeamus Heaney is an Irish poet, writer and lecturer. He lives in Dublin. Heaney has received the Nobel Prize in Literature , the Golden Wreath of Poetry , T. S. Eliot Prize and two Whitbread prizes...
describes Ireland's provinces together forming a quincunx, as the Irish word for province cúige (literally: "fifth part") also explicates. The five provinces of Ireland are UlsterUlsterUlster is one of the four provinces of Ireland, located in the north of the island. In ancient Ireland, it was one of the fifths ruled by a "king of over-kings" . Following the Norman invasion of Ireland, the ancient kingdoms were shired into a number of counties for administrative and judicial...
(north), LeinsterLeinsterLeinster is one of the Provinces of Ireland situated in the east of Ireland. It comprises the ancient Kingdoms of Mide, Osraige and Leinster. Following the Norman invasion of Ireland, the historic fifths of Leinster and Mide gradually merged, mainly due to the impact of the Pale, which straddled...
(east), ConnachtConnachtConnacht , formerly anglicised as Connaught, is one of the Provinces of Ireland situated in the west of Ireland. In Ancient Ireland, it was one of the fifths ruled by a "king of over-kings" . Following the Norman invasion of Ireland, the ancient kingdoms were shired into a number of counties for...
(west), MunsterMunsterMunster is one of the Provinces of Ireland situated in the south of Ireland. In Ancient Ireland, it was one of the fifths ruled by a "king of over-kings" . Following the Norman invasion of Ireland, the ancient kingdoms were shired into a number of counties for administrative and judicial purposes...
(south) and MeathCounty MeathCounty Meath is a county in Ireland. It is part of the Mid-East Region and is also located in the province of Leinster. It is named after the ancient Kingdom of Mide . Meath County Council is the local authority for the county...
(the center). 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.