- For Sir Francis Galton's machine for demonstrating the normal distribution named "quincunx", see bean machine.
A quincunx (IPA ['kwɪnkʌŋks]) is the arrangement of five units in the pattern corresponding to the five-spot on dice, playing cards, or dominoes. The quincunx was originally a coin issued by the Roman Republic c.211-200 BC, whose value was five twelfths (quinque + 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. Typically, a modern quincunx consists of five objects arranged in a square, with one object at each of the square's four corners and the fifth in the square's center. If the four corner objects form a rectangle, the pattern is still considered a quincunx.
The significance of the quincunx pattern originates in Pythagorean mathematical mysticism. This pattern lies at the heart of the Pythagorean tetraktys, a pyramid of ten dots. To the Pythagoreans the number five held particular significance and the quincunx pattern represented this significance.citation needed
Examples
Quincunx patterns occur in many contexts:
- A quincunx is a standard pattern for planting an orchard, especially in France.
- Quincunxes are used in modern computer graphics as a supersampling pattern for 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. [1]
- In astrology (and less commonly in astronomy), a quincunx (also known as an inconjunct) is an astrological aspect of five-twelfths of a circle, or 150°, between two objects (the Sun, Moon, planets or signs).
- In architecture, a quincuncial plan, also defined as a "cross inscribed in a square", is the plan of an edifice composed of nine bays. The central and the four angular ones are covered with domes or groin vaults; the other four are surmounted by barrel vaults.
- Initial cards are laid out in a quincunx in the eponymous card game Quincunx.
 The spots on the 5th side of a (playing) die form a quincunx. |
 The points on each face of a unit cell of a face-centred cubic lattice form a quincunx. |
 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. |
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 Bodrum Mosque in Istanbul, a typical example of building with a quincuncial plan. |
 The flag of the Solomon Islands features a quincunx of stars. |
In literature
- The English physician Sir Thomas Browne in his philosophical discourse The Garden of Cyrus (1658) elaborates upon evidence of the quincunx pattern in art, nature and mystically as 'evidence' of intelligent design.
- The Quincunx (ISBN 0-345-37113-5) is the title of a lengthy and elaborate novel by Charles Palliser set in 19th-century England, published in 1989.
- The Quincunx is the name of the lake with an island containing Mistress Masham's Repose in the novel of that name by T. H. White.
- 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.
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