Quincunx

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For Sir Francis Galton's machine for demonstrating the normal distribution named "quincunx", see bean machine.

Five dots forming a quincunx
Five dots forming a quincunx

A quincunx is the arrangement of five units in the pattern corresponding to the five-spot on dice, playing cards, or dominoes. The quincunx is named after the Roman coin of the same name.

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.

Quincunx patterns occur in many contexts:

* A quincunx was the standard tactical formation for elements of a Roman legion.
* 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]
* The spots on the 5th side of a (playing) die form a quincunx.
* 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).
* 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.
* 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.

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.