Quincunx

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

For the Roman coin denomination, see quincunx (coin).

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, which was symbolized by a quincunx of dots.

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.

The power of the Pythagorean mysteries is based upon a mystical understanding of the mathematical order of the Universe which could be summed up in visual representation of such numbers as the Tetraktys (10) and the Quincunx (5).

:- Robert Graves, The White Goddess

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 sampling pattern for anti-aliasing.
The spots on a playing card with five spots form a quincunx.
In astrology (and less commonly in astronomy), a quincunx is an angle of five-twelfths of a circle, or 150°, between two objects (the Sun, Moon or planets). In astrology this astrological aspect (the term by which specific angles between objects is known) is considered somewhat unfavorable, but less so than the aspects of opposition (180° angle) or square (90° angle).
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.

Books

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 0345371135)is the title of a lengthy and elaborate novel by Charles Palliser set in 19th-century England, published in 1989.

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