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Continuing Q week, we come to the quincunx, a geometric pattern in which five units are arranged in an x shape. That concept may have sounded complicated because there were too many letter-based phrases in the sentence, but the quincunx will be instantly familiar as the side of a standard six-sided playing die with five spots on it. The quincunx takes its distinctive name from an ancient coin of the Roman Republic from the second century BC. The little coin was worth 5/12th of an “as”–the standard bronze Republican coin of the time (which makes me glad I did not have to make change for buyers of that period).
The quincunx shape was popular with the Romans, who were inclined to numerological superstition, and subsequently, during the middle-ages, the shape found its way into many heraldic representations.
Beyond its use in money, logos, and coats-of-arms, the quincunx shape has long been used for fruit orchards. To quote the Hegarty Webber Partnership, a website created by British garden designers with an eye for history:
Thomas Browne, in his Garden of Cyrus of 1658, claimed that the Persian King Cyrus was the first to plant trees in a quincunx. He also claimed to have discovered that it also appeared in the Hanging Gardens of Babylon. Seventeenth century diarist and garden guru Sir John Evelyn also thought it was the best way to lay out apple and pear trees.
The classical Persian precedent may be doubtful, but the quincunx is a wonderful way to lay out trees. As can be seen in the illustration below, such a staggered arrangement not only creates regular parallel rows (as would a normal four by four arrangement) but additionally creates regular diagonal rows. A visitor to such an orchard would see a regular row whichever way she looked. Such layouts create the illusion of more space (since we are used to rows which are perpendicular to each other) but they make it easy for orchard-goers to mistakenly turn down diagonal rows and become lost.
Finally, and most bafflingly, the quincunx is the underlying concept for a 2 dimensional square projection of a 3 dimensional spherical space. Since a sphere represents an entire 3 dimensional frame of vision for a viewer in the center, such quincuncial projections show all aspects of a scene: above, below, side-to-side, in-front, and behind. An entire field of vision can thereby be distorted into a square. To better illustrate this concept, here is a quincuncial projections of the unusual octagonal (gothic!) crossing of Ely Cathedral in Cambridgeshire, England.
A stained glass sky-light window is immediately above the viewer and thus at the center of the composition. The floor is the grey border around the edges. The entrance door is at the top of the composition (upside down) while the central knave stretches upward from the bottom of the picture. The north and south trancepts stretch off to the left and right. Finally, since Ely cathedral is octagonal, there are 4 additional doors running along the diagonals of the composition. There! I’m glad to have cleared that up, now I’m going to go have a drink and clear my head. If you are really ready to go on a dimension warping trip into the world of panoramic photography, here is a link to other quincuncial projections. Good luck on the other side of the looking glass!