With the exception of some everyday terms like triangle and square, the majority of the proper names for geometric shapes – like pentagon, hexagon and octagon – are formed from compounds of Ancient Greek roots. In most cases, these names tend to follow the same pattern: the first part of the name is numerical, indicating the number of angles (and therefore sides) that the shape contains, whilst the second, the familiar -gon suffix, is a derivative of the Greek word for ‘corner’, gonia. This system can ultimately be used to create the names of an infinite number of shapes, from the smaller fifteen-sided pentadecagon (from pentekaideka, ‘fifteen’) and twenty-sided icosagon (eikosa, ‘twenty’) to the hundred-sided hectogon (hekaton, ‘hundred’) and thousand-sided chiliagon (khilioi, ‘thousand’). Only a handful of these names ever make their way into dictionaries, however, as not all of them are of equal interest to mathematical study and, as the number of sides a shape increases, the more outlandish its name tends to be – a ninety-nine-sided shape, for instance, would be an enneacontakaienneagon.
Amphigory, or amphigouri, is an unusual literary term for senseless or burlesque writing, or else a work of nonsense verse. Borrowed from French in the early nineteenth century, the word is believed to be formed from the Greek prefix amphi-, meaning ‘both’ or ‘around’ (as in amphibian, a creature able to live both on land and in water), and gyros, the Greek word for ‘circle’. If this were correct, amphigory would imply some sense of ‘going around the circle’, perhaps inferring that any attempt to understand such nonsensical writing is pointless and you will likely end up back where you started.
Cadre is the French word for a picture frame or supporting framework, a sense that underpins most of the word’s different uses in English. First recorded in the early nineteenth century as simply another word for a frame or structure, in the 1850s cadre gained a military association, referring to the basic framework of troops in a regiment, and a more specific use in the 1930s to describe a communist cell or faction. Borrowed directly from French into English, the word is descended from the Latin word quadrum, meaning ‘square’.
The first recorded use of the word circus in its most familiar sense of a circular arena for acrobats, clowns and other entertainers dates from 1791 in English, although throughout its history the word has also been used to refer to a bullring (1810s); a circular or semi-circular row of houses (1710s); a group of performing aircraft (1910s); and a riot or noisy uproar, a colloquial sense first used by Mark Twain in his 1869 travelogue Innocents Abroad. Originally, however, a circus was a large Roman amphitheatre used for spectacular public performances, exhibitions, races and other entertainments, of which Rome’s Circus Maximus was the largest and grandest example. Circus is the Latin word for ‘circle’, as such buildings were typically circular in shape to allow for the best all-round views from the crowd.
The familiar triangular shape of the upper-case letter delta (Δ), the fourth letter of the Greek alphabet, has ultimately led to its name being used metaphorically to refer to the triangular-shaped mouth of a river, a sense which at its earliest was used specifically to describe the mouth of the river Nile in the mid-sixteenth century. Delta is also the root of several other English words of a similar vein, including deltoid, a large triangular muscle found in the shoulder, and deltidium, the name for a small triangular space formed at the hinge of brachiopod shells.
Gyros, an Ancient Greek word for a circle or ring, is the origin of a number of English words including gyroscope, gyrate, and both dextrogyrate and sinistrogyrate, meaning ‘turning to the right’ and ‘turning to the left’ respectively. Gyromancy, meanwhile, is the name of an unusual form of divination dating from the sixteenth century in English, in which a person would walk around a circle of letters or symbols until they became dizzy and stumbled, with some significance then drawn from the point on the circle at which they fell.
The adjective quadratic is perhaps most familiar in English as the name of a type of algebraic equation, typically of the form ax2 + bx + c = 0, in which x is an unknown and a, b and c are constants. Quadratic equations like this only ever deal with the second degree or ‘square’ of an unknown quantity – so x2 is a quadratic form whereas x3 (cubic) and x4 (quartic) are not. The word is derived from the Latin for ‘square’, quadratus, and indeed on its first appearance in the language in the mid-seventeenth century, the adjective quadratic was used simply to describe things that are square or quadrangular in shape.
Both familiar uses of the word quarry – one describing the prey of a hunt and the other a large, open stone-works – date from the fourteenth century in English, but are derived from entirely different sources. In terms of hunting, quarry is descended from a Middle English word, quirre, used for the entrails of an animal which would be given to hounds as a reward for their hunt, which is ultimately descended from an Old French word, cuir, for the skin or hide of an animal. In reference to a stone-works, however, quarry is derived from its Latin equivalent quarreria or quadraria, which literally described a place where stones were ‘squared’ ready for use. In this context, quarry is descended from the Latin word for ‘square’, quadrus.
The word squadron first appeared in the English language in the mid-sixteenth century and is believed to have been adapted from its Italian equivalent squadrone, which is a derivative of the Italian word for ‘square’, squadra. Initially, squadron referred to a small group of soldiers arranged in a square formation, but this specific use of the word has since been lost and the term has been used from the late 1570s onwards in English to refer simply to any small party or block of troops.
Dating from the late eighteenth century, the verb tessellate essentially means to ‘make a mosaic’, with the related noun tessellation dating back to the mid-seventeenth century to describe a pattern or mosaic-like design comprised of a close-fitting arrangement of individual shapes. The word is derived from tessella, a diminutive of the earlier Latin term tessera, which was variously used to refer to a small square tile or counter, a six-sided die or, more specifically, to a small square or cube of wood or stone such as that which would be used to make a mosaic.
First introduced in 1914, the yuan is the principal unit of currency of the People’s Republic of China and has been used as the basis of the country’s so-called renminbi currency system since it was established in 1948. Divided into ten jiao, and in turn into a hundred fen, the name yuan means literally ‘circle’ or ‘round’ in Chinese, and is also the origin of the Japanese yen.