The 17

The polygon Gauss could draw — the constructible 17-gon Mathematics

For two thousand years geometers could construct a few regular polygons with nothing but an unmarked straightedge and a compass — the triangle, square, pentagon, hexagon — and no new one had been added since the ancient Greeks. Then in 1796 a nineteen-year-old named Carl Friedrich Gauss proved that the regular heptadecagon, the 17-sided polygon, could be constructed too. The key was that 17 is a Fermat prime — a prime of the form 2^2ⁿ + 1 (here 2⁴ + 1) — and Gauss showed exactly those primes give constructible polygons.

The discovery is said to have decided Gauss on a life in mathematics, and he asked for a 17-gon to be carved on his gravestone. (The mason demurred, saying it would look like a circle.) It is a sharp contrast with the rest of this record: 11 and 13 are primes whose polygons cannot be drawn — but 17 can.

Seventeen fundamental particles — the whole of matter Physics

Everything in the universe that physics has ever detected is built from a roster of exactly 17 fundamental particles — the Standard Model. There are twelve matter particles (six quarks and six leptons, the twelve fermions), four force-carriers (the photon of electromagnetism, the gluon of the strong force, and the W and Z of the weak force), and one more that stands apart: the Higgs boson, found at last in 2012, which gives the others their mass. Twelve plus four plus one makes 17.

That short list — 17 particles — accounts for all ordinary matter and three of the four forces of nature. It is one of the most compressed facts in all of science: the entire material world, from a neutron star to a nerve cell, assembled from just 17 kinds of thing.

The seventeen-year cicada — a prime-numbered life Life

In the forests of eastern North America live the strangest insects on the continent: the periodical cicadas, which spend either 13 or 17 years underground as nymphs and then emerge, all at once, in their millions, to sing and breed and die in a few weeks. The 17-year cicada (Magicicada septendecim) keeps time with astonishing precision, and biologists think the number is no accident: 17 is prime.

A life cycle of a prime number of years is very hard for a predator or parasite — which tend to run on shorter 2-, 3- or 4-year rhythms — to synchronise with. A predator peaking every few years can almost never line up with a brood that appears only every 17. The same logic explains why the only two periodical cicada cycles known are 17 and 13 — the two primes just large enough to outrun the things that would eat them.

Seventeen syllables — the whole of a haiku Literature

The classical Japanese haiku is built on 17 — three phrases of five, seven and five sound-units (on) totalling 17. In that tiny fixed span a haiku is meant to catch a single season, a single moment: a frog, a pond, the splash. It is very nearly the shortest fixed poetic form in world literature, and its whole discipline is to say something complete inside just 17 beats.

The count is a feature of the Japanese language's rhythm, and it travels imperfectly — English “syllables” are not quite the same as Japanese on — but the number holds as the form's signature the world over: 17, and not one more.

Chlorine, element 17 — salt, bleach, and clean water ChemistryLife

Chlorine sits at atomic number 17, a hungry green-yellow halogen one electron short of a full shell — which is why it grabs so fiercely at other atoms. Handed a sodium atom, it makes ordinary table salt; loosed as a gas it is deadly (it was the first chemical weapon of the First World War); tamed in tiny doses it is one of the great life-savers of history. The chlorination of drinking water, begun in the early 1900s, did more to lengthen human lifespans than almost any drug, by killing the microbes that cause cholera and typhoid.

Element 17 is everywhere in daily life: in household bleach, in the hydrochloric acid your own stomach makes to digest food, and in the PVC of pipes and packaging. A single reactive number doing the work of preservation and poison alike.

Seventeen columns down the flank of the Parthenon Culture

The Parthenon in Athens follows a strict rule of classical proportion: a Doric temple sets twice as many columns plus one along its long sides as across its front. With eight columns on each end, that makes 17 columns running down each flank (counting the shared corners). Walk beside the temple and you pass a colonnade of 17 — the number built into the most famous silhouette of the ancient world, a quiet piece of arithmetic holding up the marble.