Pi π

Pi is the sixteenth Greek letter, from Phoenician pe ('mouth'); its value is 80. In the numeral series the next value, 90, belonged to the obsolete letter koppa. Pi's fame is modern and mathematical: since the eighteenth century it has denoted the ratio of a circle's circumference to its diameter, a usage popularised after William Jones and Leonhard Euler; this is a modern convention, not an ancient mystical meaning.

The Greek letters doubled as numerals in the Milesian (alphabetic) system, in which each letter carried a fixed value; the practice of summing a word's letters into a number, called isopsephy, is the Greek counterpart of Hebrew gematria and appears in inscriptions, the Greek Magical Papyri and early Christian texts. Pi's Phoenician ancestry places it in a borrowing whose exact point of contact, somewhere among Al Mina, Cyprus, Crete and Euboea in the Aegean world, is still disputed, though the borrowing itself, conventionally dated to around the 8th century BCE, is agreed to be the ancestor of every European alphabet still in use, including the Latin one covered elsewhere in this atlas.

The Greeks' own contribution was to give vowels dedicated letters of their own, something the consonant-only Phoenician script never did. Its isopsephy value of 80 belongs to the Milesian alphabetic numeral system, which also needed three further, otherwise obsolete letters, digamma (also called stigma), koppa and sampi, to cover every value from 1 up to 900; none of the three survives among the 24 letters in ordinary use today.

Pi is almost certainly the Greek letter with the widest general recognition in the modern world, entirely because of a single mathematical constant: the ratio of a circle's circumference to its diameter, an irrational number beginning 3.14159, which the Welsh mathematician William Jones first denoted with the letter pi in 1706, a choice popularised and cemented by Leonhard Euler's later use of the same symbol through the 18th century. The choice of pi is thought to echo the Greek word perimetros, perimeter, rather than any of the letter's ancient meanings covered elsewhere in this atlas.

The constant's cultural reach now extends well beyond mathematics: Pi Day, an informal international observance held on March 14, chosen because that date is written 3/14 in the month-day format common in the United States, has been marked since 1988 and was formally recognised by the United States House of Representatives in 2009. In computer science, pi notation, written with a capital Pi, denotes a product of a sequence of terms, paralleling the summation notation built on sigma, discussed elsewhere in this atlas, and physicists use pi extensively throughout equations describing waves, circles and periodic motion.