Delta δ

Delta is the fourth Greek letter, from Phoenician daleth ('door'); its value is 4. Its triangular capital form gave its name to river deltas (Herodotus so described the mouths of the Nile) and, in modern mathematics and science, to the symbol for change or difference. This geometric symbolism is genuine and well attested, though the mathematical usage is modern.

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. Delta'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 4 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.

Delta's best-known modern use has classical roots of its own, distinct from the alphabet's numerical and scriptural history covered elsewhere in this atlas: the historian Herodotus, writing in the 5th century BCE, described the triangular landform where the Nile splits into channels before reaching the sea as shaped like the letter delta, and geographers have called any such landform a river delta ever since, making delta one of the few Greek letters to lend its name to a geological feature well before the modern scientific era.

In mathematics and the sciences more broadly, an uppercase delta denotes a change or difference between two values, as in a temperature difference or a change in a variable across an equation, a convention formalised in the 18th and 19th centuries alongside the rise of calculus; the related epsilon-delta definition of a mathematical limit, developed by Augustin-Louis Cauchy and Karl Weierstrass in the 19th century, pairs delta with epsilon in one of the most widely taught proofs in calculus. During the covid-19 pandemic, the World Health Organization's 2021 system for naming virus variants after Greek letters made Delta the public name for the B.1.617.2 lineage, a use with no connection to any of the letter's older meanings.