The Elamite Formula for The Area of a Regular Heptagon

Abstract: In this article, we study the inscription on the reverse of Susa Mathematical Text No.\,2, a clay tablet held in the collection of the Louvre Museum and thought to date from between 1894--1595 BC. We focus on the formula given in this text for the approximate area of a regular heptagon. We give a geometric explanation for the formula and show that this approximation is more accurate than other contemporaneous formulas in Babylonian mathematics and even that of Greek mathematician Heron who proved it almost 1800 years later. We also consider the possible ways the Susa scribes might have applied this formula to construct the regular heptagon for inscription on a clay tablet.