Zu Chongzhi Calculates Pi

Zu Chongzhi (429–500), courtesy name Wenyuan, from Qiu county in Fanyang (present-day Laishui, Hebei), lived under the Southern Song and Qi and was an outstanding scientist who made major achievements in mathematics, astronomy and the calendar, and machine building. He was rigorous in study and never followed the ancients blindly. Pi is the ratio of a circle's circumference to its diameter, an important problem in mathematics. Ancient China first used “circumference three, diameter one,” that is, pi as 3. Liu Hui of Wei in the Three Kingdoms devised the “circle-cutting method,” using regular polygons inscribed in a circle to approach its area step by step, a method containing the idea of limits, and obtained pi of about 3.1416. Building on Liu Hui, Zu Chongzhi, through repeated painstaking calculation, fixed pi to the seventh decimal place, between 3.1415926 and 3.1415927, a result that led the world for nearly a thousand years until the Arab mathematician al-Kashi surpassed it in the 15th century. Zu Chongzhi also proposed 355/113 (the “close ratio”) and 22/7 (the “approximate ratio”) as approximations of pi, and later generations call 355/113 “Zu's ratio.” His mathematical classic Zhui Shu, written with his son Zu Geng, was made a main textbook for mathematics at the Tang Imperial Academy and was lost after the Song. In astronomy and the calendar, Zu Chongzhi compiled the Daming Calendar, the first to introduce precession into a calendar, making it more precise; it was issued ten years after his death. In his honor, Purple Mountain Observatory named an asteroid it discovered “Zu Chongzhi,” and a crater on the far side of the Moon also bears his name.