Zu Chongzhi presents the Daming calendar

Zu Chongzhi (429–500) came from a family of officials that had moved south of the Yangtze during the Eastern Jin; Emperor Xiaowu of the Liu Song appointed him to the Hualin academy and granted him a house and a carriage. In the sixth year of the Daming era, 462, while an assistant in the administration of South Xu province, he submitted a memorial with a new calendar. The official calendar of He Chengtian, he wrote, already erred by three degrees in the positions of the sun and moon and by almost a day in the solstices, and put the appearances of the planets up to forty days out. His two main changes were to replace the ancient cycle of seven leap months in nineteen years, which drifted by a day every two hundred years, with 144 leap months in 391 years, and to allow for the slow shift of the winter solstice against the stars — the precession of the equinoxes. His tropical year of 365.24281481 days is within about a minute of the modern value.

Few people at court understood calendrical science. The emperor’s powerful favourite Dai Faxing objected, condemning the new system as a violation of the principles of the ancients, and, the Song shu says, the others in the debate sided with him; Zu answered him point by point, and only the secretary Chao Shangzhi supported him. According to the Nan Qi shu, the court experts could not refute Zu. In 464 Emperor Xiaowu, who “loved the unusual and admired antiquity”, decided to adopt the calendar together with the next year’s new era name, but he died before it could be introduced, and a later attempt under the Southern Qi also came to nothing. The calendar came into use only in 510, under the Liang, ten years after Zu’s death (Book of Sui); the English Wikipedia’s date of 465 contradicts the Song shu and the Nan Qi shu.

Zu Chongzhi is best known for π. The Book of Sui records that at the end of the Song he found π to lie between 3.1415926 and 3.1415927, surpassing the values of earlier scholars from Liu Xin and Zhang Heng to Liu Hui, and proposed two fractions: the “close ratio” 355/113, accurate to six decimal places, and the “approximate ratio” 22/7. His methods were set out in the Zhui shu, which the officials of the academy, the Book of Sui says, could not fathom and so neglected; the book is lost. No more precise value of π was computed for about nine centuries. With his son Zu Gengzhi he also found the volume of the sphere, and he rebuilt the south-pointing carriage (478) and built water-powered trip hammers (488).