Zu Chongzhi and the Chinese Calendar Reform of 462 AD



Zu Chongzhi (429-500 AD) is one of the most famous ancient Chinese mathematicians in both China and the Western world, but his contributions in the field of astronomy are largely ignored outside Asia, partly due to ignorance of the Chinese system of astronomy. This project seeks to address that gap in understanding, and also to explore the interesting question of whether Zu Chongzhi’s achievements, while under-rated in the West, might also be over-rated in his own homeland.

First of all, a description of Zu’s life and work will be necessary. Zu Chongzhi was born in a family with a tradition of scholarship and scientific research. The Zu clan had their ancestral home in Fanyang, to the southwest of what is now Beijing. During the barbarian rebellion of the early 300s (more of which will be spoken in the next section), however, they were forced to flee south across the Yangzi River and settle in the new southern capital of Jiankang (present-day Nanjing). Chongzhi’s grandfather Zu Chang was himself a skilled engineer and inventor who held the post of Minister of Construction (Da Jiang Qing) in the imperial court. His father Zu Shuozhi held the post of Minister by Appointment (Feng Chao Qing), somewhat equivalent to a technical consultant.

From his youth, Zu Chongzhi had a keen interest in mathematics and astronomy. His inquiring nature led him to read widely into scientific works both old and new, but always with a critical and analytical eye. In his 20s, he was appointed by the reigning emperor Liu Jun to serve in the Imperial Institute (Hualin Xueshen), the largest research body within the state. During this time, based on the work of previous experts from the Han and Wei Dynasties, he derived the most refined and accurate value for ð in the world up to that time – between 3.1415926 and 3.1415927. This value, correct to 7 decimal places, was far more exact than the previous value of 3.14 derived by Liu Hui in the Wei Dynasty, and in fact was not surpassed until the 15th century, when a value to 17 decimal places was obtained.

Zu Chongzhi was later posted out of the capital, as a staff officer to the governor of the province of South Xuzhou, based in Jingkou (present-day Zhenjiang). While holding this post, he researched into the workings of the Yuanjia calendar which had been in use since 443, discovered its flaws, and privately formulated a new calendar to replace it. Upon its completion in 462, he submitted it to the imperial court. However, due to political reasons (which will be explained in Sections 5 and 6), it did not come into use until the year 510. By then, Zu Chongzhi had been dead for10 years.

Zu Chongzhi was a man of many talents. Besides his work in astronomy and mathematics, he was said to be a master of court music and the mathematical games ‘Bo’ and ‘Sai’. He also engaged in several feats of engineering and invention in his later life. From his post in South Xuzhou, he was promoted first to magistrate of the county of Louxian, and then to Executive Secretary of Protocol (Yezhe Pushe) at the imperial court. Then, in 478, the powerful Grand Marshal Xiao Daocheng (who usurped the throne the next year) commissioned Zu to reconstruct the famous “south pointing” chariot (Zhinan Che) which had last been built by the genius inventor Ma Jun in the Wei Dynasty, 250 years ago. This chariot incorporated the figure of a man, arm outstretched, who would rotate to point south no matter which direction the chariot faced. However, the relevant technology for building it (said by modern researchers to involve advanced differential gears) had been lost in the tumultuous years since the Wei. Zu Chongzhi succeeded in this task, but a traveling “expert” from the North, named Suo Yulin, then claimed to also know how to construct such a chariot. The emperor therefore held a demonstration for both chariots in the Imperial Gardens, whereupon Suo’s chariot proved much inferior and was confiscated and burnt.


Introduction to Chinese Calendar - How the astronomers developed it

The Mathematics of the Chinese Calendar

Chinese Calendar - History and Traditions

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✍: Yang Shao-yun, et al.

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