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Zu Chongzhi |
Zu Chongzhi (traditional Chinese: 祖沖之; simplified Chinese: 祖冲之; pinyin: Zǔ Chōngzhī; Wade-Giles: Tsu Ch'ung-chih, 429–500), courtesy name Wenyuan (文遠), was a prominent Chinese mathematician and astronomer during the Liu Song and Southern Qi Dynasties.
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Zu Chongzhi's ancestry was from modern Baoding, Hebei. To flee from the ravages of war, Zu's grandfather Zu Chang moved to the Yangtze, as part of the massive population movement during the Eastern Jin. Zu Chang (祖昌) at one point held the position of "Minister of Great Works" (大匠卿) within the Liu Song and was in charge of government construction projects. Zu's father, Zu Shuo (祖朔) also served the court and was greatly respected for his erudition.
Zu was born in Jiankang. His family had historically been involved in astronomy research, and from childhood Zu was exposed to both astronomy and mathematics. When he was only a youth his talent earned him much repute. When Emperor Xiaowu of Liu Song heard of him, he was sent to an Academy, the Hualin Xuesheng (華林學省), and later at the Imperial Nanjing University (Zongmingguan) to perform research. In 461 in Nanxu (today Zhenjiang, Jiangsu), he was engaged in work at the office of the local governor.
Zu Chongzhi, along with his son Zu Gengzhi, wrote a mathematical text entitled Zhui Shu (Method of Interpolation). There is a high possibility of astronomical calculation techniques due to the accuracy of his calendars. It is said that the treatise contains formulas for the volume of the sphere, cubic equations and the accurate value of pi. Sadly, this book didn't survive to the present day, since it has been lost since the Song Dynasty.
His mathematical achievements included:
was nothing more than the π value obtain several hundred years earlier by the Greek mathematician Archimedes,however Milu 
could not be found in any Greek, Indian or Arabian manuscripts, not until 1585 Dutch mathematician Adriaan Anthoniszoom obtained this fraction; the Chinese possessed this most extraodinary fraction over a whole millennium earlier than Europe". Hence Mikami strongly urged that the fraction 
be named after Zu Chongzhi as Zu Chongzhi fraction1. In Chinese literature, this fraction is known as "Zu rate". Zu rate is a best rational approximation to π, and is the closest rational approximation to π from all fractions with denominator less than 166002.Zu was an accomplished astronomer who calculated the values of time to almost pinpoint precision. His methods of interpolating and the usage of integration is far ahead of his time. Even the astronomer's Yi Xing isn't comparable to his value(whom was beginning to utilize foreign knowledge). The Sung dynasty calendar was backwards to the "Northern barbarians" because they were implementing their daily lives with the Da Ming Li. It is said that his methods of calculation was so advance, the scholars of the Sung dynasty and Indo influence astronomers of the Tang dynasty found it confusing.
Most of Zu's great mathematical works, are recorded in his lost text Zhui Shu. Most scholars argue about his complexity. Since traditionally, the Chinese developed mathematics as algebraic, and equational. Logically, scholars assume that his work, Zhui Shu yields methods of cubic equations. His works on the accurate value of pi describes the lengthy calculations. Zu used the method of exhaustion, inscribing a 12,288-gon. Interestingly, Zu's value of pi is precise to 8 decimal places. No mathematician since his time, computed a value this precise until another 1000 years. Zu also worked on deducing the formula for the volume of the sphere.
The South Pointing Chariot device was first invented by the Chinese mechanical engineer Ma Jun (c. 200-265 AD). It was a wheeled vehicle that incorporated an early use of differential gears to operate a fixed figurine that would constantly point south, hence enabling one to accurately measure their directional bearings. This effect was achieved not by magnetics (like in a compass), but through intricate mechanics, the same design that allows equal amounts of torque applied to wheels rotating at different speeds for the modern automobile. After the Three Kingdoms period, the device fell out of use temporarily. However, it was Zu Chongzhi who successfully re-invented it in 478 AD, as described in the texts of the Song Shu (c. 500 AD) and the Nan Chi Shu, with a passage from the latter below:
When Emperor Wu of Liu Song subdued Guanzhong he obtained the south-pointing carriage of Yao Xing, but it was only the shell with no machinery inside. Whenever it moved it had to have a man inside to turn (the figure). In the Sheng-Ming reign period, Gao Di commissioned Zi Zu Chongzhi to reconstruct it according to the ancient rules. He accordingly made new machinery of bronze, which would turn round about without a hitch and indicate the direction with uniformity. Since Ma Jun's time such a thing had not been.3
as Zu Chongzhi π rate.
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