Zu Chongzhi

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Zu Chongzhi (429–500), courtesy name Wenyuan (文遠), was a prominent Chinese mathematician and astronomer during the Liu Song and Southern Qi Dynasties.

Life and works

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.

Zhui Shu

Zu Chongzhi, along with his son Zu Gengzhi written a mathematical text entitled Zhui Shu (Method of Interpolation). There is a high possibility of advance astronomical calculation techniques due to the accuracies of his calendars. It is said that the treatise contains formulas for advance linear algebra, quadratic 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:

the Daming calendar (大明曆) introduced by him in 465.
distinguishing the Sidereal Year and the Tropical Year, and he measured 45 years and 11 months per degree between those two, and today we know the difference is 70.7 years per degree.
calculating one year as 365.24281481 days, which is very close to 365.24219878 days as we know today.
calculating the number of overlaps between sun and moon as 27.21223, which is very close to 27.21222 as we know today; using this number he successfully predicted an eclipse four times during 23 years (from 436 to 459).
calculating the Jupiter year as about 11.858 Earth years, which is very close to 11.862 as we know of today.
deriving two approximations of pi, which held as the most accurate approximation for π for over nine hundred years. His best approximation was between 3.1415926 and 3.1415927, with ³⁵⁵⁄₁₁₃ (密率, Milu, detailed approximation) and ²²⁄₇ (約率, Yuelu, rough approximation) being the other notable approximations. He obtained the result by approximating a circle with a 12,288 (= 2¹¹ × 6) sided polygon. This was an impressive feat for the time, especially considering that the only device he used for recording intermediate results were merely a pile of wooden sticks laid out in certain patterns. No one discovered more of pi until 900 years later.
finding the volume of a sphere as 4πr³/3, where r is radius.
discovering the Cavalieri's principle, 1000 years before Bonaventura Cavalieri in the West.

The South Pointing Chariot

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 fo 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.

Named for him

The lunar crater Tsu Chung-Chi
1888 Zu Chong-Zhi is the name of asteroid 1964 VO1.

Notes

References

Needham, Joseph (1986). Science and Civilization in China: Volume 4, Part 2. Taipei: Caves Books, Ltd.
Du, Shiran and He, Shaogeng, "Zu Chongzhi" Encyclopedia of China (Mathematics Edition), 1st ed.

External links

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Last updated on Sunday February 24, 2008 at 11:53:04 PST (GMT -0800)
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