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| {{Chinese name|[[Zu (surname)|Zu]]}}
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| [[File:昆山亭林公园祖冲之像.jpg|thumb|right|300px|Statue of Zu Chongzi in Tinglin Park in Kunshan]]
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| '''Zu Chongzhi''' ({{zh|t=祖沖之|s=祖冲之|p=Zǔ Chōngzhī|w='''Tsu Ch'ung-chih'''}}) (429–500), [[courtesy name]] '''Wenyuan''' (文遠), was a prominent [[Chinese people|Chinese]] [[List of mathematicians|mathematician]] and [[List of astronomers|astronomer]] during the [[Liu Song]] and [[Southern Qi]] Dynasties.
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| ==Life and works==
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| Chongzhi's ancestry was from modern [[Baoding|Baoding, Hebei]]. To flee from the ravage 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" ) 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.
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| 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|Zhenjiang, Jiangsu]]), he was engaged in work at the office of the local governor.
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| Zu Chongzhi, along with his son Zu Gengzhi, wrote a mathematical text entitled ''Zhui Shu'' (Method of Interpolation). It is said that the treatise contains formulas for the volume of the sphere, cubic equations and the accurate value of pi. This book didn't survive to the present day; it has been lost since the [[Song Dynasty]].
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| His mathematical achievements included:
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| *the Daming calendar (大明曆) introduced by him in 465 A.D.
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| *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.
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| *calculating one year as 365.24281481 days, which is very close to 365.24219878 days as we know today.
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| *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).
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| *calculating the Jupiter year as about 11.858 Earth years, which is very close to 11.862 as we know of today.
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| *deriving two approximations of [[pi]], (3.1415926538932...) 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 [[Milü|<sup>355</sup>⁄<sub>113</sub>]] (密率, Milü, detailed approximation) and [[Proof that 22/7 exceeds π|<sup>22</sup>⁄<sub>7</sub>]] (約率, Yuelü, rough approximation) being the other notable approximations. He obtained the result by approximating a circle with a 12,288 (= 2<sup>12</sup> × 3) sided polygon. This was an impressive feat for the time, especially considering that the device [[Counting rods]] he used for recording intermediate results were merely a pile of wooden sticks laid out in certain patterns. Japanese mathematician [[Yoshio Mikami]] pointed out, "<math>\tfrac{22}{7}</math> was nothing more than the π value obtained several hundred years earlier by the Greek mathematician [[Archimedes]], however Milu <math>\pi=\tfrac{355}{113}</math> could not be found in any Greek, Indian or Arabian manuscripts, not until 1585 [[Netherlands|Dutch]] mathematician Adriaan Anthoniszoom obtained this fraction; the Chinese possessed this most extraordinary fraction over a whole millennium earlier than Europe". Hence Mikami strongly urged that the fraction <math>\tfrac{355}{113} </math> be named after Zu Chongzhi as Zu Chongzhi fraction.<ref>
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| {{cite book
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| | author = Yoshio Mikami
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| | title = Development of Mathematics in China and Japan
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| | publisher = B. G. Teubner
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| | page = 50
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| | year = 1913
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| | url = http://books.google.com/?id=4e9LAAAAMAAJ&q=intitle:Development+intitle:%22China+and+Japan%22+355&dq=intitle:Development+intitle:%22China+and+Japan%22+355 }}</ref> 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 16600.<ref>The next "best rational approximation" to π is <math>\frac{52163}{16604}=3.1415923874 </math>.</ref>
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| *finding the volume of a sphere as πD<sup>3</sup>/6 where D is diameter (equivalent to 4πr<sup>3</sup>/3</small>).
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| == Astronomy ==
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| Zu was an accomplished astronomer who calculated the values of time with unprecedented precision. His methods of interpolating and the usage of integration is far ahead of his time. Even the astronomer [[Yi Xing]]'s isn't comparable to his value (who 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 were so advanced, the scholars of the Sung dynasty and Indo influence astronomers of the Tang dynasty found it confusing.
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| == Mathematics ==
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| {{Pi box}}
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| The majority of Zu's great mathematical works are recorded in his lost text the ''Zhui Shu''. Most scholars argue about his complexity since traditionally the Chinese had developed mathematics as algebraic and equational. Logically, scholars assume that the ''Zhui Shu'' yields methods of cubic equations. His works on the accurate value of pi describe the lengthy calculations involved. Zu used the [[Liu Hui's π algorithm]] described earlier by [[Liu Hui]] to inscribe a 12,288-gon. Zu's value of pi is precise to six decimal places and for a thousand years thereafter no subsequent mathematician computed a value this precise. Zu also worked on deducing the formula for the volume of a sphere.
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| ==The South Pointing Chariot==
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| 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 (mechanical device)|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 [[magnetic]]s (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:
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| <blockquote>
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| 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.<ref name="needham volume 4 part 2 289">Needham, Volume 4, Part 2, 289.</ref>
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| </blockquote>
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| ==Named after him==
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| * <math> \pi \approx \tfrac{355}{113} </math> as [[Milü|Zu Chongzhi <math>\pi</math> rate]].
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| *The lunar crater [[Tsu Chung-Chi (crater)|Tsu Chung-Chi]]
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| *[[1888 Zu Chong-Zhi]] is the name of [[asteroid]] 1964 VO1.
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| *[[Zuc stream cipher]] is a new encryption algorithm.
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| ==Notes==
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| {{Reflist}}
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| ==References==
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| *Needham, Joseph (1986). ''Science and Civilization in China: Volume 4, Part 2''. Cambridge University Press
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| *Du, Shiran and He, Shaogeng, [http://203.72.198.245/web/Content.asp?ID=43669&Query=1 "Zu Chongzhi"]. ''[[Encyclopedia of China]]'' (Mathematics Edition), 1st ed.
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| ==Further reading==
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| *Needham, Joseph (1986). ''Science and Civilization in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth''. Cambridge University Press
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| ==External links==
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| {{ChineseText}}
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| *[http://www.britannica.com/eb/article-9384156/Zu-Chongzhi Encyclopædia Britannica's description of Zu Chongzhi]
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| *[http://www.chinaculture.org/gb/en_aboutchina/2003-09/24/content_26294.htm Zu Chongzhi at Chinaculture.org]
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| *[http://hua.umf.maine.edu/China/astronomy/tianpage/0014ZuChongzhi9296bw.html Zu Chongzhi at the University of Maine]
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| *{{MacTutor Biography|id=Zu_Chongzhi}}
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| {{Persondata
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| | NAME = Zu, Chongzhi
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION = Chinese mathematician-astronomer
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| | DATE OF BIRTH = 429
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| | PLACE OF BIRTH =
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| | DATE OF DEATH = 500
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| | PLACE OF DEATH =
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| }}
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| {{DEFAULTSORT:Zu, Chongzhi}}
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| [[Category:429 births]]
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| [[Category:500 deaths]]
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| [[Category:Ancient Chinese mathematicians]]
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| [[Category:Ancient Chinese astronomers]]
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| [[Category:5th-century mathematicians]]
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| [[Category:Liu Song writers]]
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| [[Category:Southern Qi politicians]]
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| [[Category:Liu Song politicians]]
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| {{Link GA|zh-classical}}
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