Editing Zu Chongzhi (section)

==Life and works==
{{more citations needed section |date=October 2018}}
Chongzhi's ancestry was from modern [[Baoding]], Hebei.<ref>(祖冲之字文远，范阳蓟人也。) ''Nan Qi Shu'', vol.52</ref> 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 ({{lang|zh-hant|祖昌}}) at one point held the position of Chief Minister for the Palace Buildings ({{lang|zh-hant|大匠卿}}) within the Liu Song<ref>(祖昌，宋大匠卿。) ''Nan Qi Shu'', vol.52 and '' Nan Shi'', vol.72</ref> and was in charge of government construction projects. Zu's father, Zu Shuozhi ({{lang|zh-hant|祖朔之}}), also served the court and was greatly respected for his erudition.

Zu was born in [[Jiankang]]. His family had historically been involved in astronomical research, and from childhood Zu was exposed to both astronomy and mathematics. When he was only a youth, his talent earned him much repute.<ref>(沖之稽古，有机思，...) ''Nan Shi'', vol.72</ref>  When [[Emperor Xiaowu of Song]] heard of him, he was sent to the Hualin Xuesheng ({{lang|zh-hant|華林學省}}) academy, and later 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. In 464, Zu moved to Louxian (today Songjiang district, Shanghai), there, he compiled the Daming calendar and calculated π.

Zu Chongzhi, along with his son [[Zu Gengzhi]], wrote a mathematical text entitled ''Zhui Shu'' ({{lang|zh-hant|綴述}}; "''Methods for Interpolation''").  It is said that the treatise contained formulas for the volume of a sphere, cubic equations and an accurate value of [[pi]].<ref>{{ cite book | last= Ho | first=Peng Yoke| author-mask=[[Ho Peng Yoke]] | title= Li, Qi & Shu: An Introduction to Science & Civilization in China |publisher=Hong Kong University Press | orig-date=1985|edition=University of Washington Press |date=1987| isbn= 9780295963624 |page= 76 | oclc=17656687 }}</ref> This book has been lost since the [[Song dynasty]].

His mathematical achievements included
*the ''Daming'' calendar ({{lang|zh-hant|大明曆}}) introduced by him in 465.
*distinguishing the [[sidereal year]] and the [[tropical year]]. He measured 45 years and 11 months per degree between those two; 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 [[Lunar_month#Draconic_month|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 π|approximations of pi]], (3.1415926535897932...) which held as the most accurate approximation for {{pi}} for over nine hundred years. His best approximation was between 3.1415926 and 3.1415927, with [[Milü|{{sfrac|355|113}}]] ({{lang|zh-hant|密率}}, [[milü]], close ratio) and [[Proof that 22/7 exceeds π|{{sfrac|22|7}}]] ({{lang|zh-hant|約率}}, yuelü, approximate ratio) being the other notable approximations. He obtained the result by approximating a circle with a 24,576 (= 2<sup>13</sup> × 3) sided polygon.<ref>{{Cite news |last=Strogatz |first=Steven |date=2024-03-07 |title=Pi Day: How One Irrational Number Made Us Modern |url=https://www.nytimes.com/article/pi-day-math-geometry-infinity.html |access-date=2024-03-15 |work=The New York Times |language=en-US |issn=0362-4331}}</ref> This was an impressive feat for the time, especially considering that the [[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, "{{sfrac|22|7}} was nothing more than the {{pi}} value obtained several hundred years earlier by the Greek mathematician [[Archimedes]], however milü {{pi}} = {{sfrac|355|113}} could not be found in any Greek, Indian or Arabian manuscripts, not until 1585 [[Netherlands|Dutch]] mathematician [[Adriaan Anthonisz|Adriaan Anthoniszoon]] obtained this fraction; the Chinese possessed this most extraordinary fraction over a whole millennium earlier than Europe". Hence Mikami strongly urged that the fraction {{sfrac|355|113}} be named after Zu Chongzhi as ''Zu's fraction''.<ref>
{{cite book
 | author = Yoshio Mikami
 | title = Development of Mathematics in China and Japan
 | publisher = B. G. Teubner
 | page = 50
 | year = 1913
 | url = https://books.google.com/books?id=4e9LAAAAMAAJ&q=intitle:Development+intitle:%22China+and+Japan%22+355 }}</ref> In Chinese literature, this fraction is known as "Zu's ratio". Zu's ratio is a [[best rational approximation]] to {{pi}}, and is the closest rational approximation to {{pi}} from all fractions with denominator less than 16600.<ref>The next "best rational approximation" to {{pi}} is {{sfrac|52163|16604}} = 3.1415923874.</ref>
*finding the volume of a [[sphere]] as {{pi}}D<sup>3</sup>/6 where D is diameter (equivalent to 4/3{{pi}}r<sup>3</sup>).