{{Short description|Chinese mathematician and inventor}}
{{pp-move-indef|small=yes}}
{{family name hatnote|[[Qin (surname)|Qin]]|lang=Chinese}}
[[File:Third order equation-Shu-shu-jiu-zhang.jpg|thumb|Third order equation Yi Jia Tang "Six Book Nine Chapters" positive and negative opening power map]]
'''Qin Jiushao''' ({{zh|c=秦九韶|p=Qín Jiǔsháo|w='''Ch'in Chiu-shao'''}}, ca. 1202–1261), [[courtesy name]] '''Daogu''' (道古), was a Chinese mathematician, meteorologist, inventor, politician, and writer of the [[Song dynasty#Southern Song, 1127–1279|Southern Song dynasty]]. He is credited for discovering [[Horner's method]] as well as inventing [[Tianchi basin]]s, a type of rain gauge instrument used to gather meteorological data.<ref>{{Cite book |title=[[Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures]]  |last=Selin |first=Helaine |author-link=Helaine Selin |publisher=Springer |year=2008 |isbn=978-1402045592 |edition=2nd |page=736}}</ref>

== Biography ==
Although Qin Jiushao was born in [[Ziyang, Sichuan]], his family came from [[Shandong]] province. He is regarded as one of the greatest mathematicians in Chinese history. This is especially remarkable because Qin did not devote his life to [[mathematics]]. He was accomplished in many other fields and held a series of bureaucratic positions in several [[Chinese provinces]].

Qin wrote ''Shùshū Jiǔzhāng'' (''[[Mathematical Treatise in Nine Sections]]'') in 1247 CE. This treatise covered a variety of topics including indeterminate equations, and the numerical solution of certain polynomial equations up to the tenth [[degree of a polynomial|degree]]. The treatise addressed [[surveying]] and military matters. Qin included a general form of the [[Chinese remainder theorem]] that used ''Da yan shu'' (大衍术) or [[algorithm]]s to solve it. In geometry, he discovered "Qin Jiushao's formula" for finding the area of a triangle from the given lengths of three sides. This formula is the same as [[Heron's formula]], proved by [[Heron of Alexandria]] about 60 BCE, though knowledge of the formula may go back to [[Archimedes]].

As precipitation was important agriculture and food production, Qin developed  [[rain gauge]]s that were widely used in 1247 during the [[Mongol Empire]]/[[Southern Song dynasty]] to gather meteorological data. Qin Jiushao later records the application of rainfall measurements in the mathematical treatise. The book also discusses the use of large [[snow gauge]]s made from bamboo situated in mountain passes and uplands, which are speculated to be first referenced to snow measurement.<ref>{{Cite book |title=Precipitation: Theory, Measurement and Distribution |last=Strangeways |first=Ian |publisher= Cambridge University Press |year=2011 |isbn=978-0521172929 |publication-date=April 14, 2011 |page=140}}</ref><ref>{{Cite book |title=Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures  |last=Selin |first=Helaine  |publisher=Springer |year=2008 |isbn=978-1402045592 |edition=2nd |publication-date=April 16, 2008 |page=736}}</ref>  
 
Qin recorded the earliest explanation of how [[Chinese calendar]] experts calculated [[astronomy|astronomical]] data according to the timing of the [[Dongzhi (solar term)|winter solstice]]. He also introduced the use of the [[0 (number)|zero symbol]] into written [[Chinese mathematics]]. He developed summation of [[arithmetic series]], in particular the interpretation of a [[polynomial]] as a nested sequence of arbitrary sums and multiples of a given number. This method of polynomial evaluation is now referred to as [[Horner's method]].

After he completed his work on mathematics, he ventured into politics. As a government official he was boastful, corrupt, and was accused of bribery and of poisoning his enemies. As a result, he was relieved of his duties multiple times. Yet in spite of these problems he managed to become very wealthy.<ref>[[Victor J. Katz]] (1993) ''A History of Mathematics: an introduction'', New York</ref>

==References==
{{Reflist|3}}

==Bibliography==
*Guo, Shuchun. ''[[Encyclopedia of China]]'' (Mathematics Volume), 1st ed.
*Qin Jiushao, [https://web.archive.org/web/20050408053452/http://www.math.sfu.ca/histmath/China/13thCenturyAD/Qin.html]. (Chinese History Timeline), 2007.
*Ulrich  Libbrecht: ''Chinese Mathematics in the Thirteenth Century'' (The Shu-Shu-Chiu-Chang of Chin Chiu shao)  Dover Publication {{isbn|0-486-44619-0}}

==External links==
* {{MacTutor Biography|id=Qin_Jiushao}}
*[https://web.archive.org/web/20050408053452/http://www.math.sfu.ca/histmath/China/13thCenturyAD/Qin.html Simon Fraser University biography for "Qin Jiushao"]
{{Song dynasty topics}}
{{Authority control}}

{{DEFAULTSORT:Qin, Jiushao}}
[[Category:1200s births]]
[[Category:1261 deaths]]
[[Category:13th-century Chinese mathematicians]]
[[Category:13th-century Chinese writers]]
[[Category:Chinese inventors]]
[[Category:Chinese meteorologists]]
[[Category:Number theorists]]
[[Category:Politicians from Ziyang]]
[[Category:Scientists from Sichuan]]
[[Category:Song dynasty government officials]]
[[Category:Song dynasty science writers]]
[[Category:Writers from Ziyang]]