Qin Jiushao (, ca. 1202–1261), courtesy name Daogu (道古), was a Chinese mathematician, meteorologist, inventor, politician, and writer. He is credited for discovering Horner's method as well as inventing

Tianchi basin Tianchi basins were meteorological measuring instruments used to gather and measure the amount of liquid precipitation over a period of time during the Song Dynasty. The instrument was devised by the Song Chinese mathematician and inventor Qin Ji ...

s, a type of rain gauge instrument used to gather meteorological data.

Biography

Although Qin Jiushao was born in

Ziyang, Sichuan Ziyang () prefecture-level city in eastern Sichuan province, China. It is bordered by the provincial capital of Chengdu to the northwest, Deyang to the north, Suining to the northeast, Chongqing municipality to the east, and Neijiang to the west ...

, his family came from

Shandong Shandong ( , ; ; alternately romanized as Shantung) is a coastal province of the People's Republic of China and is part of the East China region. Shandong has played a major role in Chinese history since the beginning of Chinese civilizati ...

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 Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern 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 10th order, as well as discussions on military matters and surveying. In the treatise Qin included a general form of the

Chinese remainder theorem In mathematics, the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer ''n'' by several integers, then one can determine uniquely the remainder of the division of ''n'' by the product of thes ...

that used ''Da yan shu'' (大衍术) or algorithms 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 Archimedes of Syracuse (;; ) was a Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scientists ...

. As precipitation was important agriculture and food production, Qin developed precipitation gauges that was widely used in 1247 during the

Southern Song dynasty The Song dynasty (; ; 960–1279) was an imperial dynasty of China that began in 960 and lasted until 1279. The dynasty was founded by Emperor Taizu of Song following his usurpation of the throne of the Later Zhou. The Song conquered the rest ...

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 gauges made from bamboo situated in mountain passes and uplands which are speculated to be first referenced to snow measurement. Qin recorded the earliest explanation of how

Chinese calendar The traditional Chinese calendar (also known as the Agricultural Calendar ��曆; 农历; ''Nónglì''; 'farming calendar' Former Calendar ��曆; 旧历; ''Jiùlì'' Traditional Calendar ��曆; 老历; ''Lǎolì'', is a lunisolar calendar ...

experts calculated astronomical data according to the timing of the winter solstice. Among his accomplishments are the introduction techniques for solving certain types of algebraic

equation In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for example, in ...

s using a numerical algorithm (equivalent to the 19th century Horner's method) and for finding

sums In mathematics, summation is the addition of a sequence of any kind of numbers, called ''addends'' or ''summands''; the result is their ''sum'' or ''total''. Beside numbers, other types of values can be summed as well: function (mathematics), fu ...

of arithmetic series. He also introduced the use of the zero symbol into written

Chinese mathematics Mathematics in China emerged independently by the 11th century BCE. The Chinese independently developed a real number system that includes significantly large and negative numbers, more than one numeral system ( base 2 and base 10), algebra, geomet ...

. 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 (Katz, 1993).

Main work

*''Shushu Jiuzhang (Mathematical Treatise in Nine Sections)'' (1248)

References

Bibliography

*Guo, Shuchun. '' Encyclopedia of China'' (Mathematics Volume), 1st ed. *Qin Jiushao

(Chinese History Timeline), 2007. *Ulrich Libbrecht: ''Chinese Mathematics in the Thirteenth Century'' (The Shu-Shu-Chiu-Chang of Chin Chiu shao) Dover Publication *

Victor J. Katz Victor Joseph Katz (born 31 December 1942, Philadelphia) is an American mathematician, historian of mathematics, and teacher known for using the history of mathematics in teaching mathematics. Biography Katz received in 1963 from Princeton Unive ...

"A history of mathematics: an introduction." New York (1993).

External links

*
Simon Fraser University biography for “Qin Jiushao”
{{DEFAULTSORT:Qin, Jiushao 1202 births 1261 deaths 13th-century Chinese mathematicians 13th-century Chinese writers Chinese inventors Chinese meteorologists Medieval Chinese mathematicians Number theorists Politicians from Ziyang Scientists from Sichuan Song dynasty politicians from Sichuan Song dynasty science writers Writers from Ziyang