Qin Jiushao (, ca. 1202–1261),

courtesy name A courtesy name (), also known as a style name, is a name bestowed upon one at adulthood in addition to one's given name. This practice is a tradition in the East Asian cultural sphere, including China, Japan, Korea, and Vietnam.Ulrich Theobald ...

Daogu (道古), was a Chinese mathematician, meteorologist, inventor, politician, and writer. He is credited for discovering

Horner's method In mathematics and computer science, Horner's method (or Horner's scheme) is an algorithm for polynomial evaluation. Although named after William George Horner, this method is much older, as it has been attributed to Joseph-Louis Lagrange by Hor ...

as well as inventing Tianchi basins, a type of rain gauge instrument used to gather meteorological data.

Biography

Although Qin Jiushao was born in Ziyang, Sichuan, 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 The provincial level administrative divisions () are the highest-level administrative divisions of China. There are 34 such divisions claimed by the People's Republic of China, classified as 23 provinces (), five autonomous regions of China, au ...

. Qin wrote ''Shùshū Jiǔzhāng'' (“

Mathematical Treatise in Nine Sections The ''Mathematical Treatise in Nine Sections'' () is a mathematical text written by Chinese Southern Song dynasty mathematician Qin Jiushao in the year 1247. The mathematical text has a wide range of topics and is taken from all aspects of th ...

”) 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

algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specificat ...

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 Hero of Alexandria (; grc-gre, Ἥρων ὁ Ἀλεξανδρεύς, ''Heron ho Alexandreus'', also known as Heron of Alexandria ; 60 AD) was a Greek mathematician and engineer who was active in his native city of Alexandria, Roman Egypt. He ...

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 Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, galaxies ...

data according to the timing of the

winter solstice The winter solstice, also called the hibernal solstice, occurs when either of Earth's poles reaches its maximum tilt away from the Sun. This happens twice yearly, once in each hemisphere ( Northern and Southern). For that hemisphere, the winte ...

. 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

) and for finding sums of

arithmetic series An arithmetic progression or arithmetic sequence () is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common differ ...

. 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 The ''Encyclopedia of China'' () is the first large-entry modern encyclopedia in the Chinese language. The compilation began in 1978. Published by the Encyclopedia of China Publishing House, the encyclopedia was issued one volume at a time, begin ...

'' (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 "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