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 Theob ...
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 Horn ...
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 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
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, four munic ...
.
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 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 problems or to perform a computation. Algorithms are used as specifications for performing ...
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 i ...
about 60 BCE, though knowledge of the formula may go back to
Archimedes.
As precipitation was important agriculture and food production, Qin developed precipitation gauges that was widely used in 1247 during the
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 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 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, galaxi ...
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 winter ...
. Among his accomplishments are the introduction techniques for solving certain types of algebraic
equations using a numerical algorithm (equivalent to the 19th century
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 Horn ...
) 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.
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