Qin Jiushao (, ca. 1202–1261),

courtesy name A courtesy name ( zh, s=字, p=zì, l=character), also known as a style name, is an additional name bestowed upon individuals at adulthood, complementing their given name. This tradition is prevalent in the East Asian cultural sphere, particula ...

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 is a coastal Provinces of China, province in East China. Shandong has played a major role in Chinese history since the beginning of Chinese civilization along the lower reaches of the Yellow River. It has served as a pivotal cultural ...

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 a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

. He was accomplished in many other fields and held a series of bureaucratic positions in several

Chinese provinces Provinces ( zh, c=省, p=Shěng) are the most numerous type of province-level divisions in the People's Republic of China (PRC). There are currently 22 provinces administered by the PRC and one province that is claimed, but not administere ...

. 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 Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algo ...

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 In geometry, Heron's formula (or Hero's formula) gives the area of a triangle in terms of the three side lengths Letting be the semiperimeter of the triangle, s = \tfrac12(a + b + c), the area is A = \sqrt. It is named after first-century ...

, proved by

Heron of Alexandria Hero of Alexandria (; , , also known as Heron of Alexandria ; probably 1st or 2nd century AD) was a Greek mathematician and engineer who was active in Alexandria in Egypt during the Roman era. He has been described as the greatest experimentali ...

about 60 BCE, though knowledge of the formula may go back to

Archimedes Archimedes of Syracuse ( ; ) was an Ancient Greece, Ancient Greek Greek mathematics, mathematician, physicist, engineer, astronomer, and Invention, inventor from the ancient city of Syracuse, Sicily, Syracuse in History of Greek and Hellenis ...

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

Mongol Empire The Mongol Empire was the List of largest empires, largest contiguous empire in human history, history. Originating in present-day Mongolia in East Asia, the Mongol Empire at its height stretched from the Sea of Japan to parts of Eastern Euro ...

Southern Song dynasty The Song dynasty ( ) was an imperial dynasty of China that ruled from 960 to 1279. The dynasty was founded by Emperor Taizu of Song, who usurped the throne of the Later Zhou dynasty and went on to conquer the rest of the Ten Kingdoms, endin ...

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, dating back to the Han dynasty, is a lunisolar calendar that blends solar, lunar, and other cycles for social and agricultural purposes. While modern China primarily uses the Gregorian calendar for officia ...

experts calculated

astronomical Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest include ...

data according to the timing of the

winter solstice The winter solstice, or hibernal solstice, occurs when either of Earth's geographical pole, poles reaches its maximum axial tilt, tilt away from the Sun. This happens twice yearly, once in each hemisphere (Northern Hemisphere, Northern and So ...

. Among his accomplishments are the introduction techniques for solving certain types of algebraic

equation In mathematics, an equation is a mathematical 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 ...

s using a numerical algorithm (equivalent to the 19th century

) and for finding

sums In mathematics, summation is the addition of a sequence of numbers, called ''addends'' or ''summands''; the result is their ''sum'' or ''total''. Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynom ...

arithmetic series An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that ...

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

Chinese mathematics Mathematics emerged independently in China 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, binary and base 10, decima ...

. 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, be ...

'' (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 1200s births 1261 deaths 13th-century Chinese mathematicians 13th-century Chinese writers Chinese inventors Chinese meteorologists Mathematicians from Imperial China Number theorists Politicians from Ziyang Scientists from Sichuan Song dynasty government officials Song dynasty science writers Writers from Ziyang