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Jia Xian (; ca. 1010–1070) was a Chinese mathematician from
Jia Xian's additive-multiplicative method implemented the "Horner" rule.Jean-Claude Martzloff, ''A History of Chinese Mathematics ''Springer, p142
Jia Xian (; ca. 1010–1070) was a Chinese mathematician from Kaifeng
Kaifeng () is a prefecture-level city in east-central Henan province, China. It is one of the Eight Ancient Capitals of China, having been the capital eight times in history, and is best known for having been the Chinese capital during the Nort ...
of the 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 ...
.
Biography
According to the history of the Song dynasty, Jia was a palaceeunuch
A eunuch ( ) is a male who has been castrated. Throughout history, castration often served a specific social function.
The earliest records for intentional castration to produce eunuchs are from the Sumerian city of Lagash in the 2nd millennium ...
of the Left Duty Group. He studied under the mathematician Chu Yan, and was well versed in mathematics, writing many books on the subject. Jia Xian described the Pascal's triangle
In mathematics, Pascal's triangle is a triangular array of the binomial coefficients that arises in probability theory, combinatorics, and algebra. In much of the Western world, it is named after the French mathematician Blaise Pascal, although ot ...
(Jia Xian triangle) around the middle of the 11th century, about six centuries before Pascal
Pascal, Pascal's or PASCAL may refer to:
People and fictional characters
* Pascal (given name), including a list of people with the name
* Pascal (surname), including a list of people and fictional characters with the name
** Blaise Pascal, Fren ...
. Jia used it as a tool for extracting square
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length adj ...
and cubic root
In mathematics, a cube root of a number is a number such that . All nonzero real numbers, have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. Fo ...
s. The original book by Jia entitled ''Shi Suo Suan Shu'' was lost; however, Jia's method was expounded in detail by Yang Hui
Yang Hui (, ca. 1238–1298), courtesy name Qianguang (), was a Chinese mathematician and writer during the Song dynasty. Originally, from Qiantang (modern Hangzhou, Zhejiang), Yang worked on magic squares, magic circles and the binomial theo ...
, who explicitly acknowledged his source: "My method of finding square and cubic roots was based on the Jia Xian method in ''Shi Suo Suan Shu''." A page from the ''Yongle Encyclopedia
The ''Yongle Encyclopedia'' () or ''Yongle Dadian'' () is a largely-lost Chinese ''leishu'' encyclopedia commissioned by the Yongle Emperor of the Ming dynasty in 1403 and completed by 1408. It comprised 22,937 manuscript rolls or chapters, in 1 ...
'' preserved this historic fact.
Jia Xian's additive-multiplicative method implemented the "Horner" rule.Jean-Claude Martzloff, ''A History of Chinese Mathematics ''Springer, p142
References