Jia Xian
Encyclopedia
Chinese mathematics
Mathematics in China emerged independently by the 11th century BC. The Chinese independently developed very large and negative numbers, decimals, a place value decimal system, a binary system, algebra, geometry, and trigonometry....
from Kaifeng
Kaifeng
Kaifeng , known previously by several names , is a prefecture-level city in east-central Henan province, Central China. Nearly 5 million people live in the metropolitan area...
of the Song Dynasty
Song Dynasty
The Song Dynasty was a ruling dynasty in China between 960 and 1279; it succeeded the Five Dynasties and Ten Kingdoms Period, and was followed by the Yuan Dynasty. It was the first government in world history to issue banknotes or paper money, and the first Chinese government to establish a...
, in the first half of the 11th century.
Biography
According to the history of the Song Dynasty, Xian was a palace eunuchEunuch
A eunuch is a person born male most commonly castrated, typically early enough in his life for this change to have major hormonal consequences...
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 invented the Jia Xian triangle
Pascal's triangle
In mathematics, Pascal's triangle is a triangular array of the binomial coefficients in a triangle. It is named after the French mathematician, Blaise Pascal...
around the first half of the 11th century, about six centuries before Pascal
Blaise Pascal
Blaise Pascal , was a French mathematician, physicist, inventor, writer and Catholic philosopher. He was a child prodigy who was educated by his father, a tax collector in Rouen...
. Jia Xian used it as a tool for extracting square
Square root
In mathematics, a square root of a number x is a number r such that r2 = x, or, in other words, a number r whose square is x...
and cubic roots. The original book by Jia Xian titled Shi Suo Suan Shu was lost; however, Jia's method was expounded in detail by Yang Hui
Yang Hui
Yang Hui , courtesy name Qianguang , was a Chinese mathematician from Qiantang , Zhejiang province during the late Song Dynasty . Yang worked on magic squares, magic circles and the binomial theorem, and is best known for his contribution of presenting 'Yang Hui's Triangle'...
, 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 preserved this historic fact.
Jia Xian's additive-multiplicative method implemented the "Horner" rule.