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Jia Xian
Northern Song mathematician whose triangular table of binomial coefficients and step-by-step root-extraction method survive through Yang Hui's quotations
In a calculation room, a wide table holds a board of black and yellow counting rods laid in neat bundles, beside an abacus, a ruler and a sheet with a circle divided into equal parts; one person sits at a far desk with their back turned, and terraced fields lie outside.
Also known as Bei Song Si Tian Jian Suan Xue Sheng
- Roles
- Mathematician
Jia Xian was a Northern Song mathematician about whom very little is recorded; Wang Zhu's notebook Wangshi tanlu names him as a pupil of the astronomer Chu Yan and a low-ranking palace officer. His Detailed Solutions to the Yellow Emperor's Nine Chapters in nine chapters is lost, but parts survive in Yang Hui's Detailed Analysis of the Nine Chapters (Xiangjie jiuzhang suanfa) of the Southern Song. According to Yang Hui he drew up a 'chart of the origin of root extraction', a triangular table of binomial coefficients used for square, cube and higher roots, now known as Jia Xian's or Yang Hui's triangle. He also devised a method of repeated multiplication and addition for finding the positive root of higher-degree equations, which Qin Jiushao later developed further. The bibliography in the History of Song also lists a two-chapter mathematical collection of his that is likewise lost.
Life and times
Dates Dates unknown; reign of Emperor Renzong of Song