CHU SHIH-CHIEH

literary name Han-ch'ing flourished c. 1280, -1303, China one of the greatest of Chinese mathematicians, who made notable contributions to the development of Chinese algebra and the theory of equations. Outside of his mathematical work, little is known of Chu's life. He was apparently a resident of Yen-shan, near Peking, and he traveled widely throughout China as a celebrated mathematician, attracting numerous pupils who wished to study under him. Chu's two surviving works are Suan-hsueh ch'i-meng (1299; "Introduction to Mathematical Studies") and Ssu-yuan yu-chien (1303; "Precious Mirror of the Four Elements"). The former was a relatively elementary work meant as a textbook for beginners. Although it was lost in China until the 19th century, it was widely adopted as a textbook in Japan and Korea in the 15th century and strongly influenced mathematics in those countries. The second work, Ssu-yuan yu-chien of 1303, is a much more important treatise. It contains Chu's original extension of the "method of the celestial element" to express four unknown quantities in the same algebraic equation (whence the "four elements" in the book's title). The Ssu-yuan yu-chien marks the apex of the development of Chinese algebra in its treatment of simultaneous equations and equations having degrees as high as 14. Chu commonly solved the latter equations using a transformation method (called fan fa) that was rediscovered by the English mathematician W.G. Horner in 1819 (Horner's method). The Ssu-yuan yu-chien also contains a noteworthy diagram of the arithmetic, or Pascal, triangle (used to determine the binomial coefficients) and has interesting studies of arithmetic and geometric progressions and series.