Zhu Shijie (, 1249–1314),

courtesy name A courtesy name (), also known as a style name, is a name bestowed upon one at adulthood in addition to one's given name. This practice is a tradition in the East Asian cultural sphere, including China, Japan, Korea, and Vietnam.Ulrich Theobald ...

Hanqing (),

pseudonym A pseudonym (; ) or alias () is a fictitious name that a person or group assumes for a particular purpose, which differs from their original or true name (orthonym). This also differs from a new name that entirely or legally replaces an individua ...

Songting (), was a Chinese mathematician and writer. He was a Chinese mathematician during the

Yuan Dynasty The Yuan dynasty (), officially the Great Yuan (; xng, , , literally "Great Yuan State"), was a Mongol-led imperial dynasty of China and a successor state to the Mongol Empire after its division. It was established by Kublai, the fifth ...

. Zhu was born close to today's Beijing. Two of his mathematical works have survived. ''Introduction to Computational Studies'' ( ''Suan hsüeh Ch'i-mong''), and ''

Jade Mirror of the Four Unknowns ''Jade Mirror of the Four Unknowns'', ''Siyuan yujian'' (), also referred to as ''Jade Mirror of the Four Origins'', is a 1303 mathematical monograph by Yuan dynasty mathematician Zhu Shijie. Zhu advanced Chinese algebra with this Magnum opus. ...

''.

''Suanxue qimeng''

The ''Suan hsüeh Ch'i-mong'' (), written in 1299, is an elementary textbook on mathematics in three volumes, 20 chapters and 259 problems. This book also showed how to measure different two-dimensional shapes and three-dimensional solids. The ''Introduction'' had an important influence on the development of mathematics in Japan. The book was once lost in China until Qing dynasty mathematician Luo Shilin bought a Korean printed edition, and re-published in Yangzhou. Since then this book was reprinted several times.

''Jade Mirror of the Four Unknowns''

Zhu's second book, ''

'', written in 1303, is his most important work. With this book, Zhu advanced Chinese algebra. The first four of the 288 problems for solution illustrate his method of the four unknowns. He shows how to convert a problem stated verbally into a system of polynomial equations (up to 14th order), by using up to four unknowns: 天 Heaven, 地 Earth, 人 Man, 物 Matter, and then how to reduce the system to a single polynomial equation in one unknown by successive elimination of unknowns. He then solved the high order equation by

Southern Song The Song dynasty (; ; 960–1279) was an Dynasties in Chinese history, 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. ...

dynasty mathematician

Qin Jiushao Qin Jiushao (, ca. 1202–1261), courtesy name Daogu (道古), was a Chinese mathematician, meteorologist, inventor, politician, and writer. He is credited for discovering Horner's method as well as inventing Tianchi basins, a type of rain gau ...

's "Ling long kai fang" method published in 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 (more than 570 years before English mathematician William Horner's method using synthetic division). To do this, he makes use of what is currently known as the

Pascal 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 ...

, which he labels as the diagram of an ancient method first discovered by

Jia Xian Jia Xian (; ca. 1010–1070) was a Chinese mathematician from Kaifeng of the Song dynasty. Biography According to the history of the Song dynasty, Jia was a palace eunuch of the Left Duty Group. He studied under the mathematician Chu Yan, and ...

before 1050. The final equation and one of its solutions is given for each of the 288 problems. Zhu also found square and cube roots by solving quadratic and cubic equations, and added to the understanding of series and progressions, classifying them according to the coefficients of the Pascal triangle. He also showed how to solve systems of

linear equation In mathematics, a linear equation is an equation that may be put in the form a_1x_1+\ldots+a_nx_n+b=0, where x_1,\ldots,x_n are the variables (or unknowns), and b,a_1,\ldots,a_n are the coefficients, which are often real numbers. The coefficien ...

s by reducing the matrix of their coefficients to

diagonal form In mathematics, a diagonal form is an algebraic form (homogeneous polynomial) without cross-terms involving different indeterminates. That is, it is :\sum_^n a_i ^m\ for some given degree ''m''. Such forms ''F'', and the hypersurfaces ''F'' = ...

. His methods pre-date

Blaise Pascal Blaise Pascal ( , , ; ; 19 June 1623 – 19 August 1662) was a French mathematician, physicist, inventor, philosopher, and Catholic Church, Catholic writer. He was a child prodigy who was educated by his father, a tax collector in Rouen. Pa ...

, William Horner, and modern matrix methods by many centuries. The preface of the book describes how Zhu traveled around China for 20 years as a teacher of mathematics. The methods of ''Jade Mirror of the Four Unknowns'' form the foundation for

Wu's method of characteristic set Wenjun Wu's method is an algorithm for solving multivariate polynomial equations introduced in the late 1970s by the Chinese mathematician Wen-Tsun Wu. This method is based on the mathematical concept of characteristic set introduced in the lat ...

References

Yoshio Mikami was a Japanese mathematician and historian of '' Japanese mathematics''. He was born February 16, 1875, in Kotachi, Hiroshima prefecture. He attended the High School of Tohoku University, and in 1911 was admitted to the Imperial University of To ...

Development of Mathematics in China and Japan, Chapter 14 Chu Shih-chieh p89-98. 1913 Leipzig. Library of Congress catalog card number 61-13497. *Du, Shiran
"Zhu Shijie"
''

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, begin ...

'' (Mathematics Edition), 1st ed. *LAM Lay-yong: Chu shih-chieh's Suan hsüeh ch'i-meng, ''Archive for the history of sciences'', Vol 21, Berlin, 1970. *Guo Shuchun (tr. modern Chinese), Chen Zaixin (English tr.), Guo Jinhai (annotation), Zhu Shijie: ''Jade mirror of the Four Unknowns'', Chinese and English bilingual, vol I & 2,Liaoning education Press, China, 2006. *Hoe, J.: ''The jade mirror of the four unknowns'', Mingming Bookroom, New Zealand, 2007. *Hoe, J.: ''Les systèmes d'équations polynômes dans le Siyuan Yujian (1303)'', Paris, Collège de France (Mémoires de l'Institut des Hautes Etudes Chinoises, Vol VI),1977. *MARTZLOFF, J-C.: ''A history of Chinese Mathematics'', Springer-Verlag, Berlin, 1997. *GRATTAN-GUINNESS, I.: ''The Norton History of the Mathematical Sciences'', 1998. *KONANTZ, E.L.:The Precious Mirror of the Four Elements, ''China journal of Science and Arts'', Vol 2, No 4, 1924. *HO Peng-Yoke: Article on Chu Shih-chieh in the ''Dictionary of Scientific Biography'', New York, 1970.hi

External links

* {{DEFAULTSORT:Zhu, Shijie 1249 births 1314 deaths 13th-century Chinese mathematicians 14th-century Chinese mathematicians Educators from Hebei Medieval Chinese mathematicians Yuan dynasty science writers Writers from Hebei