Editing Zhu Shijie

{{Short description|Chinese mathematician during the Yuan dynasty}}
{{for|the artist|Zhu Shijie (painter)}}
{{more footnotes|date=January 2013}}
{{family name hatnote|[[Zhu (surname)|Zhu]]|lang=Chinese}}
[[File:SIYUAN_YUJIAN_PDF-036-036.jpg|thumb|A page of Zhu Shijie's famous ''Jade Mirror of the Four Unknowns'']]
'''Zhu Shijie''' ({{zh|t=朱世傑|s=朱世杰|p=Zhū Shìjié|w='''Chu Shih-chieh'''}}, 1249–1314), [[courtesy name]] '''Hanqing''' ({{lang|zh-hant|漢卿}}), [[pseudonym]] '''Songting''' ({{lang|zh-hant|松庭}}), was a Chinese mathematician and writer during the [[Yuan Dynasty]].<ref>{{Cite web |title=Zhu Shijie - Biography |url=https://mathshistory.st-andrews.ac.uk/Biographies/Zhu_Shijie/ |access-date=2023-07-03 |website=Maths History |language=en}}</ref> Zhu was born close to today's Beijing. Two of his mathematical works have survived: ''Introduction to Computational Studies'' ({{lang|zh-hant|算學啓蒙}} ''Suan-hsüeh Ch'i-mong'') and ''[[Jade Mirror of the Four Unknowns]]'' ({{lang|zh-hant|四元玉鑒}} ''Ssŭ-yüan Yü-chien'').

==''Suanxue Qimeng''==
[[File:朱世杰算学启蒙中的天元术.JPG|thumb|right|280px|Suanxue Qimeng]]
The ''Suanxue Qimeng'' ({{lang|zh-hant|算學啓蒙}}), written in 1299, is an elementary textbook on mathematics in three volumes, 20 chapters and 259 problems. This book also showed how to measure two-dimensional shapes and three-dimensional solids. The ''Introduction'' strongly influenced the development of [[Japanese mathematics|mathematics in Japan]]. The book was once lost in China until the Qing dynasty mathematician Luo Shilin bought a Korean printed edition and republished it in Yangzhou.

==''Jade Mirror of the Four Unknowns''==
[[File:四元自乘演段图.jpg|thumb|right|300px|Illustrations in ''Jade Mirror of the Four Unknowns'']]
Zhu's second book, ''[[Jade Mirror of the Four Unknowns]]'' (1303) was his most important work, advancing Chinese algebra. The first four of the 288 solved problems 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 solves the high order equation by the [[Horner's method|''ling long kai fang'' (玲瓏開方)]] method of [[Southern Song]] dynasty mathematician [[Qin Jiushao]] (from ''Shùshū Jiǔzhāng,'' “[[Mathematical Treatise in Nine Sections]]” of 1247). This was more than 570 years before English mathematician [[William George Horner|William Horner]]'s method using synthetic division. Zhu makes use of what is currently known as [[Pascal triangle|Pascal's triangle]], which he refers to as discovered by [[Jia Xian]] before 1050. The final equation and one of its solutions are 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|linear equations]] by reducing the matrix of their coefficients to [[diagonal form]]. He moreover applied these methods to [[algebraic equation]]s, using a version of the [[resultant]].<ref>Mumford 2010, p. 122.</ref> His methods pre-date [[Blaise Pascal]], William Horner, and modern matrix methods by many centuries. The preface of the book describes how Zhu traveled China for 20 years teaching mathematics.

The methods of ''Jade Mirror of the Four Unknowns'' form the foundation for [[Wu's method of characteristic set]].

==References==
{{reflist}}
*Du, Shiran, [https://web.archive.org/web/20070929095946/http://203.72.198.245/web/Content.asp?ID=43658&Query=1 "Zhu Shijie"]. ''[[Encyclopedia of China]]'' (Mathematics Edition), 1st ed.
*GRATTAN-GUINNESS, I.: ''The Norton History of the Mathematical Sciences'', 1998.
*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. {{ISBN|7-5382-6923-1}} 
*HO Peng-Yoke: Article on Chu Shih-chieh in the ''Dictionary of Scientific Biography'', New York, 1970.hi
*Hoe, J.: ''The jade mirror of the four unknowns'', Mingming Bookroom, New Zealand, 2007. {{ISBN|1-877209-14-7}}
*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.
*KONANTZ, E.L.:The Precious Mirror of the Four Elements, ''China journal of Science and Arts'', Vol 2, No 4, 1924.
*LAM Lay-yong: Chu shih-chieh's Suan hsüeh ch'i-meng, ''Archive for the history of sciences'', Vol 21, Berlin, 1970.
*MARTZLOFF, J-C.: ''A history of Chinese Mathematics'', Springer-Verlag, Berlin, 1997.
*[[Yoshio Mikami|MIKAMI Yoshio]], Development of Mathematics in China and Japan, Chapter 14 Chu Shih-chieh p89-98. 1913 Leipzig. Library of Congress catalog card number 61-13497.
*Mumford, David, "What’s so Baffling About Negative Numbers? — a Cross-Cultural Comparison", in C. S. Seshadri (Ed.), ''Studies in the History of Indian Mathematics'', 2010.

==External links==
* {{MacTutor Biography|id=Zhu_Shijie}}

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{{DEFAULTSORT:Zhu, Shijie}}
[[Category:1249 births]]
[[Category:1314 deaths]]
[[Category:13th-century Chinese mathematicians]]
[[Category:14th-century Chinese mathematicians]]
[[Category:Educators from Hebei]]
[[Category:Mathematicians from Imperial China]]
[[Category:Yuan dynasty science writers]]
[[Category:Writers from Hebei]]