Zhu Shijie

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Page from Zhu's work Introduction to the Study of Mathematics
Illustrations from The precious mirror of the four elements with Pascal's triangle

Zhu Shijie ( Chinese  朱世傑  /  朱世杰 , Pinyin Zhū ​​Shìjié , W.-G. Chu Shih-Chieh ; * around 1260 in Yan Shan ; † around 1320 ) was one of the most important Chinese mathematicians .

Little is known about his life, but two of his mathematical works have survived. Introduction to the Study of Mathematics ( 算 學 啟蒙 , Suànxué qǐméng ) from 1299 is a basic textbook of mathematics. Zhu covers about 260 problems in the fields of arithmetic and algebra . The book also showed how to measure different two-dimensional shapes and three-dimensional bodies. The Chinese original has been lost; however, it was used as a textbook in Japan and Korea . A Chinese version of the book was reconstructed from a Korean translation in 1839.

Zhu's second book, The Precious Mirror of the Four Elements ( 四 元 玉 鑒 , Sì yuán yù jiàn ) from 1303 is his most important work. With this book, Zhu brought Chinese algebra to the highest level. It includes an explanation of his four element method that can be used to represent algebraic equations with four unknowns. Zhu also explained how to find square roots and added the understanding of series and sequence. At the beginning of the book there is a picture that shows the representation of the binomial coefficients , now called Pascal's triangle .

The book Siyuan yujian also contains a conversion method for solving polynomial equations of the fourth degree, which Zhu fan fa called and which William George Horner and Paolo Ruffini rediscovered in Europe 500 years later .


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