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Siyuan yujian
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Blaise Pascal first described his triangle for generating the coefficients of a binomial expansion in 1665. The Chinese version, however, is centuries older. It was included as an illustration in Zhu Shijie's Siyuan yujian (1303; ā€œPrecious Mirror of Four Elementsā€), where it was already called the ā€œOld Method.ā€
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Siyuan yujian

work by Zhu Shijie
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Blaise Pascal first described his triangle for generating the coefficients of a binomial expansion in 1665. The Chinese version, however, is centuries older. It was included as an illustration in Zhu Shijie's Siyuan yujian (1303; ā€œPrecious Mirror of Four Elementsā€), where it was already called the ā€œOld Method.ā€
Blaise Pascal first described his triangle for generating the coefficients of a binomial expansion in 1665. The Chinese version, however, is centuries older. It was included as an illustration in Zhu Shijie's Siyuan yujian (1303; ā€œPrecious Mirror of Four Elementsā€), where it was already called the ā€œOld Method.ā€

The Siyuan yujian, or "Precious Mirror of the Four Elements," is a significant mathematical work by Zhu Shijie, a Chinese mathematician who lived around 1300 CE. This book represents the culmination of the Chinese "method of the celestial unknown," a form of algebraic computation using counting rods.12

Zhu Shijie's primary contribution in the Siyuan yujian was demonstrating that this method could solve a wide array of problems by introducing techniques to eliminate unknown variables between equations. The work also featured a diagram similar to Pascal's triangle, which likely influenced Zhu's discovery of a key combinatoric identity. The "method of the celestial unknown" allowed for the representation of polynomials and equations, advancing algebraic problem-solving in traditional Chinese mathematics.12

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4 Britannica Sources
  1. Zhu Shijie
  2. East Asian mathematics - The method of the celestial unknown
  3. Zu Geng
  4. East Asian mathematics - The ā€œTen Classicsā€

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