Journal for History of Mathematics (한국수학사학회지)

The Korean Society for History of Mathematics (한국수학사학회)
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Hong JeongHa's Tianyuanshu and Zhengcheng Kaifangfa

홍정하(洪正夏)의 천원술(天元術)과 증승개방법(增乘開方法)

  • Received : 2014.04.25
  • Accepted : 2014.06.08
  • Published : 2014.06.30
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Abstract

Tianyuanshu and Zengcheng Kaifangfa introduced in the Song-Yuan dynasties and their contribution to the theory of equations are one of the most important achievements in the history of Chinese mathematics. Furthermore, they became the most fundamental subject in the history of East Asian mathematics as well. The operations, or the mathematical structure of polynomials have been overlooked by traditional mathematics books. Investigation of GuIlJib (九一集) of Joseon mathematician Hong JeongHa reveals that Hong's approach to polynomials is highly structural. For the expansion of $\prod_{k=11}^{n}(x+a_k)$, Hong invented a new method which we name Hong JeongHa's synthetic expansion. Using this, he reveals that the processes in Zhengcheng Kaifangfa is not synthetic division but synthetic expansion.

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References

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  3. On the publication of Hong JeongHa's GuIlJib vol.28, pp.5, 2015, https://doi.org/10.14477/jhm.2015.28.5.233
  4. One Quadratic Equation, Different Understandings: the 13th Century Interpretations by Li Ye and Later Commentaries in the 18th and 19th Centuries vol.30, pp.3, 2017, https://doi.org/10.14477/jhm.2017.30.3.137
  5. Siyuan Yujian in the Joseon Mathematics vol.30, pp.4, 2017, https://doi.org/10.14477/jhm.2017.30.4.203
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  7. Haidao Suanjing in Joseon Mathematics vol.32, pp.6, 2014, https://doi.org/10.14477/jhm.2019.32.6.259
  8. Zengcheng Kaifangfa and Zeros of Polynomials vol.33, pp.6, 2020, https://doi.org/10.14477/jhm.2020.33.6.303