한국수학사학회지 (Journal for History of Mathematics)

한국수학사학회 (The Korean Society for History of Mathematics)
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홍정하(洪正夏)의 천원술(天元術)과 증승개방법(增乘開方法)

Hong JeongHa's Tianyuanshu and Zhengcheng Kaifangfa

  • 투고 : 2014.04.25
  • 심사 : 2014.06.08
  • 발행 : 2014.06.30
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초록

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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참고문헌

  1. Guo ShuChun ed. ZhongGuo Kexue Jishu Dianji Tonghui Shuxuejuan, Henan Jiaoyu Pub. Co., 1993. 郭書春主編, 中國科學技術典籍通彙 數學卷全五卷, 河南敎育出版社, 1993.
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  3. Hong JeongHa, GuIlJib (1724), Seoul National University Library. 洪正夏, 九一集 (1724), 서울大學校圖書館.
  4. Hong JeongHa, GuIlJib (1724), corrected by Hong YeongSeok, 1868, Tohoku University Library. 洪正夏, 九一集 (1724), 洪永錫校字, 1868, 東北大學圖書館.
  5. Li Peiye, Yuan Min, Yigu Yanduan Shiyi, Shanxi Chuban Jituan, Shanxi Kexue Jishu Pub. Co., 2009. 李培業, 袁敏, 益古演段釋義 , 陝西出版集團, 陝西科學技術出版社, 2009.
  6. Park Yul, SanHak WonBon, 1700, Korea University Library. 朴繘, 算學原本 , 1700, 高麗大學校圖書館.
  7. Takebe Katahiro, Japanese Commentary to Suanxue Qimeng, 1690. 建部賢弘, 算學啓蒙諺解大成, 1690.
  8. Hong Sung Sa, Theory of Equations in the history of Chosun Mathematics, Proceeding Book 2, The HPM Satellite Meeting of ICME-12, 719-731, 2012.
  9. Hong Sung Sa, Hong Young Hee, Mathematics Teachers and Professors in Chosun Dynasty, The Korean Journal for History of Mathematics, 19(3) (2006), 1-20. 홍성사, 홍영희, 朝鮮의 算學訓導와 算學敎授, 한국수학사학회지, 19(3) (2006), 1-20.
  10. Hong Sung Sa, Hong Young Hee, Kim Chang Il, GouGuShu in the 18th century Chosun, The Korean Journal for History of Mathematics, 22(2) (2009), 1-12. 홍성사, 홍영희, 김창일, 18世紀朝鮮의 句股術, 한국수학사학회지 22(2) (2009), 1-12.
  11. Hong Sung Sa, Hong Young Hee, Kim Chang Il, Hong JungHa's Number Theory, The Korean Journal for History of Mathematics 24(4) (2011), 1-6. 홍성사, 홍영희, 김창일, 洪正夏의 數論, 한국수학사학회지 24(4) (2011), 1-6.
  12. Hong Sung Sa, Hong, Young Hee, Kim Young Wook, SanHak WonBon of Park Yul, The Korean J. for History of Mathematics 18(4) (2005), 1-16. 홍성사, 홍영희, 김영욱, 朴繘의 算學原本, 한국수학사학회지, 18(4), (2005), 1-16.
  13. Hong Sung Sa, Hong Young Hee, Kim Young Wook, Liu Yi and Hong JungHa's KaiFangShu, The Korean Journal for History of Mathematics, 24(1) (2011), 1-13. 홍성사, 홍영희, 김영욱, 劉益과 洪正夏의 開方術, 한국수학사학회지 24(1) (2011), 1-13.
  14. Hong Sung Sa, Hong Young Hee, Lee Seung On, TianYuanShu and Numeral Systems in Eastern Asia, Journal for History of Mathematics, 25(4) (2012), 1-10.
  15. Hong Sung Sa, Hong Young Hee, Lee Seung On, Mathematical Structures of Joseon mathematician Hong JeongHa, Journal for History of Mathematics, 27(1) (2014), 1-14. https://doi.org/10.14477/jhm.2014.27.1.001
  16. Kim Chang Il, Hong Sung Sa, Hong Young Hee, Chosun Mathematician Hong JungHa's Genealogy, The Korean Journal for History of Mathematics 23(3) (2010), 1-20. 김창일, 홍성사, 홍영희, 朝鮮算學者洪正夏의 系譜, 한국수학사학회지 23(3) (2010), 1-20.
  17. Kim Young Wook, Hong Sung Sa, Zhengcheng Kaifangfa, a method of computation in the 13th century China, Proceeding, Annual meeting of The Korean Society for History of Mathematics, 2009, 13-14. 김영욱, 홍성사, 增乘開方法, 13世紀中國의 計算法, Proceeding, 한국수학사학회 연례학술발표대회, 13-14, 2009.

피인용 문헌

  1. Zeros of Polynomials in East Asian Mathematics vol.29, pp.6, 2016, https://doi.org/10.14477/jhm.2016.29.6.317
  2. Kaifangfa and Translation of Coordinate Axes vol.27, pp.6, 2014, https://doi.org/10.14477/jhm.2014.27.6.387
  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
  6. 동양수학사에서의 조선수학의 역할과 의미 vol.31, pp.4, 2018, https://doi.org/10.14477/jhm.2018.31.4.169
  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