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정약용(丁若鏞)의 산서(算書) 구고원류(勾股源流)의 다항식(多項式)의 수학적(數學的) 구조(構造)

Mathematical Structures of Polynomials in Jeong Yag-yong's Gugo Wonlyu

  • 투고 : 2016.10.01
  • 심사 : 2016.10.27
  • 발행 : 2016.10.31

초록

This paper is a sequel to our paper [3]. Although polynomials in the tianyuanshu induce perfectly the algebraic structure of polynomials, the tianyuan(天元) is always chosen by a specific unknown in a given problem, it can't carry out the role of the indeterminate in ordinary polynomials. Further, taking the indeterminate as a variable, one can study mathematical structures of polynomials via those of polynomial functions. Thus the theory of polynomials in East Asian mathematics could not be completely materialized. In the previous paper [3], we show that Jeong Yag-yong disclosed in his Gugo Wonlyu(勾股源流) the mathematical structures of Pythagorean polynomials, namely polynomials p(a, b, c) where a, b, c are the three sides gou(勾), gu(股), xian(弦) of a right triangle, respectively. In this paper, we show that Jeong obtained his results through his recognizing Pythagorean polynomials as polynomial functions of three variables a, b, c.

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, 河南敎育出版社, 1993.)
  2. HONG Sung Sa, HONG Young Hee, KIM Chang Il, Gougushu in the 18th century Chosun, The Korean Journal for History of Mathematics 20(4) (2007), 1-22.(홍성사, 홍영희, 김창일, 18世紀 朝鮮의 句股術, 한국수학사학회지 20(4) (2007), 1-22.)
  3. HONG Sung Sa, HONG Young Hee, LEE Seung On, Mathematical Structures of Jeong Yagyong's Gugo Wonlyu, Journal for History of Mathematics, 28(6) (2015), 301-310. https://doi.org/10.14477/jhm.2015.28.6.301
  4. JEONG Yag-yong, Gugo Wonlyu, Yeoyudang Jeonseo Boyu Four, Gyeongin Munhwasa, 1975.(丁若鏞, <<勾股源流>>, 與猶堂全書補遺四, 景仁文化社, 1975.)
  5. JEONG Yag-yong, Gugo Wonlyu, Book I-III, National Library of Korea.(丁若鏞, <<勾股源流>> I-III卷, 國立中央圖書館, http://www.nl.go.kr.)
  6. JING Yushu ed. Zhongguo Lidai Suanxue Jicheng, Shandong Renmin Pub. Co., 1994.(靖玉樹 編勘, <<中國歷代算學集成>>, 山東人民出版社, 1994.)
  7. WU Wenjun ed. Zhongguo Shuxueshi Daxi Vol. 8, Beijing Normal Univ. Pub. Co., 2000.(吳文俊 主編, <<中國數學史大系>> 第八卷, 北京師範大學出版社, 2000.)
  8. The Annals of the Joseon Dynasty.(朝鮮王朝實錄. http://sillok.history.go.kr)

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