Approximate Solutions of Equations in Chosun Mathematics

방정식(方程式)의 근사해(近似解)

  • Hong, Sung-Sa (Department of Mathematics, Sogang University) ;
  • Hong, Young-Hee (Department of Mathematics, Sookmyung Women's University) ;
  • Kim, Chang-Il (Department of Mathematics Education, Dankook University)
  • Received : 2012.07.01
  • Accepted : 2012.08.16
  • Published : 2012.08.30

Abstract

Since JiuZhang SuanShu(九章算術), the basic field of the traditional mathemtics in Eastern Asia is the field of rational numbers and hence irrational solutions of equations should be replaced by rational approximations. Thus approximate solutions of equations became a very important subject in theory of equations. We first investigate the history of approximate solutions in Chinese sources and then compare them with those in Chosun mathematics. The theory of approximate solutions in Chosun has been established in SanHakWonBon(算學原本) written by Park Yul(1621 - 1668) and JuSeoGwanGyun(籌書管見, 1718) by Cho Tae Gu(趙泰耉, 1660-1723). We show that unlike the Chinese counterpart, Park and Cho were concerned with errors of approximate solutions and tried to find better approximate solutions.

구장산술이래 동양의 전통 수학은 유리수체를 기본으로 이루어져 있다. 따라서 방정식의 무리수해는 허용되지 않으므로 근사해를 구하는 방법은 방정식론에서 매우 중요한 과제가 되었다. 중국의 사료에 나타나는 근사해에 관한 역사를 먼저 기술하고, 이를 조선산학에 나타나는 근사해에 관한 사료와 비교한다. 조선의 근사해에 대한 이론은 박율(1621 - 1668) 의 산학원본 (算學原本) 과 조태구 (趙泰耉, 1660-1723) 의 주서관견(籌書管見)에 이미 정립되었다. 중국의 이론과 달리 두 산학자 모두 근사해의 오차에 관심을 가지고 더 좋은 근사해를 구하는 방법을 얻어내었음을 밝힌다.

References

  1. 朴繘, <算學原本>, 國立中央圖書館, 1700.
  2. 趙泰耉, <籌書管見>, 1718, 韓國科學技術史資料大系, 數學編, 2卷, 驪江出版社, 1985.
  3. 郭書春, <九章算術 譯注>, 上海古籍出版社, 2009.
  4. <中國科學技術典籍通彙> 數學卷 全五卷, 河南敎育出版社, 1993.
  5. <中國歷代算學集成> 上, 中, 下, 山東人民出版社, 1994.
  6. I. G. Bashmakova and G. S. Smirnova, The Beginnings and Evolution of Algebra, tr. A. Shenitzer, The Mathematical Association of America, 2000.
  7. U. Libbrecht, Chinese Mathematics in the Thirteenth Century, The Shu-shu chiuchang of Ch'in Chiu-shao, The MIT Press, 1973.
  8. K. Shen, J. N. Crossley, A. W.-C. Lun, The Nine Chapters on the mathematical Art, Oxford Univ. Press, 1999.
  9. Hong Sung Sa, Theory of Equations in the history of Chosun Mahtematics, Proceeding Book 2, The HPM Satellite Meeting of ICME-12, 719-731, 2012.
  10. Hong Sung Sa, Hong Young Hee, Chosun Mathematics in the early 18th century(18 世紀 初 朝鮮 算學), The Korean Journal for History of Mathematics(한국수학사학회지) 25(2012), No. 2, 1-9.
  11. Hong Sung Sa, Hong Young Hee, Kim Young Wook, Liu Yi and Hong Jung Ha's KaiFangShu(劉益과 洪正夏의 開方術), The Korean Journal for History of Mathematics(한국수학사학회지) 24(2011), No. 1, 1-13.
  12. Kim Young Wook, Hong Sung Sa, Hong Young Hee, Park Yul's SanHakWonBon(朴繘의 算學原本), The Korean Journal for History of Mathematics(한국수학사학회지) 18(2005), No. 4, 1-16.