Division Algorithm in SuanXue QiMeng

  • Received : 2013.09.10
  • Accepted : 2013.10.20
  • Published : 2013.11.30


The Division Algorithm is known to be the fundamental foundation for Number Theory and it leads to the Euclidean Algorithm and hence the whole theory of divisibility properties. In JiuZhang SuanShu(九章算術), greatest common divisiors are obtained by the exactly same method as the Euclidean Algorithm in Elements but the other theory on divisibility was not pursued any more in Chinese mathematics. Unlike the other authors of the traditional Chinese mathematics, Zhu ShiJie(朱世傑) noticed in his SuanXue QiMeng(算學啓蒙, 1299) that the Division Algorithm is a really important concept. In [4], we claimed that Zhu wrote the book with a far more deeper insight on mathematical structures. Investigating the Division Algorithm in SuanXue QiMeng in more detail, we show that his theory of Division Algorithm substantiates his structural apporaches to mathematics.


  1. Guo ShuChun tr. comm. JiuZhang SuanShu YiZhu, ShangHai GuJi Pub. Co., 2009. (郭書春 譯注, <<九章筭術 譯注>>, 上海古籍出版社, 2009).
  2. Guo ShuChun ed. ZhongGuo KeXue JiShu DianJi TongHui ShuXueJuan, HeNanJiaoYu 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.)
  3. Hong Sung Sa, Hong Young Hee, Lee Seung On,"TianYuanShu and Numerical Systems in Eastern Asia", The Korean Journal for History of Mathematics 25(4) (2012), 1-10. (홍성사, 홍영희, 이승온, '天元術과 記數法', 한국수학사학회지, 25(4) (2012), 1-10).
  4. Hong Sung Sa, Hong Young Hee, Lee Seung On, "Mathematical Structures and Suan- Xue QiMeng", Journal for History of Mathematics 26(2-3) (2013), 123-130.

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  1. Mathematical Structures of Joseon mathematician Hong JeongHa vol.27, pp.1, 2014,