Indefinite Problem in Wasan


  • Received : 2013.11.03
  • Accepted : 2013.11.28
  • Published : 2013.11.30


Japanese mathematics, namely Wasan, was well-developed before the Meiji period. Takebe Katahiro (1664-1739) and Nakane Genkei (1662-1733), among a great number of mathematicians in Wasan, maybe the most famous ones. Taking Takebe and Nakane's indefinite problems as examples, the similarities and differences are made between Wasan and Chinese mathematics. According to investigating the sources and attitudes to these problems which both Japanese and Chinese mathematicians dealt with, the paper tries to show how and why Japanese mathematicians accepted Chinese tradition and beyond. As a typical sample of the succession of Chinese tradition, Wasan will help people to understand the real meaning of Chinese tradition deeper.


  1. Hua Luogeng, A Story on the ratio of a circle's circumference to its diameter by Zu Chongzhi, Hua Luogeng's collection of scientific works, Shanghai: Shanghai Jiaoyu Publishing Co., 1984, 47-80. (华罗庚, 从祖冲之的圆周率谈起, 华罗庚科普著作选集, 上海: 上海 教育出版社, 1984, 47-80.)
  2. Li Jimin, Interpretation of "TongGiLu", History of Chinese Mathematics Lunwen Ji, vol. 1, Jinan: Shandong Jiaoyu Publishing Co., 1985, 24-36. (李继闵, "通其率"考释, 中国数学 史论文集(1), 济南: 山东教育出版社, 1985, 24-36.)
  3. The Japan Academy ed., A History of Japanese Mathematics before Meiji Period, vol. 2, Tokyo: Linchuan Bookstore, 1979, 310-318. (日本学士院编, 明治前日本数学史(2), 东京: 临川 书店, 1979, 310-318.)
  4. Qu Anjing, Chinese Astronomy and Mathematics, Beijing, Science Publishing Co., 2005. (曲安京, 中国历法与数学, 北京, 科学出版社, 2005, 74-91.)
  5. Qu Anjing, "The Succession and Innovation of Wasan to Chinese Mathematics -A case study on Seki's interpolation", Journal for History of Mathematics 26(4) (2013), 219-232. (曲安京. 和算对中算的继承与创新-以关孝和的内插法为例. Journal for History of Mathematics 26(4) (2013), 219-232.)
  6. Takebe Katahiro, The Method of Successive Divisions, possession of Tohoku University Library. (建部贤弘, 累约术, (日本) 东北大学图书馆藏, 冈本文库写)0304.
  7. Tamotsu Tsuchikura, The Method of Successive Divisions by Takebe Katahiro and Nakane Genkei, Knobloch, Komatsu, Liu (ed.). Seki, Founder of Modern Mathematics in Japan. Tokyo: Springer, 2013, 343-352.
  8. Tsuchikura, et al. ed., Invitation to History of Mathematics in East Asia-Collected Works of Fujiwara Matsusaburo on the History of Mathematics, Sendai: Tohoku University Publishing House, 2007, 21-30. (土倉保等编, 東洋数学史への招待ー藤原松三郎数学史論文集, 仙台: 東北大学出版会, 2007, 21-30.)
  9. Wu Wentsun, Mathematics Mechanization, Beijing: Science Press & Dordrecht: Kluwer Academic Publishers, 2000, 1-66.