和算？中算的？承？？新-以？孝和的內？法？例 = The Succession and Innovation of Wasan to Chinese Mathematics -A case study on Seki's interpolation

다국어 초록 (Multilingual Abstract)

Japanese mathematics, namely Wasan, was well-developed before the Meiji period. Seki Takakazu (1642?-1708) is the most famous one. Taking Seki's interpolation as an example, the similarities and differences are made between Wasan and Chinese mathematics. According to investigating the sources and attitudes to this problem which both Japanese and Chinese mathematicians dealt with, the paper tries to show how and why Japanese mathematicians accepted Chinese tradition and beyond. Professor Wu Wentsun says that, in the whole history of mathematics, there exist two different major trends which occupy the main stream alternately. The axiomatic deductive system of logic is the one which we are familiar with. Another, he believes, goes to the mechanical algorithm system of program. The latter featured traditional Chinese mathematics, as well as Wasan. As a typical sample of the succession of Chinese tradition, Wasan will help people to understand the real meaning of the mechanical algorithm system of program deeper.

참고문헌 (Reference)

1 小川束, "関孝和によるベルヌーィ数の發見" 京都大学数理解析研究所 1-18, 2008

2 竹之内修, "関孝和《括要算法…卷元》垜積術" 京都大学数理解析研究所 157-162, 2007

3 黄宗羲, "授时历故, 嘉业堂从书本" 1923

4 Qu Anjing, "The Cubic Interpolation in Chinese Mathematical Astronomy" 15 (15): 131-143, 1996

5 Yoshio Mikami, "Seki Takakazu’s Achievements, and Comparison and Relationship with the Algorithm of China and Yanbe of Keihan Area" (20) : 554-555, 1933

6 Feng Lisheng, "On the Structural Principle of the 3-power Interpolation in Shoushi Calendar in View of Seki’s Leicai zhaocha fa" 20 (20): 132-142, 2001

7 Wu Wentsun, "Mathematics Mechanization" Science Press, Kluwer Academic Publishers 1-66, 2000

8 Xu Zelin, "Jananese Mathemticians’Inheritance and Development to the Methord of Interpolation in Old China, In Studies in the History of Mathematics, vol. 7" Inner Mongolia University Press 124-133, 2001

9 Tsuchikura, "Invitation to History of Mathematics in East Asia—Collected Works of Fujiwara Matsusaburo on the History of Mathematics" Tohoku University Publishing House 57-72, 2007

10 Qu Anjing, "Explorations on Chinese Mathematical Astronomy" Northwest University Press 309-321, 1994

11 Hirayama, "Complete Works of Seki Takakazu—General Algorithms" Osaka Education Book Publishing House 273-282, 1974

12 Hirayama, "Complete Works of Seki Takakazu—Collected Books by Seki" Osaka Education Book Publishing House 423-464, 1974

13 China Bookstore, "Collected Monographs on Astronomy, Music and Calendars from the Dynastic Histories, vol. 10" China Bookstore 3595-3620, 1976

14 Huang Ding, "An Outline of a Glimpse of Astronomical Achievements, vol. 12" Photocopy of Laogu Cutural Campany 163-, 1984

15 Li Yan, "A Study on Interpolations of Chinese Mathematicians" Science Press 62-73, 1957

16 The Japan Academy, "A History of Japanese Mathematics before Meiji Period, vol. 2" Linchuan Bookstore 148-154, 1979

17 Qian Baocong, "A History of Chinese Mathematics" Science Press 189-197, 1964