Solving Sangaku: A Traditional Solution to a Nineteenth Century Japanese Temple Problem

다국어 초록 (Multilingual Abstract)

This paper demonstrates how a nineteenth century Japanese votive temple problem known as sangaku from Okayama prefecture can be solved using traditional mathematical methods of the Japanese Edo (1603–1868 CE). We compare a modern solution to a sangaku problem from Sacred Geometry: Japanese Temple Problems of Tony Rothman and Hidetoshi Fukagawa with a traditional solution of Ōhara Toshiaki (?–1828).
Our investigation into the solution of Ōhara provides an example of traditional Edo period mathematics using the tenzan jutsu symbolic manipulation method, as well as producing new insights regarding the contextual nature of the rules of this technique.

참고문헌 (Reference)

1 大原利明, "算法点竄指南" 早稲田大古典籍総合データベース 1810

2 下平和夫, "日本人の数学: 和算" 和算, 河出書房新社 1972

3 A. Hirayama, "平山諦, 学術を中心とした和算史上の人々" 富士短期大学出版部 1965

4 Kanchō Betsu Kanpō Shūroku, "官庁別官報輯録" 技報堂 1994

5 E. Kiritani, "Vanishing Japan: Traditions, Crafts and Culture" Tuttle Publishing 1995

6 F. Soddy, "The bowl of integers and the hexlet" 139 : 77-79, 1927

7 M. Morimoto, "The Suanxue Qimen and Its Influence on Japanese Mathematics, Seki, Founder of Modern Mathematics in Japan. A Commemoration on His Tercentenary" 39 : 119-132, 2013

8 O. Bottema, "The Malfatti problem" 1 : 43-50, 2001

9 P. J. Lu, "The Blossoming of Japanese Mathematics" 454 : 2008

10 Y. Aida, "Sanpo Tenshoho Shinan"

11 T. Rothman, "Sacred Mathematics—Japanese Temple Geometry" Princeton University Press 2008

12 S. Shio, "Prohibition of Import of Certain Chinese Books and the Policy of the Edo Government" 57 (57): 290-303, 1937

13 M. Morimoto, "Mathematical Treatise on Technique of Linkage : An Annotated English Translation of Takebe Katahiro’s Tetsujutsu Sankei" 13 : 157-286, 2012

14 I. Reader, "Letters to the Gods: The Form and Meaning of Ema" 18 (18): 23-50, 1991

15 H. Fukagawa, "Japanese Temples Geometry Problems: San Gaku" Charles Babbage Research Foundation 1989

16 H. Kotera, "Japanese Temple Geometry Problem Sangaku"

17 T. Rothman, "Japanese Temple Geometry" 278 (278): 84-91, 1997

18 J. Robertson, "Emagined Community : Votive Tablets(ema)and Strategic Ambivalence in Wartime Japan" 67 (67): 43-77, 2008

19 J. Winter, "East Asian Paintings: Materials, Structures and Deterioration Mechanisms" Archetype Publications 2008

20 K. Shimodaira, "Charles Scribner’s Sons" Detroit 2008

21 N. Dershowitz, "Calendrical Calculations" Cambridge University Press 2008

22 J. Casey, "A Sequel to Euclid" Hodges, Figgis, and Co. 1881

23 D. E. Smith, "A History of Japanese Mathematics" Cosimo, Inc 2000