Study on the mathematics which TAKEBE brothers learned from SEKI Takakazu and the development

2014 Fiscal Year Final Research Report

• Project/Area Number: 23540126
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Ochanomizu University
• Principal Investigator: MAJIMA Hideyuki お茶の水女子大学, 大学院人間文化創成科学研究科, 教授 (50111456)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 建部賢弘 / 累遍増約術 / 円周率 / 行列式 / 関孝和 / 綴術算経 / 終結式 / 解伏題之法

Outline of Final Research Achievements

SEKI Takakazu is a Japanese mathematician in an early period of the Edo era, known as the first person to study the so-called resultant and determinant in the world. These works are found in Kai-fukudai-no-ho and Taisei-sanke. Recently, we found different versions of the Kai-fukudai-no-ho, called the Sangaku-genkun. From the documents, we can follow the process of his discovery of determinant.
SEKI Takakazu found the so-called Aitken’ s delta-sequenced process in his calculation of pi in Katsuyo-Sampo, but there were some errors in it and he only claimed that his approximate number of pi was a bit less than 3.14159265359. TAKEBE Katahiro followed Seki's method and discovered another method of calculation of pi and elavorate the true number by a little more than 40 digits written in Tetsujutsu-Sankei, Fukyu-Tetsujutsu and Kohai-Setsuyaku-Syu. We can follow the process of his discovery of the method (repeated application of the procedure of incremental divisor)of calculation of pi.

Free Research Field

数学