2005 Fiscal Year Final Research Report Summary
Study of History of Mathematics, in particular, of Japanese Mathematics in early Edo Period and of Analysis in the Nineteenth Century
| Project/Area Number |
16540119
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
KOMATSU Hikosaburo Tokyo Univ.of Sci., Fac.of Sci.I, Professor, 理学部第一部, 教授 (40011473)
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| Co-Investigator(Kenkyū-buntansha) |
WATANABE Junsei Tokyo Gakugei Univ., Fac.of Pedag., Assistant, 教育学部, 助手 (10262221)
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| Project Period (FY) |
2004 – 2005
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| Keywords | Japanese Mathematics in the Edo Period / Seki Takakazu / Trilogy of Seki / Complete Books of Mathematics / Fourier's Theory of Heat / Scientific Documents in Manchu / Euclid / Anatomy |
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| Research Abstract |
The first step of the historical study is to read extant documents correctly. When they remain only in manuscripts, one has to collate available texts and reconstruct the original. Its importance is well recognized in the fields of Mathematics in the Edo Period and Science in Manchu in the Qing Dynasty, which are the investigators' main subjects. When the editors of the organ journal Kagakusi Kenkyu of the History of Science Society of Japan rejected the paper [1] by Komatsu et al. in 2002, one of the reasons they gave was that the paper cited "Collected Works of Seki Takakazu" which has no collation notes. Yet we do not think even an article in the "Collected Works" has ever been collated in any publications.
The main achievements of Komatsu are : first, to have collated Seki's Trilogy, "Methods of Solving Explicit Problems," "Methods of Solving Implicit Problems" and "Method of Solving Concealed Problems" and thus reconstructed the Text by Yamaji Nusizumi [2],[5] ; secondly, to have collated and interpreted about half of the twenty volumes of "Complete Books of Mathematics" by Seki and Takebe brothers. The collated texts of the eighth, nineth and tenth volumes are printed in the Final Report.
Moreover, he has shown that Fourier not only formulated his Expansion Theorem and Integrall Theorem but also proved them in his "Analytic Theory of Heat" [6].
Watanabe has studied Manchu manuscripts "suwan fa yuwan ben bithe", which is a part of "Elements," and "ge ti ciowan lu bithe," which is a book of medicine and anatomy, Romanized and translated them into English and Japanese. These may be the first substantial study in the world on these texts [7], [8].
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Research Products
(19 results)
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[Journal Article] A postscript2004
Author(s)
Hikosaburo Komatsu
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Journal Title
Surikaisekikenkyusho Kokyuroku (in Japanese) 1392
Pages: 246-248
Description
「研究成果報告書概要(欧文)」より
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