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Methods and Logic of Mathematics in Pre-modern Japan

Research Project

Project/Area Number 22540155
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionYokkaichi University

Principal Investigator

OGAWA Tsukane  四日市大学, 環境情報学部, 教授 (90204081)

Co-Investigator(Kenkyū-buntansha) MORIMOTO Mitsuo  四日市大学, 関孝和数学研究所, 副所長 (80053677)
Project Period (FY) 2010-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords関孝和 / 建部賢弘 / 建部賢明 / 大成算経 / 至誠賛化流 / 同文算指 / 日本数学史 / 国際研究者交流(中国,韓国) / 近世日本数学史 / 淇澳集 / 円理
Outline of Final Research Achievements

Analyzing the annual reports of the Shisei Sanka school, the "Kiou Shu," which include a lot of problems proposed by the pupils, I confirmed that they had tried to maintain their prestige by collecting difficult problems but there had been no remarkable development in their mathematical skill. It means that they enjoyed mathematics as a stereotypical hobby only.
The representative mathematicians in pre-modern Japan, Seki Takakazu, Takebe Katahiro, and Takebe Kataakira, revealed their view of mathematics and a lot of mathematical arts in their 20 volumes of the "Taisei Sankei". But it is very difficult to understand their work because they lacked the mathematical language or means to describe their mathematics. I analyzed several volumes of this work in detail to determine this clearly.
As for the "Collected Works of Seki Takakazu", which will be published by Iwanami Shoten, I read some of his Chinese writings in Japanese and translated them into modern Japanese.

Report

(6 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Annual Research Report
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (34 results)

All 2015 2014 2013 2012 2011 2010

All Journal Article (8 results) (of which Peer Reviewed: 1 results) Presentation (22 results) (of which Invited: 4 results) Book (4 results)

  • [Journal Article] 『大成算経』の畸零について2013

    • Author(s)
      小川束
    • Journal Title

      九州数学史シンポジウム講演記録集

      Volume: 2 Pages: 1-8

    • Related Report
      2012 Annual Research Report
  • [Journal Article] 『淇澳集』における解法の構造について2012

    • Author(s)
      小川束
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1787 Pages: 156-168

    • Related Report
      2012 Annual Research Report
  • [Journal Article] Mathematical Treatise on the Technique of Linkage: An Annotated English Translation of Takebe Katahiro's Tetsujutsu Sankei Preserved in the National Archives of Japan2012

    • Author(s)
      Morimoto Mitsuo
    • Journal Title

      SCIAMVS

      Volume: 13 Pages: 157-286

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] ユークリッドの互除法の珠算への応用2011

    • Author(s)
      小川束
    • Journal Title

      数学文化

      Volume: 16 Pages: 22-36

    • Related Report
      2011 Annual Research Report
  • [Journal Article] 珠算による江戸時代の無限級数の再現にむけて2011

    • Author(s)
      小川束
    • Journal Title

      数学文化

      Volume: 16 Pages: 56-63

    • Related Report
      2011 Annual Research Report
  • [Journal Article] 加賀の数学者・和田耕藏の著作2011

    • Author(s)
      森本光生
    • Journal Title

      和算研究所紀要

      Volume: 11 Pages: 3-9

    • Related Report
      2010 Annual Research Report
  • [Journal Article] 至誠賛化流と『起原解』について2010

    • Author(s)
      小川束
    • Journal Title

      数理解析研究所講究録

      Volume: 1677 Pages: 1-9

    • Related Report
      2010 Annual Research Report
  • [Journal Article] 算学啓蒙重注の著者2010

    • Author(s)
      森本光生
    • Journal Title

      数理解析研究所講究録

      Volume: 1677 Pages: 63-72

    • Related Report
      2010 Annual Research Report
  • [Presentation] Historical Documents for dedicating a Mathematical Plate to Sojiji Temple2015

    • Author(s)
      OGAWA Tsukane
    • Organizer
      International Symposium on the History of Mathematics in East Asia
    • Place of Presentation
      Hotel Kintetsu Aquavilla Ise-Shima
    • Year and Date
      2015-03-06 – 2015-03-09
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 『大成算経』に蒐集された珠算法2014

    • Author(s)
      小川束
    • Organizer
      数学協会
    • Place of Presentation
      東京大学
    • Year and Date
      2014-09-14
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 建部賢弘の数学思想再訪2014

    • Author(s)
      小川束
    • Organizer
      京都大学数理解析研究所集会「数学史の研究」
    • Place of Presentation
      京都大学
    • Year and Date
      2014-09-01 – 2014-09-04
    • Related Report
      2014 Annual Research Report
  • [Presentation] Takebe Katahiro --- a Man of his Time: His Life and Mathematical Thought2014

    • Author(s)
      OGAWA Tsukane
    • Organizer
      Takebe Conference 2014
    • Place of Presentation
      御茶の水女子大学
    • Year and Date
      2014-08-25 – 2014-08-30
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 建部賢弘とそろばん2014

    • Author(s)
      小川束
    • Organizer
      数学協会
    • Place of Presentation
      大東文化大学
    • Year and Date
      2014-06-01
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 至誠賛化流の数学2014

    • Author(s)
      小川束
    • Organizer
      東アジア数学史国際研究集会(第II期第2回)
    • Place of Presentation
      京都大学人文科学研究所
    • Related Report
      2013 Annual Research Report
  • [Presentation] 『割算書』「金かねかへの分」の新解釈2013

    • Author(s)
      小川束
    • Organizer
      京都大学数理解析研究所研究集会「数学史の研究」
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Annual Research Report
  • [Presentation] Mathematics in the Shisei-Sanka(至誠賛化)School2013

    • Author(s)
      小川束
    • Organizer
      The Second International Symposium for the History of Mathematics in East Asia
    • Place of Presentation
      京都大学人文科学研究所
    • Related Report
      2012 Annual Research Report
  • [Presentation] 『大成算経』の「雑技」について2012

    • Author(s)
      小川束
    • Organizer
      京都大学数理解析研究所研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2012-02-10
    • Related Report
      2011 Annual Research Report
  • [Presentation] 至誠賛化流の幾何学2012

    • Author(s)
      小川束
    • Organizer
      京都大学数理解析研究所研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2012 Annual Research Report
  • [Presentation] Clavius's Epitome Arithmeticae Practicae and the Tongwen Suanzhi2011

    • Author(s)
      小川束
    • Organizer
      The 5^<th> International Symposium on Ancient Chinese Boos and Records of Science and Technology
    • Place of Presentation
      Tsinghua University
    • Year and Date
      2011-09-24
    • Related Report
      2011 Annual Research Report
  • [Presentation] 『淇澳集』における解法の構造について2011

    • Author(s)
      小川束
    • Organizer
      京都大学数理解析研究所研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2011-08-23
    • Related Report
      2011 Annual Research Report
  • [Presentation] 『大成算経』の数第三を論ず2011

    • Author(s)
      小川束
    • Organizer
      International Program for a Study of the History of Mathematics in East Asia
    • Place of Presentation
      前橋工科大学
    • Year and Date
      2011-03-09
    • Related Report
      2010 Annual Research Report
  • [Presentation] 『大成算経』前集に関する初歩的考察2011

    • Author(s)
      森本光生
    • Organizer
      International Program for a Study of the History of Mathematics in East Asia
    • Place of Presentation
      前橋工科大学
    • Year and Date
      2011-03-09
    • Related Report
      2010 Annual Research Report
  • [Presentation] 『大成算経』の数学思想-象形思想の系譜2011

    • Author(s)
      小川束
    • Organizer
      九州数学史シンポジウム
    • Place of Presentation
      九州大学大学院数理学研究院
    • Year and Date
      2011-02-15
    • Related Report
      2010 Annual Research Report
  • [Presentation] 建部賢弘の数学観2011

    • Author(s)
      森本光生
    • Organizer
      九州数学史シンポジウム
    • Place of Presentation
      九州大学大学院数理学研究院
    • Year and Date
      2011-02-14
    • Related Report
      2010 Annual Research Report
  • [Presentation] 近世日本数学の方法と論理2010

    • Author(s)
      小川束
    • Organizer
      京都大学数理解析研究所研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-08-25
    • Related Report
      2010 Annual Research Report
  • [Presentation] 建部賢弘の数学哲学2010

    • Author(s)
      森本光生
    • Organizer
      RIMS研究集会「数学史の研究」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-08-23
    • Related Report
      2010 Annual Research Report
  • [Presentation] Methods and Logic in Traditional Japanese Mathematics2010

    • Author(s)
      小川束
    • Organizer
      International Conference on the History of Modern Mathematics 1800-1930
    • Place of Presentation
      Northwest University, Xi'an, China (中国、西安、西北大学)
    • Year and Date
      2010-08-16
    • Related Report
      2010 Annual Research Report
  • [Presentation] Mathematical Philosophy of Takebe Katahiro2010

    • Author(s)
      森本光生
    • Organizer
      International Conference on the History of Modern Mathematics 1800-1930
    • Place of Presentation
      Northwest University, Xi'an, China (中国、西安、西北大学)
    • Year and Date
      2010-08-12
    • Related Report
      2010 Annual Research Report
  • [Presentation] Three Essentials of Takebe Katahiro2010

    • Author(s)
      森本光生
    • Organizer
      The 7^<th> International Symposium on the History of Mathematics and Mathematical Education Using Chinese Characters (ISHME7)
    • Place of Presentation
      中国、内蒙古、フフホト、内蒙古師範大学科学技術史研究院
    • Year and Date
      2010-08-07
    • Related Report
      2010 Annual Research Report
  • [Presentation] 大成算経巻之四三要について2010

    • Author(s)
      森本光生
    • Organizer
      日本数学史学会年会
    • Place of Presentation
      同志社大学今出川キャンパス寧静館
    • Year and Date
      2010-05-23
    • Related Report
      2010 Annual Research Report
  • [Book] 数学史の研究2015

    • Author(s)
      小川束(編者)
    • Total Pages
      259
    • Publisher
      京都大学数理解析研究所
    • Related Report
      2014 Annual Research Report
  • [Book] 江戸時代の数学最前線2014

    • Author(s)
      小川束・森本光生
    • Total Pages
      223
    • Publisher
      技術評論社
    • Related Report
      2014 Annual Research Report
  • [Book] 和算でわかる行列式ーー江戸時代の数学最前線2014

    • Author(s)
      小川束,森本光生
    • Total Pages
      230
    • Publisher
      技術評論社
    • Related Report
      2013 Annual Research Report
  • [Book] 発微算法2011

    • Author(s)
      小川束
    • Total Pages
      54
    • Publisher
      研成社
    • Related Report
      2010 Annual Research Report

URL: 

Published: 2010-08-23   Modified: 2019-07-29  

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