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Global Mathematical Arts in 13th Century Influenced on Japanese Mathematics

Research Project

Project/Area Number 16K01162
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Sociology/History of science and technology
Research InstitutionOsaka Kyoiku University

Principal Investigator

Jochi Shigeru  大阪教育大学, グローバルセンター, 教授 (00571283)

Research Collaborator Liu Bowen  
Project Period (FY) 2016-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Keywords科学技術史 / 数学史 / 和算 / 「古代」と「近世」 / 東アジア / 李氏朝鮮 / 台湾 / 算木数学 / 珠算数学 / 『楊輝算法』 / 『算法統宗』 / 方陣 / 『指明算法』 / 天文学史 / 暦算
Outline of Final Research Achievements

In 13th century,Chinese mathematicians studied high degree equations,that is to say, "Tianyuan-shu" and solving method of them. They used "counting rods”, thus it was the last era of the“ancient are”. In other hands, the 15-17th century, Southern Chinese mathematicians used abacus, studied merchants'mathematics.
Because the "Yang Hui Suanfa" was used the "counting rods", therefore it must be the ancient era. We, however,discovered some version of "Yang Hui Suanfa" at south Korean, and Korean mathematicians in the pre-modern age proofread it. They studied not only the "Yang Hui Suanfa" for the classical mathematical arts, but also studied it as the highest mathematical science. Seki Takakazu (1645?-1708) also proofread the "Yang Hui Suanfa", but his method was not the same as Korean mathematicians (Yonsei University, rear book no. (1) 510). We conclude that Eastern mathematicians studied the "Yang Hui Suanfa", as the highest mathematical science for the pre-modern era.

Academic Significance and Societal Importance of the Research Achievements

13世紀に起こった中国数学は、古代の完成形ではなく、ユーラシア大陸にまたがる文明の成立による新たな数学の誕生と言える。
近世日本の寺子屋で学ばれた鶴亀算は、同じ問題が古代の『孫子算経』(孫子、5世紀頃)にあるが解き方は異なっている。さらに、建部賢弘(1664-1739)は『算学啓蒙』(朱世傑、1299年)に注釈を行い、近世数学を完成させている。しかし、数学の進歩という観点だけではなく、古代数学を超克する態度をもつものとして、「近世」数学は13世紀から始まったものと言える。『楊輝算法』(楊輝、1275年)の開方法(高次方程式の解法)、『算学啓蒙』の天元術が挙げられる。

Report

(4 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (34 results)

All 2018 2017 2016 Other

All Int'l Joint Research (3 results) Journal Article (11 results) (of which Int'l Joint Research: 5 results,  Peer Reviewed: 8 results,  Open Access: 10 results,  Acknowledgement Compliant: 5 results) Presentation (13 results) (of which Int'l Joint Research: 4 results,  Invited: 2 results) Book (1 results) Remarks (3 results) Funded Workshop (3 results)

  • [Int'l Joint Research] 台湾大学(その他の国・地域)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] 台湾大学/台湾・教育部(文部科学省に相当)(台湾)

    • Related Report
      2017 Research-status Report
  • [Int'l Joint Research] 台湾大学(台湾)

    • Related Report
      2016 Research-status Report
  • [Journal Article] 朝鮮木版本『楊輝算法』の考察-高麗大学校木版本の発見をふまえて2018

    • Author(s)
      城地 茂
    • Journal Title

      京都大学数理解析研究所講究録(別冊)

      Volume: B69 Pages: 219-228

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] 台湾大学蔵『続神壁算法評林』(会田安明、1807年)と算額2018

    • Author(s)
      城地 茂・Liu Bowen
    • Journal Title

      京都大学数理解析研究所講究録(別冊)

      Volume: B69 Pages: 99-108

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] 大学予科教育からみた台湾大学の和算書2018

    • Author(s)
      城地 茂
    • Journal Title

      国際センター年報

      Volume: 22 Pages: 12-16

    • Related Report
      2018 Annual Research Report
  • [Journal Article] 朝鮮木版本『楊輝算法』の考察 -高麗大学校木版本の発見をふまえて2018

    • Author(s)
      城地茂
    • Journal Title

      (京都大学)数理解析研究所講究録

      Volume: B69 Pages: 218-228

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] 台湾大学蔵『続神壁算法評林』(会田安明、1807 年)と算額2018

    • Author(s)
      城地茂・Liu Bowen
    • Journal Title

      (京都大学)数理解析研究所講究録

      Volume: B69 Pages: 99-108

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] 大学予科教育からみた台湾大学の和算書2018

    • Author(s)
      城地茂
    • Journal Title

      (大阪教育大学)国際センター年報

      Volume: 22 Pages: 12-16

    • Related Report
      2017 Research-status Report
    • Open Access
  • [Journal Article] 『楊輝算法』(1275年)の関孝和写本(1661年)と延世大学校写本2017

    • Author(s)
      城地茂・Liu Bowen
    • Journal Title

      (京都大学)数理解析研究所講究録・別冊

      Volume: 印刷中

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] 台湾大学蔵『続神壁算法評林』 (会田安明、1708年)と算額2017

    • Author(s)
      城地茂・Liu Bowen
    • Journal Title

      (京都大学)数理解析研究所講究録・別冊

      Volume: 印刷中

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] 台湾の小学校における円周率の教育と数学史2017

    • Author(s)
      城地茂
    • Journal Title

      (大阪教育大学)国際センター年報

      Volume: 21 Pages: 15-21

    • Related Report
      2016 Research-status Report
    • Open Access / Acknowledgement Compliant
  • [Journal Article] 朝鮮木版本『楊輝算法』の考察 高麗大学校本と延世大学校本2017

    • Author(s)
      城地茂
    • Journal Title

      (京都大学)数理解析研究所講究録・別冊

      Volume: 印刷中

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] 格子乗算の起源2017

    • Author(s)
      城地茂・張耀祖・Chang Hao, Liu Bowen
    • Journal Title

      (京都大学)数理解析研究所講究録・別冊

      Volume: 印刷中

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Presentation] 『算法諸約術』(斎藤元章、1805年)と三河・由精堂和算塾(?-1882年?)2018

    • Author(s)
      城地 茂
    • Organizer
      第14回全国和算研究大会(佐野)
    • Related Report
      2018 Annual Research Report
  • [Presentation] 台湾へ渡った和算書2018

    • Author(s)
      城地 茂
    • Organizer
      2018年度 日本科学史学会年会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 國立台灣大學之和算(日本數學)資料初探2017

    • Author(s)
      城地茂
    • Organizer
      第十一屆科學史研討會
    • Place of Presentation
      台湾・南台科技大学
    • Year and Date
      2017-03-27
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] The Influence of Chinese Mathematics on Japanese Mathematics and the Epoch of Japanese Mathematics2017

    • Author(s)
      Shigeru Jochi
    • Organizer
      25th ICHST
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] 『九章算術』(1世紀)「開不尽法」 と会田安明『算法零約術』(19世紀)2017

    • Author(s)
      城地茂
    • Organizer
      京都大学数理解析研究所研究集会
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] 台北帝国大学数学教室と加藤平左ヱ門教授の和算書2017

    • Author(s)
      城地茂
    • Organizer
      日本科学史学会年会
    • Related Report
      2017 Research-status Report
  • [Presentation] 和算における無限の概念について2017

    • Author(s)
      城地茂
    • Organizer
      和算教材化研究会
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] 会田安明『算法零約術坤之巻』と無理数2017

    • Author(s)
      城地茂
    • Organizer
      第13回全国和算研究大会
    • Related Report
      2017 Research-status Report
  • [Presentation] Prof. Kato Heizaemon and His Studies of Wasan at Taihoku (Taibei) Imperial University2016

    • Author(s)
      Jochi Shigeru
    • Organizer
      INTERNATIONAL SYMPOSIUM ON THE HISTORY OF MATHEMATICS IN EAST ASIA (ISHMEA)-II-6
    • Place of Presentation
      けいはんなプラザ
    • Year and Date
      2016-11-10
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 会田安明による算額問題の評価2016

    • Author(s)
      城地茂
    • Organizer
      日本数学会・2016年度秋季総合分科会
    • Place of Presentation
      関西大学
    • Year and Date
      2016-09-15
    • Related Report
      2016 Research-status Report
  • [Presentation] 台湾大学蔵、『続神壁算法評林』(会田安明、1708年)と算額2016

    • Author(s)
      城地茂・Liu Bowen
    • Organizer
      RIMS研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2016-08-29
    • Related Report
      2016 Research-status Report
  • [Presentation] 『楊輝算法』と朝鮮銅活字印刷技術2016

    • Author(s)
      城地茂
    • Organizer
      日本科学史学会2016年総会
    • Place of Presentation
      工学院大学
    • Year and Date
      2016-05-28
    • Related Report
      2016 Research-status Report
  • [Presentation] 会田安明『続神壁算法評林』について2016

    • Author(s)
      城地茂
    • Organizer
      日本数学史学会2016年度年総会
    • Place of Presentation
      同志社大学
    • Related Report
      2016 Research-status Report
  • [Book] The study of the history of mathematics 20162018

    • Author(s)
      Shigeru Jochi (ed.)
    • Total Pages
      226
    • Publisher
      RIMS, Kyoto University
    • Related Report
      2018 Annual Research Report
  • [Remarks] 日本数学・天文学史

    • URL

      http://www.osaka-kyoiku.ac.jp/%7Ejochi/

    • Related Report
      2018 Annual Research Report
  • [Remarks] 日本科学技術史

    • URL

      http://www.osaka-kyoiku.ac.jp/%7Ejochi/

    • Related Report
      2017 Research-status Report
  • [Remarks] 日本数学史・天文学史

    • URL

      http://www.osaka-kyoiku.ac.jp/~jochi/

    • Related Report
      2016 Research-status Report
  • [Funded Workshop] RIMS Workshop, the study of the history of mathematics2018

    • Related Report
      2018 Annual Research Report
  • [Funded Workshop] The Study of the Hisitory of Mathematics, 2017 RIMS2017

    • Related Report
      2017 Research-status Report
  • [Funded Workshop] RIMS研究集会2016

    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2016-08-29
    • Related Report
      2016 Research-status Report

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Published: 2016-04-21   Modified: 2022-02-22  

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