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Mass production of Theorems of Elementary Geometry and its Application

Research Project

Project/Area Number 12680184
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Science education
Research InstitutionKumamoto University

Principal Investigator

OKAZAKI Hiromitsu  Kumamoto University, Faculty of Education, Assistant Professor, 教育学部, 助教授 (70093995)

Co-Investigator(Kenkyū-buntansha) YAMAMOTO Sinya  Kumamoto University, Faculty of Education, Professor, 教育学部, 教授 (20145402)
Project Period (FY) 2000 – 2001
Project Status Completed (Fiscal Year 2001)
Budget Amount *help
¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2001: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2000: ¥600,000 (Direct Cost: ¥600,000)
Keywordselementary geometry / proof problem / inference rule / automatic proof / 初等幾何定理
Research Abstract

In our previous research, we got the computer program of the mass production of the theorems of the elementry geometry. The several inference rules, of Gentzen's logical calculus system LK were used in the program. To product the useful theorems, we need many geometrical axioms. In the mathematical textbooks of junior high school, about twenty geometrical axioms appear. But many other propositions used indirectly to prove the geometrical problems. The purpose of this research is to find those propositions and use them as the geometrical axioms. At first, we searched them in the talking and the solutions to the geometrical problems in the school lessons. Secondly, we searched them in the old textbooks whose descriptions of the geometrical proofs were precise. And we got over fifty geometrical axioms. Using these axioms, we can get the useful theorems of elementary geometry.

Report

(3 results)
  • 2001 Annual Research Report   Final Research Report Summary
  • 2000 Annual Research Report
  • Research Products

    (3 results)

All Other

All Publications (3 results)

  • [Publications] 山本信也: "トロイトラインの「幾何学的直観教授」に於ける「空間的直観能力」の養成"数学教育学研究[全国数学教育学会]. 第7号. 105-116 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Sinya Yamamoto: "The Meaning of Spatial Imagination in Geometrical Intuitive Instruction of P. Treutlein"Journal of JASME : Research in Mathematics Education. Vol.7. (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] 山本信也: "トロイトラインの「幾何学的直感教授」に於ける「空間的直感能力」"数学教育学研究〔全国数学教育学会〕. 第7号. 105-116 (2001)

    • Related Report
      2001 Annual Research Report

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Published: 2000-04-01   Modified: 2016-04-21  

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