Mass production of Theorems of Elementary Geometry and its Application
| Project/Area Number |
12680184
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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 |
Science education
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| Research Institution | Kumamoto University |
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Principal Investigator |
OKAZAKI Hiromitsu Kumamoto University, Faculty of Education, Assistant Professor, 教育学部, 助教授 (70093995)
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| Co-Investigator(Kenkyū-buntansha) |
YAMAMOTO Sinya Kumamoto University, Faculty of Education, Professor, 教育学部, 教授 (20145402)
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| Project Period (FY) |
2000 – 2001
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| Project Status |
Completed (Fiscal Year 2001)
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| 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)
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| Keywords | elementary geometry / proof problem / inference rule / automatic proof / 初等幾何定理 |
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| 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.
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Report
(3 results)
Research Products
(3 results)
