2001 Fiscal Year Final Research Report Summary

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 Type	Single-year Grants
Section	一般
Research Field	Science education
Research Institution	Kumamoto 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
Keywords	elementary geometry / proof problem / inference rule / automatic proof
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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