삼차방정식에 관한 Omar Khayyām의 기하학적 해법의 재해석과 시각화 -항이 4개인 삼차방정식의 6가지-
Reinterpretation and visualization of Omar-Khayyam's geometric solution for the cubic equation -– 6 cases of the cubic equation with 4 terms -
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초록
This research is devoted to investigate Omar Khayyām's geometric solution for the cubic equation using conic sections in the Medieval Islam as a useful alternative connecting logic geometry with analytic geometry at a secondary school. We also introduce Omar Khayyām's 25 cases classification of the cubic equation with all positive coefficients. Moreover we study 6 cases with 4 terms of 25 cubic equations and in particular we reinterpret geometric methods of solving in 2015 secondary Mathematics curriculum and visualize them by means of dynamic geometry software.
Abstract
This research is devoted to investigate Omar Khayyām's geometric solution for the cubic equation using conic sections in the Medieval Islam as a useful alternative connecting logic geometry with analytic geometry at a secondary school. We also introduce Omar Khayyām's 25 cases classification of the cubic equation with all positive coefficients. Moreover we study 6 cases with 4 terms of 25 cubic equations and in particular we reinterpret geometric methods of solving in 2015 secondary Mathematics curriculum and visualize them by means of dynamic geometry software.
참고문헌 (11)
- "2015", ~
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- 김향숙, "해석기하학개론" (2011), 경문사
- 김향숙, "삼차방정식의 기하학적 해법에 대한 재조명과 시각화", East Asian Mathematical Journal, 34(4), pp.403~427 (2018), 영남수학회[DOI]
- 김미연, "Omar Khayyām의 원뿔곡선을 이용한 Depressed cubic equations 해법", 박사, pp.2020
- 반은섭, "삼차방정식의 기하학적 해결을 위한 수학적 지식의 연결 과정 분", 박사, pp.2016
- 반은섭, "오마르 카얌(Omar Khayyam)이 제시한 삼차방정식의 기하학적 해법의 교육적 활용", 학교수학, 18(3), pp.589~609 (2016), 대한수학교육학회
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- Sinclair, Nathalie M, "Mathematical applications of conic sections in problem solving in ancient Greece and medieval Islam", pp.1995