Browse > Article
http://dx.doi.org/10.7858/eamj.2021.031

Reinterpretation and visualization of Omar-Khayyam's geometric solution for the cubic equation - 6 cases of the cubic equation with 4 terms -  

Kim, Hyang Sook (Department of Computer Engineering & Institute of Natural Science Inje University)
Kim, Mi Yeoun (Department of Computer Aided Sciences Inje University)
Sim, Hyo Jung (Department of Computer Aided Sciences Inje University)
Park, Myeong Eun (Department of Computer Aided Sciences Inje University)
Publication Information
East Asian mathematical journal / v.37, no.4, 2021 , pp. 499-521 More about this Journal
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.
Keywords
the cubic equation; Omar Khayyam's geometric solution; conics; reinterpretation; 2015 secondary Mathematics curriculum; visualization; dynamic geometry software;
Citations & Related Records
연도 인용수 순위
  • Reference
1 교육부, 수학과 교육과정, 교육부 고시 제 2015-74호 [별책 8], 2015.
2 김향숙.박혜경, Biot의 원뿔곡선에 관한 conjecture의 재해석, East Asian Mathematical J. 35(2019), 141-162.
3 김향숙.박진석. 해석기하학개론[제2판]. 경문사, 2011.
4 김향숙.김양.박시은, 삼차방정식의 기하적 해법에 대한 재조명과 시각화, East Asian Mathematical J. 34(2018), 403-427.
5 반은섭, 삼차방정식의 기하학적 해결을 위한 수학적 지식의 연결 과정 분석, 한국교원대학교 박사학위논문, (2016).
6 반은섭.신재홍.류희찬, 오마르카얌(Omar Khayyam)이 제시한 삼차방정식의 기하학적 해법의 교육적 활용, 대한수학교육학회지 제18권 제3호(2016), 589-609.
7 Berggren, J. L., Episodes in the Mathematics of Medieval Islam, Springer-Verlag, New York, (1986).
8 Connor, M. G., A historical survey of methods of solving cubic equations, A thesis of master of science, Univ. of Richmond, (1956).
9 Sinclair, Nathalie M., Mathematical applications of conic sections in problem solving in ancient Greece and medieval Islam, Simon Fraser Univ, (1995).
10 Mardia, K. V., Omar Khayyam, Rene Descartes and Solution to Algebraic Equations, Omar Khayyam Club, London, (1999).
11 김미연, Omar Khayyam의 원뿔곡선을 이용한 Depressed cubic equations 해법, 인제대학교 박사학위논문, (2020).