East Asian mathematical journal

  • 제37권4호
  • /
  • Pages.499-521
  • /
  • 2021
  • /
  • 1226-6973(pISSN)
  • /
  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

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 -

  • 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)
  • 투고 : 2021.06.02
  • 심사 : 2021.08.25
  • 발행 : 2021.08.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

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.

키워드

과제정보

This work was supported by 2019 Inje University research grant.

참고문헌

  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. 김미연, Omar Khayyam의 원뿔곡선을 이용한 Depressed cubic equations 해법, 인제대학교 박사학위논문, (2020).
  6. 반은섭, 삼차방정식의 기하학적 해결을 위한 수학적 지식의 연결 과정 분석, 한국교원대학교 박사학위논문, (2016).
  7. 반은섭.신재홍.류희찬, 오마르카얌(Omar Khayyam)이 제시한 삼차방정식의 기하학적 해법의 교육적 활용, 대한수학교육학회지 제18권 제3호(2016), 589-609.
  8. Berggren, J. L., Episodes in the Mathematics of Medieval Islam, Springer-Verlag, New York, (1986).
  9. Connor, M. G., A historical survey of methods of solving cubic equations, A thesis of master of science, Univ. of Richmond, (1956).
  10. Mardia, K. V., Omar Khayyam, Rene Descartes and Solution to Algebraic Equations, Omar Khayyam Club, London, (1999).
  11. Sinclair, Nathalie M., Mathematical applications of conic sections in problem solving in ancient Greece and medieval Islam, Simon Fraser Univ, (1995).