East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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The reinterpretation and visualization for methods of solving problem by Khayyam and Al-Kāshi for teaching the mathematical connection of algebra and geometry

대수와 기하의 수학적 연결성 지도를 위한 Khayyam과 Al-Kāshi의 문제 해결 방법 재조명 및 시각화

  • Kim, Hyang Sook (Department of Computer Engineering & Institute of Natural Science Inje University) ;
  • Park, See Eun (Department of Computer-Aided Sciences Inje University)
  • Received : 2021.02.22
  • Accepted : 2021.08.25
  • Published : 2021.08.31
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Abstract

In order to propose ways to implement mathematical connection between algebra and geometry, this study reinterpreted and visualized the Khayyam's geometric method solving the cubic equations using two conic sections and the Al-Kāshi's method of constructing of angle trisection using a cubic equation. Khayyam's method is an example of a geometric solution to an algebraic problem, while Al-Kāshi's method is an example of an algebraic a solution to a geometric problem. The construction and property of conics were presented deductively by the theorem of "Stoicheia" and the Apollonius' symptoms contained in "Conics". In addition, I consider connections that emerged in the alternating process of algebra and geometry and present meaningful Implications for instruction method on mathematical connection.

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References

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