Pappus가 보인 일반각의 3등분문제 해결의 재조명과 시각화
The Reinterpretation and the Visualization of Pappus’ methods for Trisecting the Angle
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The purpose of this paper is to reinterpret and visualize Pappus’ methods for trisecting the angle by utilizing the Nicomedes’ conchoid and Apollonius’ symptom of a hyperbola. In particular, we reinterpret the Pappus’ three results which are the methods of hyperbola and circle, the trisection of the arc and focus and directrix of the hyperbola by 3 steps(analysis, construction, and proof) in the current middle school curriculum of Mathematics. Moreover, we visualize the construction of an hyperbola which is represented by means of an eccentricity.
Abstract
The purpose of this paper is to reinterpret and visualize Pappus’ methods for trisecting the angle by utilizing the Nicomedes’ conchoid and Apollonius’ symptom of a hyperbola. In particular, we reinterpret the Pappus’ three results which are the methods of hyperbola and circle, the trisection of the arc and focus and directrix of the hyperbola by 3 steps(analysis, construction, and proof) in the current middle school curriculum of Mathematics. Moreover, we visualize the construction of an hyperbola which is represented by means of an eccentricity.
참고문헌 (12)
- 김향숙, "이차곡선을 활용한 정칠각형에 관한 Abū Sahl의 작도법의 GSP를 통한 재조명", 수학교육, 50(2), pp.233~246 (2011), 한국수학교육학회
- 김향숙, "원뿔곡선에 관한 Apollonius의 Symptoms 재조명과 시각화", 수학교육, 52(1), pp.83~95 (2013), 한국수학교육학회
- 김향숙, "중세 이슬람이 보인 입방배적문제 해결방법들의 재조명과 시각화", East Asian Mathematical Journal, 30(2), pp.173~195 (2014), 영남수학회[DOI]
- 박진석, "해석기하학개론" (2011), 경문사
- 박진석, "수학사와 함께 떠나는 수학여행" (2017), 경문사
- 하형수, "원뿔曲線을 활용한 作圖不能問題의 再解析과 視覺化", pp.2017
- Berggren, J. L., "Episodes in the Mathematics of Medieval Islam" (1986), Springer-Verlag
- Heath, T. L., "Apollonius of Perga : Treatise on conic sections-The conics of Apollonius" (1896), university press
- Hogendijk, J. P., "On the trisection of an angle and the construction of a regular nonagon by means of conic sections in medieval Islamic geometry", the 2nd International Symposium of the History of Arabic Science (1979)
- Knorr, W., "Textual Studies in ancient and medieval geometry" (1990), Birkhauser
- Sinclair, Nathalie M., "Mathematical applications of conic sections in problem solving in ancient Greece and medieval Islam", pp.1995