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Area of triangles associated with a curve

심규철|김동수
대한수학회 (The Korean Mathematical Society)|2014.05|대한수학회보 (Bulletin of the KMS)|제51권 제3호|pp. 901-909

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참고문헌

키워드

areatriangleparabolastrictly convex curveplane curvature
주제분류수학

초록

It is well known that the area U of the triangle formed by three tangents to a parabola X is half of the area T of the triangle formed by joining their points of contact. In this article, we study some properties of U and T for strictly convex plane curves. As a result, we establish a characterization for parabolas.

Abstract

It is well known that the area U of the triangle formed by three tangents to a parabola X is half of the area T of the triangle formed by joining their points of contact. In this article, we study some properties of U and T for strictly convex plane curves. As a result, we establish a characterization for parabolas.

참고문헌 (10)

  1. W. A. Day, "Inequalities for areas associated with conics", Amer. Math. Monthly, 98(1), pp.36~39 (1991)
  2. M. P. do Carmo, "Differential Geometry of Curves and Surfaces" (1976), Prentice-Hall
  3. 김동수, "A CHARACTERIZATION OF CONIC SECTIONS", 호남수학학술지, 33(3), pp.335~340 (2011), 호남수학회
  4. D. -S. Kim, "Some characterizations of spheres and elliptic paraboloids,", Linear Algebra Appl, 437(1), pp.113~120 (2012)
  5. D. -S. Kim, "Some characterizations of spheres and elliptic paraboloids II", Linear Algebra Appl, 438(3), pp.1356~1364 (2013)
  6. 김동수, "On the Archimedean characterization of parabolas", 대한수학회보, 50(6), pp.2103~2114 (2013), 대한수학회
  7. 김동수, "Some Characterizations of Parabolas", Kyungpook Mathematical Journal, 53(1), pp.99~104 (2013), 경북대학교 자연과학대학 수학과
  8. J. Krawczyk, "On areas associated with a curve", Zesz. Nauk. Uniw. Opol. Mat, 29, pp.97~101 (1995)
  9. B. Richmond, "How to recognize a parabola", Amer. Math. Monthly, 116(10), pp.910~922 (2009)
  10. S. Stein, "Archimedes. What did he do besides cry Eureka?" (1999), Mathematical Association of America

관련 논문AI추천

Area of triangles associated with a curve II김동수, 김영호, Dae Heui Park, Wonyong Kim대한수학회 · 대한수학회보2015 · 제52권 제1호Areas associated with a Strictly Locally Convex Curve김동서, 김동수, 김영호, 배현선경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제2호ON TRIANGLES ASSOCIATED WITH A CURVE김동서, 김동수, 김영호대한수학회 · 대한수학회보2015 · 제52권 제3호Area properties associated with strictly convex curves김동수, 김인천, 방신옥대한수학회 · 대한수학회보2022 · 제59권 제2호CENTROID OF TRIANGLES ASSOCIATED WITH A CURVE김동서, 김동수대한수학회 · 대한수학회보2015 · 제52권 제2호Some Characterizations of Parabolas김동수, 김영호, 박종호경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2013 · 제53권 제1호

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