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It is well-known that the area of parabolic region between a parabola and any chord P1P2 on the parabola is four thirds of the area of triangle △P1P2P. Here we denote by P the point on the parabola where the tangent is parallel to the chord P1P2. In the previous works, the first and third authors of the present paper proved that this property is a characteristic one of parabolas. In this paper, with respect to triangles △P1P2Q where Q is the intersection point of two tangents to X at P1 and P2 we establish some characterization theorems for parabolas.
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참고문헌 (16)
참고문헌 신청
A. B´enyi / 2000 / Archimedean properties of parabolas / Amer. Math. Monthly 107 (10) : 945 ~ 949
A. B´enyi / 2003 / A generalized Archimedean property / Real Anal. Exchange 29 (2) : 881 ~ 889
B. Richmond / 2009 / How to recognize a parabola / Amer. Math. Monthly 116 (10) : 910 ~ 922
D.-S. Kim / 2007 / A characterization of ellipses / Amer. Math. Monthly 114 (1) : 66 ~ 70
D.-S. Kim / 2012 / Some characterizations of spheres and elliptic paraboloids / Linear Algebra Appl 437 (1) : 113 ~ 120
A. B´enyi / 2003 / A generalized Archimedean property / Real Anal. Exchange 29 (2) : 881 ~ 889
B. Richmond / 2009 / How to recognize a parabola / Amer. Math. Monthly 116 (10) : 910 ~ 922
D.-S. Kim / 2007 / A characterization of ellipses / Amer. Math. Monthly 114 (1) : 66 ~ 70
D.-S. Kim / 2012 / Some characterizations of spheres and elliptic paraboloids / Linear Algebra Appl 437 (1) : 113 ~ 120
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