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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 consider whether this property and similar ones characterizes parabolas. As a result, we present three conditions which are necessary and sufficient for a strictly convex curve in the plane to be an open part of a parabola.
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참고문헌 (12)
참고문헌 신청
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
D.-S. Kim / 2013 / Some characterizations of spheres and elliptic paraboloids II / Linear Algebra Appl 438 (3) : 1356 ~ 1364
J. Krawczyk / 1995 / On areas associated with a curve / Zesz. Nauk. Uniw.Opol. Mat 29 : 97 ~ 101
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
D.-S. Kim / 2013 / Some characterizations of spheres and elliptic paraboloids II / Linear Algebra Appl 438 (3) : 1356 ~ 1364
J. Krawczyk / 1995 / On areas associated with a curve / Zesz. Nauk. Uniw.Opol. Mat 29 : 97 ~ 101
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