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Archimedes showed that the area between a parabola and any chord AB on the parabola is four thirds of the area of triangle ∆ABP, where P is the point on the parabola at which the tangent is parallel to the chord AB. Recently, this property of parabolas was proved to be a characteristic property of parabolas. With the aid of this characterization of parabolas, using centroid of triangles associated with a curve we present two conditions which are necessary and sufficient for a strictly locally convex curve in the plane to be a parabola.
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참고문헌 (16)
참고문헌 신청
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
D.-S. Kim / 2013 / Some characterizations of spheres and elliptic paraboloids II / Linear Algebra Appl 438 (3) : 1356 ~ 1364
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
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