Center of Gravity and a Characterization of Parabolas

• Journal title : Kyungpook mathematical journal
• Volume 55, Issue 2,  2015, pp.473-484
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2015.55.2.473
Title & Authors
Center of Gravity and a Characterization of Parabolas
KIM, DONG-SOO; PARK, SOOKHEE; KIM, YOUNG HO;

Abstract
Archimedes determined the center of gravity of a parabolic section as follows. For a parabolic section between a parabola and any chord AB on the parabola, let us denote by P the point on the parabola where the tangent is parallel to AB and by V the point where the line through P parallel to the axis of the parabola meets the chord AB. Then the center G of gravity of the section lies on PV called the axis of the parabolic section with $\small{PG=\frac{3}{5}PV}$. In this paper, we study strictly locally convex plane curves satisfying the above center of gravity properties. As a result, we prove that among strictly locally convex plane curves, those properties characterize parabolas.
Keywords
Archimedes;center of gravity;area;parabolic section;locally strictly convex curve;curvature;
Language
English
Cited by
1.
CENTROID OF TRIANGLES ASSOCIATED WITH A CURVE,;;

대한수학회보, 2015. vol.52. 2, pp.571-579
1.
CENTROIDS AND SOME CHARACTERIZATIONS OF PARALLELOGRAMS, Communications of the Korean Mathematical Society, 2016, 31, 3, 637
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