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;
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 . 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.
Archimedes;center of gravity;area;parabolic section;locally strictly convex curve;curvature;