Center of Gravity and a Characterization of Parabolas

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 axi...

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Veröffentlicht in:Kyungpook mathematical journal 2015, 55(2), , pp.473-484
Hauptverfasser: KIM, DONG-SOO, PARK, SOOKHEE, KIM, YOUNG HO
Format: Artikel
Sprache:eng
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Zusammenfassung: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 PG = 3 5PV . 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. KCI Citation Count: 10
ISSN:1225-6951
0454-8124
DOI:10.5666/KMJ.2015.55.2.473