Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Center of Gravity and a Characterization of Parabolas

  • KIM, DONG-SOO (Department of Mathematics, Chonnam National University) ;
  • PARK, SOOKHEE (Department of Mathematics, Chonnam National University) ;
  • KIM, YOUNG HO (Department of Mathematics, Kyungpook National University)
  • Received : 2014.10.29
  • Accepted : 2014.12.11
  • Published : 2015.06.23
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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 $PG=\frac{3}{5}PV$. 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.

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References

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