Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON THE ARCHIMEDEAN CHARACTERIZATION OF PARABOLAS

  • Kim, Dong-Soo (Department of Mathematics Chonnam National University) ;
  • Kim, Young Ho (Department of Mathematics Kyungpook National University)
  • Received : 2013.01.24
  • Published : 2013.11.30
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Abstract

Archimedes knew that the area between a parabola and any chord AB on the parabola is four thirds of the area of triangle ${\Delta}ABP$ where P is the point on the parabola at which the tangent is parallel to AB. We consider whether this property (and similar ones) characterizes parabolas. We present five conditions which are necessary and sufficient for a strictly convex curve in the plane to be a parabola.

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References

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