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 On the Archimedean characterization of parabolas Bull. Korean Math. Soc. 2013 Vol. 50, No. 6, 2103-2114 https://doi.org/10.4134/BKMS.2013.50.6.2103Printed November 1, 2013 Dong-Soo Kim and Young Ho Kim Chonnam National University, Kyungpook National University 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. Keywords : Archimedes, area, parabola, strictly convex curve, curvature MSC numbers : 53A04 Downloads: Full-text PDF