On the Archimedean characterization of parabolas
Bull. Korean Math. Soc. 2013 Vol. 50, No. 6, 2103-2114
https://doi.org/10.4134/BKMS.2013.50.6.2103
Published online 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
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