Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2013; 50(6): 2103-2114

Printed November 1, 2013

https://doi.org/10.4134/BKMS.2013.50.6.2103

Copyright © The Korean Mathematical Society.

On the Archimedean characterization of parabolas

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