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http://dx.doi.org/10.4134/BKMS.2013.50.6.2103

ON THE ARCHIMEDEAN CHARACTERIZATION OF PARABOLAS  

Kim, Dong-Soo (Department of Mathematics Chonnam National University)
Kim, Young Ho (Department of Mathematics Kyungpook National University)
Publication Information
Bulletin of the Korean Mathematical Society / v.50, no.6, 2013 , pp. 2103-2114 More about this Journal
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;
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