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http://dx.doi.org/10.4134/BKMS.2015.52.2.571

CENTROID OF TRIANGLES ASSOCIATED WITH A CURVE  

Kim, Dong-Soo (Department of Mathematics Chonnam National University)
Kim, Dong Seo (Department of Mathematics Chonnam National University)
Publication Information
Bulletin of the Korean Mathematical Society / v.52, no.2, 2015 , pp. 571-579 More about this Journal
Abstract
Archimedes showed 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 the chord AB. Recently, this property of parabolas was proved to be a characteristic property of parabolas. With the aid of this characterization of parabolas, using centroid of triangles associated with a curve we present two conditions which are necessary and sufficient for a strictly locally convex curve in the plane to be a parabola.
Keywords
centroid; parabola; triangle; plane curvature; strictly locally convex curve;
Citations & Related Records
Times Cited By KSCI : 6  (Citation Analysis)
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