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)
• Published : 2015.03.31

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.

Acknowledgement

Supported by : National Research Foundation of Korea (NRF)

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