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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)
  • Received : 2014.03.14
  • 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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  2. CENTROIDS AND SOME CHARACTERIZATIONS OF PARALLELOGRAMS vol.31, pp.3, 2016, https://doi.org/10.4134/CKMS.c150165
  3. Areas associated with a Strictly Locally Convex Curve vol.56, pp.2, 2016, https://doi.org/10.5666/KMJ.2016.56.2.583
  4. Various centroids and some characterizations of catenary rotation hypersurfaces vol.42, pp.13036149, 2018, https://doi.org/10.3906/mat-1703-61