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CENTROID OF TRIANGLES ASSOCIATED WITH A CURVE
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 Title & Authors
CENTROID OF TRIANGLES ASSOCIATED WITH A CURVE
Kim, Dong-Soo; Kim, Dong Seo;
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 Abstract
Archimedes showed that the area between a parabola and any chord AB on the parabola is four thirds of the area of triangle , 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;
 Language
English
 Cited by
1.
Center of Gravity and a Characterization of Parabolas,;;;

Kyungpook mathematical journal, 2015. vol.55. 2, pp.473-484 crossref(new window)
1.
Center of Gravity and a Characterization of Parabolas, Kyungpook mathematical journal, 2015, 55, 2, 473  crossref(new windwow)
2.
CENTROIDS AND SOME CHARACTERIZATIONS OF PARALLELOGRAMS, Communications of the Korean Mathematical Society, 2016, 31, 3, 637  crossref(new windwow)
3.
Areas associated with a Strictly Locally Convex Curve, Kyungpook mathematical journal, 2016, 56, 2, 583  crossref(new windwow)
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