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ON THE ARCHIMEDEAN CHARACTERIZATION OF PARABOLAS
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 Title & Authors
ON THE ARCHIMEDEAN CHARACTERIZATION OF PARABOLAS
Kim, Dong-Soo; Kim, Young Ho;
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 Abstract
Archimedes knew 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 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;
 Language
English
 Cited by
1.
AREA OF TRIANGLES ASSOCIATED WITH A CURVE,;;

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AREA OF TRIANGLES ASSOCIATED WITH A CURVE II,;;;;

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3.
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ON TRIANGLES ASSOCIATED WITH A CURVE,;;;

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Center of Gravity and a Characterization of Parabolas,;;;

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7.
Areas associated with a Strictly Locally Convex Curve,;;;;

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8.
CENTROIDS AND SOME CHARACTERIZATIONS OF PARALLELOGRAMS,;;;;;;;

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1.
Center of Gravity and a Characterization of Parabolas, Kyungpook mathematical journal, 2015, 55, 2, 473  crossref(new windwow)
2.
AREA OF TRIANGLES ASSOCIATED WITH A CURVE, Bulletin of the Korean Mathematical Society, 2014, 51, 3, 901  crossref(new windwow)
3.
CENTROIDS AND SOME CHARACTERIZATIONS OF PARALLELOGRAMS, Communications of the Korean Mathematical Society, 2016, 31, 3, 637  crossref(new windwow)
4.
CENTROID OF TRIANGLES ASSOCIATED WITH A CURVE, Bulletin of the Korean Mathematical Society, 2015, 52, 2, 571  crossref(new windwow)
5.
ON TRIANGLES ASSOCIATED WITH A CURVE, Bulletin of the Korean Mathematical Society, 2015, 52, 3, 925  crossref(new windwow)
6.
Areas associated with a Strictly Locally Convex Curve, Kyungpook mathematical journal, 2016, 56, 2, 583  crossref(new windwow)
7.
AREA OF TRIANGLES ASSOCIATED WITH A CURVE II, Bulletin of the Korean Mathematical Society, 2015, 52, 1, 275  crossref(new windwow)
8.
AREA OF TRIANGLES ASSOCIATED WITH A STRICTLY LOCALLY CONVEX CURVE, Honam Mathematical Journal, 2015, 37, 1, 41  crossref(new windwow)
9.
Area properties associated with a convex plane curve, Georgian Mathematical Journal, 2017, 24, 3  crossref(new windwow)
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