ON TRIANGLES ASSOCIATED WITH A CURVE

Title & Authors
ON TRIANGLES ASSOCIATED WITH A CURVE
Kim, Dong-Soo; Kim, Dong Seo; Kim, Young Ho;

Abstract
It is well-known that the area of parabolic region between a parabola and any chord $\small{P_1P_2}$ on the parabola is four thirds of the area of triangle $\small{{\Delta}P_1P_2P}$. Here we denote by P the point on the parabola where the tangent is parallel to the chord $\small{P_1P_2}$. In the previous works, the first and third authors of the present paper proved that this property is a characteristic one of parabolas. In this paper, with respect to triangles $\small{{\Delta}P_1P_2PQ}$ where Q is the intersection point of two tangents to X at $\small{P_1}$ and $\small{P_2}$ we establish some characterization theorems for parabolas.
Keywords
area;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
1.
Area properties associated with a convex plane curve, Georgian Mathematical Journal, 2017, 24, 3
2.
Center of Gravity and a Characterization of Parabolas, Kyungpook mathematical journal, 2015, 55, 2, 473
3.
Areas associated with a Strictly Locally Convex Curve, Kyungpook mathematical journal, 2016, 56, 2, 583
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