AREA OF TRIANGLES ASSOCIATED WITH A STRICTLY LOCALLY CONVEX CURVE

• Journal title : Honam Mathematical Journal
• Volume 37, Issue 1,  2015, pp.41-52
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2015.37.1.41
Title & Authors
AREA OF TRIANGLES ASSOCIATED WITH A STRICTLY LOCALLY CONVEX CURVE
Kim, Dong-Soo; Kim, Dong Seo; Bae, Hyun Seon; Kim, Hye-Jung;

Abstract
It is well known that the area U of the triangle formed by three tangents to a parabola X is half of the area T of the triangle formed by joining their points of contact. Recently, it was proved that this property is a characteristic one of parabolas. That is, among strictly locally convex $\small{C^{(3)}}$ curves in the plane $\small{\mathbb{R}^2}$ parabolas are the only ones satisfying the above area property. In this article, we study strictly locally convex curves in the plane $\small{\mathbb{R}^2}$. As a result, generalizing the above mentioned characterization theorem for parabolas we present some conditions which are necessary and sufficient for a strictly locally convex $\small{C^{(3)}}$ curve in the plane to be an open part of a parabola.
Keywords
triangle;trapezoid;area;parabola;strictly locally convex curve;plane curvature;
Language
English
Cited by
1.
Center of Gravity and a Characterization of Parabolas,;;;

Kyungpook mathematical journal, 2015. vol.55. 2, pp.473-484
1.
Center of Gravity and a Characterization of Parabolas, Kyungpook mathematical journal, 2015, 55, 2, 473
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