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;

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 curves in the plane parabolas are the only ones satisfying the above area property. In this article, we study strictly locally convex curves in the plane . 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 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

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