AREA OF TRIANGLES ASSOCIATED WITH A CURVE II

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 52, Issue 1, 2015, pp.275-286
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2015.52.1.275

Title & Authors

AREA OF TRIANGLES ASSOCIATED WITH A CURVE II

Kim, Dong-Soo; Kim, Wonyong; Kim, Young Ho; Park, Dae Heui;

Kim, Dong-Soo; Kim, Wonyong; Kim, Young Ho; Park, Dae Heui;

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. In this article, we consider whether this property and similar ones characterizes parabolas. As a result, we present three conditions which are necessary and sufficient for a strictly convex curve in the plane to be an open part of a parabola.

Keywords

triangle;area;parabola;strictly convex curve;plane curvature;

Language

English

Cited by

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AREA OF TRIANGLES ASSOCIATED WITH A STRICTLY LOCALLY CONVEX CURVE,;;;;

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

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