Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2014; 51(3): 901-909

Published online May 31, 2014 https://doi.org/10.4134/BKMS.2014.51.3.901

Copyright © The Korean Mathematical Society.

Area of triangles associated with a curve

Dong-Soo Kim and Kyu-Chul Shim

Chonnam National University, Chonnam National University

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 study some properties of $U$ and $T$ for strictly convex plane curves. As a result, we establish a characterization for parabolas.

Keywords: triangle, area, parabola, strictly convex curve, plane curvature

MSC numbers: 53A04