Area of triangles associated with a curve II
Bull. Korean Math. Soc. 2015 Vol. 52, No. 1, 275-286
https://doi.org/10.4134/BKMS.2015.52.1.275
Printed January 31, 2015
Dong-Soo Kim, Wonyong Kim, Young Ho Kim, and Dae Heui Park
Chonnam National University, Chonnam National University, Kyungpook 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 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
MSC numbers : 53A04
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