Area of triangles associated with a curve II
Differential Geometry
2014-04-14 v1
Abstract
It is well known that the area of the triangle formed by three tangents to a parabola is half of the area 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
Cite
@article{arxiv.1404.2969,
title = {Area of triangles associated with a curve II},
author = {Dong-Soo Kim and Wonyong Kim and Young Ho Kim and Dae Heui Park},
journal= {arXiv preprint arXiv:1404.2969},
year = {2014}
}
Comments
12 pages. arXiv admin note: substantial text overlap with arXiv:1401.4751