English

Area of triangles associated with a curve II

Differential Geometry 2014-04-14 v1

Abstract

It is well known that the area UU of the triangle formed by three tangents to a parabola XX is half of the area TT 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