Areas associated with a Strictly Locally Convex Curve

• Journal title : Kyungpook mathematical journal
• Volume 56, Issue 2,  2016, pp.583-595
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2016.56.2.583
Title & Authors
Areas associated with a Strictly Locally Convex Curve
Kim, Dong-Soo; Kim, Dong Seo; Kim, Young Ho; Bae, Hyun Seon;

Abstract
Archimedes showed that for a point P on a parabola X and a chord AB of X parallel to the tangent of X at P, the area S of the region bounded by the parabola X and chord AB is four thirds of the area T of triangle $\small{{\Delta}ABP}$. It is well known that the area U formed by three tangents to a parabola is half of the area T of the triangle formed by joining their points of contact. Recently, the first and third authors of the present paper and others proved that among strictly locally convex curves in the plane $\small{{\mathbb{R}}^2}$, these two properties are characteristic ones of parabolas. In this article, in order to generalize the above mentioned property \$S
Keywords
triangle;area;parabola;strictly locally convex curve;plane curvature;
Language
English
Cited by
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