Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2021; 36(4): 801-815

Online first article December 11, 2020      Printed October 31, 2021

https://doi.org/10.4134/CKMS.c200314

Copyright © The Korean Mathematical Society.

Chord and area properties of strictly convex curves

Dong-Soo Kim, Incheon Kim

Chonnam National University; Chonnam National University

Abstract

Ellipses have a lot of interesting geometric properties. It is quite natural to ask whether such properties of ellipses and some related ones characterize ellipses. In this paper, we study some chord properties and area properties of ellipses. As a result, using the curvature and the support function of a strictly convex curve, we establish four characterization theorems of ellipses and hyperbolas centered at the origin.

Keywords: Chord, area, ellipse, hyperbola, curvature function, support function, strictly convex curve

MSC numbers: 53A04