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.
Dong-Soo Kim, Incheon Kim
Chonnam National University; Chonnam National University
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
2018; 33(1): 237-245
2017; 32(3): 709-714
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