Chord and area properties of strictly convex curves
Commun. Korean Math. Soc.
Published online December 11, 2020
Dong-Soo Kim and 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 curvature and 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
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