2014/04/10 by Kim, Dong-Soo, Kim, Wonyong, Kim, Young Ho +1
#53A04 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1404.2969
It is well known that the area U of the triangle formed by three tangents to a parabola X is half of the area T 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.