2015/02/04 by Dong-Soo Kim, Kim, Dong-Soo, Dong Seo Kim +1
Mathematics · #53A04 #Differential Geometry (math.DG) #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1502.01205
openalex publication_date 2015/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Archimedes showed that the area between a parabola and any chord AB on the parabola is four thirds of the area of triangle ΔABP, where P is the point on the parabola at which the tangent is parallel to the chord AB. Recently, this property of parabolas was proved to be a characteristic property of parabolas. With the aid of this characterization of parabolas, using centroid of triangles associated with a curve we present two conditions which are necessary and sufficient for a strictly locally convex curve in the plane to be a parabola.