Characterization of the circle by equipower properties
type: Item
instance of: scholarly article
title: Characterization of the circle by equipower properties
zbMATH Open document ID: 0726.52002
DOI: 10.1007/BF01191886
author: Luciana Zuccheri
published in: Archiv der Mathematik
publication date: 1992-01-01T00:00:00Z
review text: It is well-known that, if E is a disk, then every point of the plane not belonging to its boundary is a power point of E. The author considers the problem of finding how many distinct power points, interior or exterior to a convex body E, ensure that E is a disk. In the interior points case, she extends a result obtained by J. B. Kelly and J. Rosenbaum in the year 1946, proving that with the sole convexity assumption on E two interior power points are sufficient. In the exterior points case, she proves that three non-collinear power points ensure that E is a disk, whereas in general two or more collinear power points do not suffice. This result is obtained by using a measure theoretic argument.
Mathematics Subject Classification ID: 52A10
zbMATH DE Number: 4198921
zbMATH Keywords: power points
zbMATH Keywords: convex body
zbMATH Keywords: disk
MaRDI profile type: Publication
cites work: On a transformation of a plane convex curve
cites work: Chord Functions of Convex Bodies
cites work: A Three-Point Solution to Hammer's X-Ray Problem
full work available at URL: https://doi.org/10.1007/bf01191886
OpenAlex ID: W1986736081
description: scientific article; zbMATH DE number 4198921