On a characterization of circles and spheres
type: Item
instance of: scholarly article
title: On a characterization of circles and spheres
zbMATH Open document ID: 0844.52003
author: Yanyan Li
published in: Beiträge zur Algebra und Geometrie
publication date: 1995-11-29T00:00:00Z
full work available at URL: https://eudml.org/doc/233078
full work available at URL: no.2
review text: If a rectangle is circumscribed about a circular disc, the disc will always touch each side of the rectangle at its midpoint. The author shows that this property characterizes the circular disc among all two-dimensional convex domains. Moreover, if the point of contact of a convex domain with the edge of every circumscribing rectangle is always close to the midpoint (or if the quadratic mean distance is small), then the domain is close to a disc in the Hausdorff metric (resp. quadratic mean metric). This is also generalized to higher dimensions; a convex body \(K\) in \(E^d\) is a ball if and only if it touches the center of every facet of every circumscribed box. Again, if the centers of the facets of circumscribed boxes are close to the points of contact with \(K\), then \(K\) is close to a ball in the Hausdorff metric.
Mathematics Subject Classification ID: 52A10
Mathematics Subject Classification ID: 52A20
zbMATH DE Number: 821691
zbMATH Keywords: characterizations of ball
zbMATH Keywords: characterizations of disc
zbMATH Keywords: stable properties
reviewed by: Robert Dawson
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 821691