Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-24T11:37:06.026Z Has data issue: false hasContentIssue false
  • English
  • Français

Variations of Classic Characterizations of Ellipsoids and a Short Proof of the False Centre Theorem

Part of: General convexity

Published online by Cambridge University Press:  21 December 2009

L. Montejano  and
E. Morales-Amaya
L. Montejano
Affiliation:
Instituto de Matemáticas, UNAM, Circuito exterior, C.U., México D.F., 04510, México. E-mail: [email protected]
E. Morales-Amaya
Affiliation:
Centro de Investigación en Matemáticas, A.C., A.P., 402, Guanajuato, Gto., C.P. 3600, México. E-mail: [email protected]
Get access

Abstract

Variations and generalizations of several classical theorems concerning characterizations of ellipsoids are developed. In particular, these lead to a short and comprehensible proof of the false centre theorem.

MSC classification

Secondary: 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces)
Type
Research Article
Information
Mathematika , Volume 54 , Issue 1-2 , December 2007 , pp. 35 - 40
Copyright
Copyright © University College London 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Aitchison, P. W., Petty, C. M. and Rogers, C. A., A convex body with a false centre is an ellipsoid. Mathematika 18 (1971), 50–59.CrossRefGoogle Scholar
2Burton, G. R., Some characterizations of the ellipsoid. Israel J. Math. 28 (1977), 339–349.Google Scholar
3Buseman, H., The Geometry of Geodesics. Academic Press (New York, 1955).Google Scholar
4Larman, D. G., A note on the false centre problem. Mathematika 21 (1974), 216–227.Google Scholar
5Rogers, C. A., Sections and projections of convex bodies. Portugaliae Math. 24 (1965), 99–103.Google Scholar
6Rogers, C. A., An equichordal problem. Geom. Dedicata 10 (1981), 73–78.CrossRefGoogle Scholar