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An extremal property of the hypersphere

Published online by Cambridge University Press:  24 October 2008

A. M. Macbeath
A. M. Macbeath
Affiliation:
Clare CollegeCambridge
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Extract

It was shown by Sas (1) that, if K is a plane convex body, then it is possible to inscribe in K a convex n-gon occupying no less a fraction of its area than the regular n-gon occupies in its circumscribing circle. It is the object of this note to establish the n-dimensional analogue of Sas's result, giving incidentally an independent proof of the plane case. The proof is a simple application of the Steiner method of symmetrization.

Type
Research Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 47 , Issue 1 , January 1951 , pp. 245 - 247
Copyright
Copyright © Cambridge Philosophical Society 1951

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References

REFERENCES

(1)Sas, E.Über ein Extremumeigenschaft der Ellipsen. Compositio Math. 6 (1939), 468–70.Google Scholar
(2)Bonnesen, T. and Fenchel, W.Theorie der konvexen Körper (Ergebnisse der Math.) (Berlin, 1934).Google Scholar