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Sets of constant width contained in a set of given minimal width

Published online by Cambridge University Press:  26 February 2010

H. G. Eggleston
H. G. Eggleston
Affiliation:
7 Hauxton Road, Trumpington, Cambridge
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Extract

In this note it is shown that

(i) there is a plane convex set of minimal width λ which does not contain any convex set whose width is constant and greater than λ/(3—31/2),

(ii) every plane convex set of minimal width λ contains a convex set whose width is constant and is equal to λ/(3—31/2).

Type
Research Article
Information
Mathematika , Volume 2 , Issue 1 , June 1955 , pp. 48 - 55
Copyright
Copyright © University College London 1955

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References

[1]Bonnesen, T. and Fenohel, W., Theorie der Konvexen Körper (reprinted New York, 1948).Google Scholar
[2]Hausdorff, F., Mengenlehre (3rd Ed., New York, 1948).Google Scholar