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Two inequalities for convex sets in the plane

Published online by Cambridge University Press:  17 April 2009

P.R. Scott
P.R. Scott
Affiliation:
Department of Pure Mathematics, University of Adelaide, Adelaide, South Australia.
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Abstract

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Let K be a bounded, closed, convex set in the euclidean plane having diameter d, width w, inradius r, and circumradius R. We show that

and

where both these inequalities are best possible.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 19 , Issue 1 , August 1978 , pp. 131 - 133
Copyright
Copyright © Australian Mathematical Society 1979

References

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[2]Sholander, Marlow, “On certain minimum problems in the theory of convex curves”, Trans. Amer. Math. Soc. 73 (1952), 139–173.CrossRefGoogle Scholar
[3]Yaglom, I.M. and Boltyanskiĭ, V.G., Convex figures (translated by Kelly, Paul J. and Walton, Lewis F.. Holt, Rinehart and Winston, New York, 1961).Google Scholar