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Sets of constant width, the spherical intersection property and circumscribed balls

Published online by Cambridge University Press:  17 April 2009

G. T. Sallee
G. T. Sallee
Affiliation:
Department of Mathematics, University of California, Davis, California 95616, U.S.A.
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Abstract

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It is well-known that if W is a set of costant width λ then the circumsphere and the insphere of W are concentric and their radii sum to λ. Here this fact is generalized to sets of constant relative width and it is shown that the result does not depend no W being of constant width, but rather on W satisfying the spherical intersection property; that is, W = ∩{ω + λB:ω ɛ W}.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 33 , Issue 3 , June 1986 , pp. 369 - 371
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Eggleston, H.G., “Sets of constant width in finite dimensional Banach spaces”, Israel J. Math. 3 (1965), 163–172.CrossRefGoogle Scholar
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[3]Maehara, H., “Convex bodies forming pairs of constant width”, J. Geom. 22 (1984), 101–107.CrossRefGoogle Scholar
[4]Sallee, G.T., “Pairs of sets of constant relative width”. J. Geom., (to appear).Google Scholar