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Illuminating sets of constant width

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Oded Schramm
Oded Schramm
Affiliation:
Mathematics Department, Fine Hall, Princeton University, Princeton NJ 08544, USA.
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Abstract

The problem of illuminating the boundary of sets having constant width is considered and a bound for the number of directions needed is given. As a corollary, an estimate for Borsuk's partition problem is inferred. Also, the illumination number of sufficiently symmetric strictly convex bodies is determined.

MSC classification

Secondary: 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces)
Type
Research Article
Information
Mathematika , Volume 35 , Issue 2 , December 1988 , pp. 180 - 189
Copyright
Copyright © University College London 1988

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