Beitr\"age zur Algebra und Geometrie
Contributions to Algebra and Geometry
Volume 37 (1996), No. 1, 9-15.
Invariante Beleuchtung konvexer K\"orper
Benulf Wei{\ss}bach
Abstract
To each convex body $K$ one can assign an isometrical invariant $L^* (K)$,
which is the smallest number of directions illuminating the boundaries of all
congruent copies of $K$. The main result of the present paper is an upper
bound for $L^* (K)$ if $K$ belongs to the set of bodies of constant width in
a d-dimensional euclidean space. Besides a proof is given for the assertion
by M. Lassak that each three-dimensional body of constant width can be
illuminated by six directions, mutually orthogonal or opposite.
MSC 1991: 52A40