An Estimate for the Problem of Illumination of the Boundary of a Convex Body in E3

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Abstract

Let A be a convex body in Euclidean space E3. We denote by H(A) the smallest number of homothetic ‘reduced copies’ of A by which it is possible to cover the whole of A. The conjecture of Hadwiger is H(A) ≤ 8. We prove that H(A) ≤ 16.

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