A NOTE ON THE ILLUMINATION OF CONVEX-BODIES

Let K subset-of E(d) be a convex body and let l(r)(K) denote the minimum number of r-dimensional affine subspaces of E(d) lying outside K with which it is possible to illuminate K, where 0 less-than-or-equal-to r less-than-or-equal-to d - 1. We give a new proof of the theorem that l(r)(K) greater-than-or-equal-to inverted right perpendicular (d + 1)/(r + 1) inverted left perpendicular with equality for smooth K.