THE VIEW-OBSTRUCTION PROBLEM FOR SPHERES IN R(5)

In the view-obstruction problem, congruent, closed convex bodies centr ed al the points (1/2,...,1/2) + Z(n) in R(n) are expanded uniformly u ntil they block all rays from the origin into the open positive cone. The central problem is to determine the minimal blocking size. In the case of spheres of diameter 1 and cubes of side 1 these values are kno wn for n = 2, 3 and 4. Here we show that in R(5), this value for the s phere of diameter 1 is root 41/42.