A MARKOV-TYPE CHAIN FOR THE VIEW-OBSTRUCTION PROBLEM FOR SPHERES IN R(4)

In the view-obstruction problem, congruent, closed, convex bodies cent red at the points (1/2,1/2,...,1/2) + Z(n) in R(n) are expanded unifor mly until they block all rays from the origin into the open positive c one. The central problem is to determine the minimal blocking size. In the case of spheres of diameter 1, this value is denoted by nu(n) and is known for dimensions n = 2, 3. Here we show that nu(4) = root 11/1 5 and obtain a Markoff type chain of isolated extreme values.