ABSTRACT
The view-obstruction problem was originally formulated by Cusick [2], though it had been studied in another formulation by Wills [16] and Betke and Wills [1] in the case of boxes. Its generalisations were formulated and studied by Dumir, Hans-Gill and Wilker [3, 4] where rays were replaced by subspaces (flats). In [4], they observed that the problem of obstructing the view through lines is related to the billiard ball motion problem considered by Schoenberg [12, 13, 14] (see also Kőnig and Szűcs [10].) Generalisations to higher dimensional trajectories were considered by Schoenberg [15] in the case of boxes. The problem is in some sense related to the problem regarding the covering minima considered by Kannan and Lovász [9]. Dumir et al [3, 4] solved the problem of obstructing the view through (n-1)-dimensional subspaces (flats) for convex bodies in Rn centred at the origin o. In the special case of spheres centred at o, the relevant constants for obstructing the view through subspaces (flats) of dimension n-2 were also determined, together with Markoff type chains for related extreme values. Here we shall determine the relevant constants for view-obstruction. through (n-3)-dimensional subspaces (flats). These results together with earlier ones suggest conjectures for the cases when (n-k)-dimensional subspaces (flats) are considered (see conjectures I, II in Section 2).
