The view-obstruction problem for 5-dimensional cubes
The view obstruction problem for the \(n\)-cube is equivalent to the conjecture that, for any \(n\) positive integers \(v_1,\dots, v_n\), there is a real number \(x\) such that \(\|v_i x\|\geq (n+1)^{-1}\), \(i=1,\dots, n\). Here \(\|y\|\) denotes the distance from \(y\) to the nearest integer. The problem goes back to the reviewer (1968) and Cusick (1973), who also gave the useful geometric interpretation and various generalizations. Here he gives a lower bound for \(n=5\). The proof is based on methods by \textit{W. Bienia, L. Goddyn, P. Gvozdjak, A. Sebö} and \textit{M. Tarsi} [J. Comb. Theory, Ser. B 72, No. 1, 1-9 (1998; Zbl 0910.05064)].
scientific article; zbMATH DE number 1300155