dispersion numbers | rendezvous values

Let E be a compact connected subset of d-dimensional Euclidean space. Gross and Stadje proved that there is a unique real number a(E) such that for all x_1, x_2, ..., x_n element E, there exists y element E with 1/n sum_(j = 1)^n sqrt( sum_(k = 1)^d (x_(j, k) - y_k)^2) = a(E). The magic constant m(E) of E is defined by m(E) = (a(E))/(diam(E)), where diam(E) congruent max_(u, v element E) sqrt( sum_(k = 1)^d (u_k - v_k)^2).