The Steinitz-Gross Theorem on Sums of Vectors

Abstract

α1α2, …, αp are n-dimensional vectors,,;they are arranged to form a closed polygon.Denote by R(α1, α2, …, αp) the radius of the smallest circumscribed hypersphere with centre at 0 ; by R(α1, α2, …, αp) the minimum of(α1, α2, …, αp)for all possible reorderingsof α2, …, αp−1 and by cn the least possible constant such thatfor all possible choices of p and α1α2, … , αp.