2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33249We provide a lower bound construction showing that the union of unit balls in three-dimensional space has quadratic complexity, even if they all contain the origin. This settles a conjecture of Sharir.5 pages, 5 figuresComputational GeometryF.2.2The union of unit balls has quadratic complexity, even if they all contain the origintext