2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152853Let $f(d)$ be the smallest number so that every set in $R^d$ of diameter 1 can be partitioned into $f(d)$ sets of diameter smaller than 1. Borsuk's conjecture was that $f(d)\! =\!d\!+\!1$. We prove that $f(d)\! \ge\! (1.2)^{\sqrt d}$ for large~$d$.3 pagesMetric GeometryCombinatoricstext