2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67601We obtain a new motivated proof of the reciprocity law for Dedekind sums by computing the constant coefficient of the Ehrhart polynomial for a rectangular triangle in two ways. On the one hand, the constant term is the Euler characteristic, and on the other hand it is given by a cotangent Laurent expansion.Number TheoryCombinatorics11L03; 52C05text