2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141914We prove that the length difference between a closed periodic curve and its parallel curve at a sufficiently small distance is proportional to the rotation index. As an application, the rotation index of a curve could be estimated by means of Cauchy-Crofton formula.5 pages, 2 figuresDifferential Geometry53A04; 53C65text