2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/108970The classical Tait-Kneser theorem states that the osculating circles of a smooth plane curve, free from curvature extrema, are pairwise disjoint. We prove a number of analogs of this theorem, e.g., for ovals of osculating cubics, osculating polynomials and trigonometric polynomials; in each case, we will obtain a non-differentiable foliation with smooth leaves.14 pages, 6 figures, v2: references addedDifferential GeometryAlgebraic Geometry53A20; 51N15text