2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65911Consider an analytic map of a neighborhood of 0 in a vector space to a Euclidean space. Suppose that this map takes all germs of lines passing through 0 to germs of circles. Such a map is called rounding. We introduce a natural equivalence relation on roundings and prove that any rounding, whose differential at 0 has rank at least 2, is equivalent to a fractional quadratic rounding. A fractional quadratic map is just the ratio of a quadratic map and a quadratic polynomial. We also show that any rounding gives rise to a quadratic map between spheres. The known results on quadratic maps between spheres have some interesting implications concerning roundings.14 pages, v3: minor changes to improve readabilityMetric GeometryDifferential Geometry15A63text