2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101209In this paper, we examine how well a rational point P on an algebraic variety X can be approximated by other rational points. We conjecture that if P lies on a rational curve, then the best approximations to P on X can be chosen to lie along a rational curve. We prove this conjecture for a wide range of examples, and for a great many more examples we deduce our conjecture from Vojta's Main Conjecture.49 pages, 3 figures. Exposition improved, particularly in the proofs of the main theorems, and the connection with accumulating subvarieties made explicitNumber TheoryAlgebraic Geometry14G05text