UsingBest projection the Euler‒Urmaev system of equations, it is shown that only that surface allows one to obtain projections onto a plane without distortion, the coefficient of the metric form of which is a harmonic function. Since this quantity is not harmonious for the surface of an ellipsoid, the problem arises of finding such a projection in which the length distortions are minimal. To solve the problem of finding ideal projections unambiguously, it is necessary: first, to select a measure of linear distortion at a given point in a given direction; second, to select a general measure of linear distortion at a point; and third, to select a length distortion criterion for the entire mapping area. Definitions for the ideal and best projections are formulated.