The problem of finding the best projection from a set of projections in which the sum of the extremal scales is equal to two is an optimal control problem with an equality type constraint, which is solved by the Lagrange multiplier method with subsequent integration of the corresponding Euler‒Ostrogradsky system. The resulting best projection is related to the best conformal projection and to the ideal projection according to the Airy criterion. In particular, the mapping functions of an Airy ideal projection are equal to half the sum of the mapping functions of the best conformal projection and the best of the set of close-to-equal-area projections. The three projections mentioned above provide a triad of related objects.