ItArithmetic mean principle is demonstrated that the Gauss–Kruger projection is not the best conformal projection for the meridional zone, but, in accordance with Chebyshev’s theorem, for a region bounded by two curves with equal linear scale factors. These curves intersect the meridional zone at two points on the equator, forming a doubly connected region. Using the properties of the projections within triad, based on the Gauss–Kruger projection, both an ideal projection according to the Airy criterion and the best projection from a set of close-to-equal-area projections were constructed. A comparison of distortions and corrections to the angles of the resulting projections was carried out. The relationships between the Airy ideal projection for the aforementioned region and the UTM and Cassini–Soldner projections are demonstrated.