In order to best preserve distances from more than three points one can use advanced techniques. The next map demonstrates this.
The projection is produced by covering the United States with a lattice of latitude and longitude points, then computing the spherical distances between these points, and then computing plane coordinates for these points. The plane coordinates are computed to minimize, in the least squares sense, the difference between the plane distances and the spherical distances. The map outline information is then interpolated by cubic splining and drawn by computer using a 10,000 coordinate digital file.
W. Tobler, 1971, “Numerical Approaches to Map projections”, pp. 51-66 of I. Kretschmer, Studies in Theoretical Cartography, Vienna, Deuticke