It is often asserted that transportation costs increase at a decreasing rate with geographic distance. In other words, they have a concave down shape. On the map that follows the transport cost idea is represented by the square root of the spherical distance from the map center, but the map has also been made to preserve spherical areas.
X = R (2?)1/2 sin(? sin?)
Y = R (2?)1/2 cos(? sin?)
where ? is the co-latitude (spherical distance from the map center) and ? is the longitude.