In the Eckert III projection, "no point is free of all scale distortion, but the Equator is free of angular distortion" (Snyder and Voxland, 1989).
Area is not preserved.
Meridians are elliptical curves that are equally spaced elliptical curves. The meridians +/- 180° from the central meridian are semicircles. The poles and the central meridian are straight lines one half the length of the Equator.
Parallels are equally spaced straight lines.
See Meridians and Parallels. Pole lines are half the length of the Equator. Symmetry exists at the central meridian or the Equator.
Scale is correct only along 37° and 55’ N and S. Features close to poles are compressed in the north-south direction.
Mapping the world.
Eckert III Projection
Source: Snyder and Voxland, 1989