About the Eckert IV & VI Projections
Max Eckert published six pseudo-cylindrical projections in 1906. All six projections have poles and central meridians half the length of the equator. Eckert I, III, and IV all have equidistant parallels of latitude, but are not equal area. Eckert II, IV, and VI are equal area projections. Eckert II has an angular shape with a hexagonal outline and straight line half-meridians from the the equator to the pole. This is considered a novelty projection and will not be discussed further. Eckert IV has been used in a number of American atlases and textbooks, and has been used for thematic insets on National Geographic Society world sheets. Eckert VI has been used for climate maps published by Prentice-Hall, and was popular with the Russian B.S.A.M. (Great Soviet Atlas).
Both the Eckert IV and VI projections are pseudo-cylindrical projections. Ie. mathematical projections with straight line parallels (like a cylindrical projection) but with curved meridians (unlike a cylindrical projection). With the exception of the central meridian, Eckert IV meridians are semi-ellipses, whilst the Eckert VI meridians are sinusoidal. Unlike many of the pseudo-cylindrical projections, the poles are represented as flat edges in both projections.
Local angles and shape are correct at the intersection of the central meridian with North/South parallels at 40 degrees 30 minutes for Eckert IV, and 49 degrees 16 minutes for Eckert VI. Eckert IV stretches shapes and scale by 40% in the north-south direction, along the equator. This stretching reduces to zero at latitude 40 degrees 30 mins North/South, and becomes a compression towards the poles. Eckert VI stretches shapes and scale by 29% in the north-south direction along the equator. This stretching reduces to zero at 49 degrees 16 minutes north and south, and becomes a compression towards the poles. Hence Eckert VI appears to have less distortion in the lower and mid latitudes, but distortion appears visually greater near the eastern and western edges.
Author's Note: The Eckert IV & VI projections are amongst the best projections presented here at Equal-Area-Maps.com. The exact choice probably depends on the latitudes of greatest interest. Unlike the Mollweide projection, both have flat polar edges, which might be preferable for some applications. Unfortunately both projections only have moderate software support. Both are supported by ESRI and the Proj4 library, but not Proj4JS.
See our interactive Eckert IV Projection world map and interactive Eckert VI Projection world map (overlays on both maps are disabled due to the lack of Proj4JS support).