About the Behrmann Projection
By spacing the parallels appropriately, it is possible to devise a cylindrical projection which also has the equal area property. This was first performed by Lambert in 1772 who chose the Equator for his standard parallel (ie. free of shape distortion). Similar projections were produced by Gall in 1855, who chose a standard parallel of 45 degrees North and South; and by Walter Behrmann in 1910, who chose a standard parallel of 30 degrees North and South. Behrmann chose these particular standard parallels to minimize the maximum angular deformation for the entire map, using a process of Gauss Least Squares, and Tissot Distortion Analysis.
The Behrmann projection is a cylindrical projection with straight parallels and meridians. By choosing a standard parallel of 30 degrees, equatorial regions tend to be stretched in a north-south direction, but polar regions are compressed in a north-south direction. This is a trade-off: the earlier Lambert projection had no distortion at the equator but had extreme distortion at the poles.
As a historical note, the cylindrical equal area projection acquired a degree of notoriety during the 1960s when Arno Peters (apparently independently) devised a projection virtually identical to Gall's. This used a standard parallel of 44.138 degrees and was intended to show the relative sizes of the equatorial third world regions relative to the more temperate richer regions. The few professional cartographers who commented, were very critical. Despite this, it has seen widespread use by various socially concerned agencies including the United Methodist Church, the Vatican, the World Council of Churches, and various UN agencies. Some of the critics probably disliked the underlying politics, although it also has practical geometric problems. Although the Gall-Peters projection is an equal area projection, it has a lot more shape distortion than most equal area projections. As pointed out by its critics, the most visible distortion is at lower latitudes, exactly where it is meant to be more representative.
Author's Note: Of the projections presented here at Equal-Area-Maps.com, the Behrmann projection is one of the more practical for online mapping. It has support from both ESRI and Proj4, and can be easily added to the Proj4JS library (as of August 2009, the author's addition to the Proj4JS project is pending). Although the Behrmann projection probably has the lowest level of shape distortion of any of the cylindrical equal area projections, it still has a high level of shape distortion in the polar regions when compared to the Mollweide and Sinusoidal pseudo-cylindrical projections.