Gall–Peters projection

The Gall–Peters projection is a rectangular map projection that maps all areas such that they have the correct sizes relative to each other. Like any equal-area projection, it achieves this goal by distorting most shapes. The projection is a particular example of the cylindrical equal-area projection in that it sets latitudes 45° north and south as the regions on the map that have no distortion.

The projection is named after James Gall and Arno Peters. Gall is credited with describing the projection in 1855 at a science convention. He published a paper on it in 1885. Peters brought the projection to a wider audience beginning in the early 1970s by means of the "Peters World Map". The name "Gall–Peters projection" seems to have been used first by Arthur H. Robinson in a pamphlet put out by the American Cartographic Association in 1986.

Maps based on the projection are promoted by UNESCO, and they are also widely used by British schools. In the U.S. state of Massachusetts, Boston Public Schools began phasing in these maps in March 2017, becoming the first public school district in the United States to adopt Gall–Peters maps as their standard.

The Gall–Peters projection achieved notoriety in the late 20th century as the centerpiece of a controversy about the political implications of map design.

The projection is conventionally defined as:

where λ is the longitude from the central meridian in degrees, φ is the latitude, and R is the radius of the globe used as the model of the earth for projection. For longitude given in radians, remove the π/180° factors.

Stripping out unit conversion and uniform scaling, the formulae may be written:

where λ is the longitude from the central meridian (in radians), φ is the latitude, and R is the radius of the globe used as the model of the earth for projection. Hence the sphere is mapped onto the vertical cylinder, and the cylinder is stretched to double its length. The stretch factor, 2 in this case, is what distinguishes the variations of cylindric equal-area projection.

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