Gall–Peters projection world map

[Pigeon]

The Gall–Peters projection, named after James Gall and Arno Peters, is one specialization of a configurable equal-area map projection known as the equal-area cylindric or cylindrical equal-area projection. It achieved considerable notoriety in the late 20th century as the centerpiece of a controversy surrounding the political implications of map design.

In 1967 Arno Peters, a German filmmaker and historian, devised a map projection identical to Gall's orthographic projection and presented it in 1973 as a "new invention." He promoted it as a superior alternative to the Mercator projection, which was suited to navigation but also used commonly in world maps.

The Mercator projection increasingly inflates the sizes of regions according to their distance from the equator. This inflation results, for example, in a representation of Greenland that is larger than Africa, whereas in reality Africa is 14 times as large. Since much of the technologically underdeveloped world lies near the equator, these countries appear smaller on a Mercator and therefore, according to Peters, seem less significant.[citation needed] On Peters's projection, by contrast, areas of equal size on the globe are also equally sized on the map. By using his "new" projection, poorer, less powerful nations could be restored to their rightful proportions.

[Pigeon]

The HEALPix projection is a general class of spherical projections, sharing several key properties, which map the 2-sphere to the Euclidean plane. Any of these can be followed by partitioning (pixelising) the resulting region of the 2-plane. In particular, when one of these projections (the H=4, K=3 HEALPix projection), is followed by a pixelisation of the 2-plane, this is generally referred as the HEALPix pixelisation, which is widely used in physical cosmology for maps of the cosmic microwave background. This pixelisation can be thought of as mapping the sphere to twelve square facets (diamonds) on the plane followed by the binary division of these facets into pixels, though it can be derived without using the projection. The associated software package HEALPix implements the algorithm. The HEALPix projection (as a general class of spherical projections) is represented by the keyword HPX in the FITS standard for writing astronomical data files. It was approved as part of the official FITS World Coordinate System (WCS) by the IAU FITS Working Group on April 26, 2006.

The spherical projection combines a cylindrical equal area projection, the Lambert cylindrical equal-area projection, for the equatorial regions of the sphere and a pseudocylindrical equal area projection, an interrupted Collignon projection, for the polar regions

[Kat]

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... south up is always better too!