Azimuthal equidistant projection

The azimuthal equidistant projection is an azimuthal map projection distinguished by two key properties: all points on the map are shown at proportionally correct distances from a chosen center point, and all points are depicted at the correct azimuth, or direction, from that center point. This makes it the exponential map on a sphere. A common application is the polar projection, where all meridians appear as straight lines radiating from the pole, and distances from the pole are accurately represented. The flag of the United Nations features a well-known example of this polar azimuthal equidistant projection.

History

While the projection may have been used by ancient Egyptians for star maps in holy texts, the earliest surviving written description comes from an 11th-century work by the scholar al-Biruni. The oldest known terrestrial map using this projection is a pair of hemispheres created by Glareanus around 1510. However, Spanish and Portuguese cartographers employed it even earlier, as polar azimuthal hemispheres conveniently visualized the boundary established by the Treaty of Tordesillas in 1494. The projection appears in many Renaissance maps; Gerardus Mercator used it for an inset of the north polar region on his famous 1569 world map, and a world map by ‛Ali b.

Ahmad al-Sharafi of Sfax from 1571 is another early example. In France and Russia, it is known as the "Postel projection" after Guillaume Postel, who used it for a map in 1581. Many modern star chart planispheres also utilize the polar azimuthal equidistant projection. In the 21st century, the projection has been adopted by Flat Earthers as a map of a flat Earth, citing its use on the UN flag and its depiction of Antarctica as a ring around the map's edge.

Mathematical definition

Mathematically, a central point on the globe is chosen; all distances and azimuths from this point to any other point are correct. This center projects to the center of a circular map.

Points along a given azimuth project along a straight line from the center, and the distance from the center to any projected point equals the great-circle arc length on the globe. A limitation is that the maximum displayable distance is half the Earth's circumference, roughly 20,000 km. Distortions are minimal for distances under 10,000 km, moderate from 10,000 to 15,000 km, and severe beyond 15,000 km.