Azimuthal equidistant projection

Lore & Background

The azimuthal equidistant projection is an azimuthal map projection with two key properties: all points on the map are at proportionally correct distances from the center point, and all points are at the correct azimuth (direction) from that center. This makes it the exponential map on a sphere. A common application is a polar projection, where all meridians (lines of longitude) appear as straight lines, and distances from the pole are shown accurately. The flag of the United Nations features an example of a polar azimuthal equidistant projection.

The earliest known text describing this projection is an 11th-century work by al-Biruni, though it may have been used by ancient Egyptians for star maps. The oldest surviving terrestrial map using it is a pair of hemispheres by Glareanus from around 1510, but Spanish and Portuguese mapmakers used it earlier for polar azimuthal hemispheres that helped visualize the boundary agreed at the Treaty of Tordesillas in 1494. Gerardus Mercator employed it for an inset of the north polar regions on his 1569 map. Another early example is the 1571 world map by ‛Ali b.

Ahmad al-Sharafi of Sfax. In France and Russia, it is called the "Postel projection" after Guillaume Postel, who used it for a map in 1581. Many modern star chart planispheres use the polar form. In the 21st century, Flat Earthers have adopted this projection as a map of the Flat Earth, citing its use on the UN flag and its depiction of Antarctica as a ring around the Earth’s edge.

Reader's Guide

The azimuthal equidistant projection is significant because it uniquely preserves both correct distances and correct azimuth directions from a single center point, making it valuable for navigation and communication. Its mathematical definition allows any point on the globe to serve as the center, with all other points plotted at their true great-circle distance and azimuth. This property has made it useful for polar maps, where meridians appear as straight lines and distances from the pole are accurate. The projection appears on the flag of the United Nations, a widely recognized symbol.

In practical applications, it helps operators of directional antennas determine the correct azimuth to point toward a distant transmitter or receiver. When centered on a point whose antipode lies on land, that antipode smears into a large circle, distorting nearby landmasses. Despite these limitations, the projection remains in use for star charts and specialized terrestrial maps.