The azimuthal equidistant projection is a type of map projection

Map projection

A map projection is any method of representing the surface of a sphere or other three-dimensional body on a plane. Map projections are necessary for creating maps. All map projections distort the surface in some fashion...

.
A useful application for this type of projection is a polar

Polar coordinate system

In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a fixed point and an angle from a fixed direction....

 projection in which all distances measured from the center of the map along any longitudinal line are accurate; an example of a polar azimuthal equidistant projection can be seen on the United Nations flag.

This projection is used by the USGS in the National Atlas of the United States of America, and for large-scale mapping of Micronesia

Micronesia

Micronesia is a subregion of Oceania, comprising thousands of small islands in the western Pacific Ocean. It is distinct from Melanesia to the south, and Polynesia to the east. The Philippines lie to the west, and Indonesia to the southwest....

. It is useful for showing airline distances from center point of projection and for seismic and radio work.

Distances and directions to all places are true only from the center point of projection. Distances are correct between points along straight lines through the center. All other distances are incorrect. Distortion of areas and shapes increases dramatically, the further away one gets from center point.

Some types of wide-angle camera lenses, known as "fisheye lens

Fisheye lens

In photography, a fisheye lens is a wide-angle lens that takes in a broad, panoramic and hemispherical image. Originally developed for use in meteorology to study cloud formation and called "whole-sky lenses", fisheye lenses quickly became popular in general photography for their unique, distorted...

es" produce an azimuthal equidistant projection of the photographed scene onto the photographic medium. These lenses allow a much wider field of view than perspective

Perspective (visual)

Perspective, in context of vision and visual perception, is the way in which objects appear to the eye based on their spatial attributes; or their dimensions and the position of the eye relative to the objects...

 lenses, which are limited to significantly less than 180 degrees.

History

While it may have been used by ancient Egyptians for star maps in some holy books, the earliest text describing the azimuthal equidistant projection is an 11th-century work by al-Biruni.

In some countries this projection is named "Postel projection" after Guillaume Postel

Guillaume Postel

Guillaume Postel was a French linguist, astronomer, Cabbalist, diplomat, professor, and religious universalist.Born in the village of Barenton in Basse-Normandie, Postel made his way to Paris to further his education...

, who used it for a map in 1581.

External links

• Table of examples and properties of all common projections, from radicalcartography.net
• Online Azimuthal Equidistant Map Generator
• An interactive Java Applet to study the metric deformations of the Azimuthal Equidistant Projection.
• GeographicLib provides a class for performing azimuthal equidistant projections centered at any point on the ellipsoid.
• Concept and mathematics of the Azimuthal Equidistant Projection for the marine navigator.