Azimuthal equidistant projection
Map projection preserving correct distances and azimuths from a center point.
The azimuthal equidistant projection is a type of azimuthal map projection. Its defining characteristic is that it preserves two specific properties from a single, chosen center point: all other points on the map are shown at the correct azimuth, or direction, from that center, and the distance to any other point is proportionally correct. Mathematically, this projection is the exponential map on a sphere. A common and useful application is the polar projection, where all lines of longitude appear as straight lines radiating from the pole, and distances from that pole are accurately represented. The flag of the United Nations features an example of this polar azimuthal equidistant projection.
The projection has a long history. It may have been used by ancient Egyptians for star charts in holy texts, but the earliest known written description comes from an 11th-century work by the scholar al-Biruni. The oldest surviving terrestrial map using this projection is a pair of hemispheres created by Glareanus around 1510. However, Spanish and Portuguese cartographers used it even earlier, as polar azimuthal hemispheres conveniently illustrated the boundary established by the 1494 Treaty of Tordesillas. The projection appears in many Renaissance maps; Gerardus Mercator employed it for an inset of the north polar region on his famous 1569 world map. Another early example is a 1571 world map by ‛Ali b. Ahmad al-Sharafi of Sfax. In France and Russia, the projection is known as the "Postel projection" after Guillaume Postel, who used it for a map in 1581. Many modern star chart planispheres also use this projection. In the 21st century, the polar azimuthal equidistant projection has been adopted by Flat Earthers as a representation of a flat Earth, partly due to its appearance on the UN flag and its depiction of Antarctica as a ring around the map's edge.
Mathematically, a point on the globe is selected as the center. This point projects to the center of a circular map. All points along a given azimuth from the center project along a straight line, and the angle of that line from the vertical equals the azimuth. The distance from the center to any other projected point is the great-circle arc length on the globe. When the center is the north pole, the mathematical equations simplify considerably. A limitation of the projection is that the maximum displayable distance i
- type
- Map projection
- first_text_description
- 11th-century work by al-Biruni
- also_known_as
- Postel projection (in France and Russia)
- notable_use
- Flag of the United Nations
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.
Did You Know?
- The earliest text describing the azimuthal equidistant projection is an 11th-century work by al-Biruni.
- The projection appears on the flag of the United Nations as a polar azimuthal equidistant projection.
Frequently Asked Questions
Who is Azimuthal equidistant projection?
It is an azimuthal map projection that guarantees true distances and true compass bearings from one chosen center point to every other location on the map. In France and Russia, fans also know it by the alias Postel projection.
What are Azimuthal equidistant projection's powers/role?
Its signature ability is preserving both distance and azimuth direction from the center to any other point, making it mathematically equivalent to the exponential map on a sphere. That dual-fidelity trait makes it a go-to tool for polar maps, star charts, and communication-network planning.
Why is Azimuthal equidistant projection important?
It is the projection chosen for the United Nations flag, giving the organization a globally recognized visual identity. It has also served as a workhorse for polar cartography, celestial charts, and modern telecom planning for centuries.
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