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While it may have been used by ancient Egyptians for star maps in some holy books, [1] the earliest text describing the azimuthal equidistant projection is an 11th-century work by al-Biruni. [2] The extorsion of the map from that of a globe consists, mainly in the straightening out of the meridian lines allowing each to retain their original value from Greenwich, the equator to the two poles.” —US Patent No. 497,917 by Alexander Gleason When the center point is the north pole, φ 0 equals π / 2 {\displaystyle \pi /2} and λ 0 is arbitrary, so it is most convenient to assign it the value of 0. This assignment significantly simplifies the equations for ρ u and θ to:

## Flat Earth Maps SET OF 2 MAPS- Flat Earth Map - 24 x 36 Flat Earth Maps SET OF 2 MAPS- Flat Earth Map - 24 x 36

An interactive Java Applet to study the metric deformations of the Azimuthal Equidistant Projection.

### References

In May 1893, Gleason patented the invention of the “New Standard Map of the World”, a projection of the earth centered on the north pole, which can be found ( here). The relationship between the coordinates ( θ, ρ) of the point on the globe, and its latitude and longitude coordinates ( φ, λ) is given by the equations:

## Azimuthal equidistant projection - Wikipedia Azimuthal equidistant projection - Wikipedia

The so-called “Gleason Map” is an old map published in the 19th century. The author was a flat-Earther who claimed the map as the “flat Earth map.” In reality, the map is just a normal azimuthal equidistant map centered on the North Pole. cos ρ R = sin φ 0 sin φ + cos φ 0 cos φ cos ( λ − λ 0 ) tan θ = cos φ sin ( λ − λ 0 ) cos φ 0 sin φ − sin φ 0 cos φ cos ( λ − λ 0 ) {\displaystyle {\begin{aligned}\cos {\frac {\rho }{R}}&=\sin \varphi _{0}\sin \varphi +\cos \varphi _{0}\cos \varphi \cos \left(\lambda -\lambda _{0}\right)\\\tan \theta &={\frac {\cos \varphi \sin \left(\lambda -\lambda _{0}\right)}{\cos \varphi _{0}\sin \varphi -\sin \varphi _{0}\cos \varphi \cos \left(\lambda -\lambda _{0}\right)}}\end{aligned}}} Some social media users are saying that Alexander Gleason’s 19th Century “New Standard Map of the World” is proof that the earth is flat and that Antarctica is not a continent but an ice ring that circles the earth’s edges. They are wrong. The earth is not flat. The map has been misinterpreted.

Edward S. Kennedy, 1996, Mathematical geography, in Roshdi Rashed, ed., Encyclopedia of the History of Arabic Science, Vol. 1, Routledge, London and New York. Snyder, John P.; Voxland, Philip M. (1989). An Album of Map Projections. Professional Paper 1453. Denver: USGS. p.228. ISBN 978-0160033681. Archived from the original on 2010-07-01 . Retrieved 2018-03-29.