Flat Earth Map  Gleason's New Standard Map Of The World  Large 24 x 36 1892
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Flat Earth Map  Gleason's New Standard Map Of The World  Large 24 x 36 1892
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Description
The azimuthal equidistant projection is an azimuthal map projection. It has the useful properties that all points on the map are at proportionally correct distances from the center point, and that all points on the map are at the correct azimuth (direction) from the center point. A useful application for this type of projection is a polar projection which shows all meridians (lines of longitude) as straight, with distances from the pole represented correctly. The flag of the United Nations contains an example of a polar azimuthal equidistant projection. A disadvantage of the new map is that you can’t see all of the Earth’s surface at once, but remember this is true for the globe as well. Our map is actually more like the globe in this respect than other flat maps. To see all of the globe, you have to rotate it; to see all of the new map, you simply have to flip it over, as you can see below 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}}} The shadow [earth] casts on the moon during an eclipse is round, regardless of where the moon is in the sky,” Steffen said. But while Gleason argued the earth is flat in his book, his application to the U.S. Patent Office for the map appears to contradict this. The application states that the map is extracted from the earth as a globe. Specifically, Gleason said: “The extortion 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.”
The Most Accurate Flat Map of Earth Yet  Scientific American
As Gleason’s map is centered on the north pole, the edges indicate the south pole. Experts told Reuters that Antarctica is clearly visible as the white ring on the perimeter of the map, contrary to claims by social media users that the continent is not shown. Scientific American is part of Springer Nature, which owns or has commercial relations with thousands of scientific publications (many of them can be found at www.springernature.com/us). Scientific American maintains a strict policy of editorial independence in reporting developments in science to our readers. 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.
References
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: With the circumference of the Earth being approximately 40,000km (24,855mi), the maximum distance that can be displayed on an azimuthal equidistant projection map is half the circumference, or about 20,000km (12,427mi). For distances less than 10,000km (6,214mi) distortions are minimal. For distances 10,000–15,000km (6,214–9,321mi) the distortions are moderate. Distances greater than 15,000km (9,321mi) are severely distorted. Anyone who cares can make observations (of the moon’s phases, of time zones, of constellations) that can all be understood in the context of a round earth but would be hard to explain otherwise without separate reasons for each observation,” he added, VERDICT
Azimuthal equidistant projection  Wikipedia Azimuthal equidistant projection  Wikipedia
Steffen also said that individuals can perform a similar experiment using geometry and Polaris, or the north star, as a function of latitude. R ( π 2 − φ ) , θ = λ {\displaystyle \rho =R\left({\frac {\pi }{2}}\varphi \right),\qquad \theta =\lambda ~~} Limitation [ edit ]
One can’t make everything perfect. The Mercator map has a boundary cut error: one makes a cut of 180 degrees along the meridian of the international date line from pole to pole and unrolls the Earth’s surface, thus putting Hawaii on the farleft side of the map and Japan on the farright side of the map creating an additional distance error in the process. A pilot flying a great circle route straight from New York to Tokyo passes over northern Alaska. His route looks bent on a Mercator map—a flexion error. North America is lopsided to the north: Canada is bigger than it should be, and Mexico is too small. All these errors are important. Ignoring one of them can lead you to badlooking maps no one would prefer. I usually work on general relativity and cosmology. I have always loved geometrical things. As a kid I was fascinated by map projections. When I was 14, I made a painted globe of Mars based on a flat Mercator Mars map by the astronomer E. M. Antoniadi. Since becoming an emeritus professor at Princeton, I have fondly returned to some of my childhood interests.
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