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 far-left side of the map and Japan on the far-right 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 bad-looking maps no one would prefer. 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:

Gleason Map – FlatEarth.ws

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. 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.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). Steffen also said that individuals can perform a similar experiment using geometry and Polaris, or the north star, as a function of latitude. Jason Steffen, an assistant professor in physics and astronomy at the University of Nevada, Las Vegas, told Reuters that the south pole “is the entire edge of the map, and the ring is Antarctica.” The Winkle tripel is a map to hang on your wall. Ours is a more accurate one you can hold in your hand.

Flat Earth - Great Circle Routes on Gleason Map – GeoGebra Flat Earth - Great Circle Routes on Gleason Map – GeoGebra

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. Goldhaber-Gordon added that this experiment would show that “locations close to the south pole appear far apart on the map,” although that is not the reality. 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 GleasonPurple circles: 15,000 km radius circles Applications [ edit ] An azimuthal equidistant projection centered on Sydney The shadow [earth] casts on the moon during an eclipse is round, regardless of where the moon is in the sky,” Steffen said. 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}}}