This double-sided map has a Goldberg-Gott error score of only 0.881 versus 4.563 for the Winkel tripel. It beats the Winkel tripel in each of the six error terms! It has zero boundary cut error since continents and oceans are continuous over the circular edge. It has a remarkable property no single-sided flat map possesses: distance errors between pairs of points (such as cities) are bounded, being off by only at most plus or minus 22.2 percent. In the Mercator and Winkel tripel projections, distance errors blow up as one approaches the poles and boundary cuts.

Gleason Map – FlatEarth.ws

Gleason might have claimed that the map is the “flat-Earth map” but his explanation written in his patent for the map is contradictory: Purple circles: 15,000 km radius circles Applications [ edit ] An azimuthal equidistant projection centered on SydneyR ( π 2 − φ ) , θ = λ {\displaystyle \rho =R\left({\frac {\pi }{2}}-\varphi \right),\qquad \theta =\lambda ~~} Limitation [ edit ] Azimuthal equidistant projection maps can also be useful to show ranges of missiles, as demonstrated by the map centered on North Korea showing the country's missile range. 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.

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

Previously, Goldberg and I identified six critical error types a flat map can have: local shapes, areas, distances, flexion (bending), skewness (lopsidedness) and boundary cuts. These are illustrated by the famous Mercator projection, the base template for Google maps. It has perfect local shapes but is bad at depicting areas. Greenland appears as large as South America even though it covers only one seventh the area on the globe. 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. The Winkle tripel is a map to hang on your wall. Ours is a more accurate one you can hold in your hand. An interactive Java Applet to study the metric deformations of the Azimuthal Equidistant Projection.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. 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]

New correct map of the flat surface, stationary earth

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: David A. KING (1996), "Astronomy and Islamic society: Qibla, gnomics and timekeeping", in Roshdi Rashed, ed., Encyclopedia of the History of Arabic Science, Vol. 1, p. 128–184 [153]. Routledge, London and New York. From the registered patent, he never mentioned that the Earth is flat. On the contrary, he said that he made the map from a globe, which explains how a north-pole centered azimuthal equidistant map is designed. ReferencesThanks for reading Scientific American. Create your free account or Sign in to continue. Create Account

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

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 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.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. 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: