# Equal Earth projection

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The Equal Earth map projection is an equal-area pseudocylindrical projection for world maps, invented by Bojan Šavrič, Bernhard Jenny, and Tom Patterson in 2018. It is inspired by the widely used Robinson projection, but unlike the Robinson projection, retains the relative size of areas. The projection equations are simple to implement and fast to evaluate. [1]

## Contents

The features of the Equal Earth projection include: [2] [3]

• The curved sides of the projection suggest the spherical form of Earth.
• Straight parallels make it easy to compare how far north or south places are from the equator.
• Meridians are evenly spaced along any line of latitude.
• Software for implementing the projection is easy to write and executes efficiently.

According to the creators, the projection was created in response to the decision of the Boston public schools to adopt the Gall-Peters projection for world maps in March 2017, which generated a controversy in the world of cartography. At that time Šavrič, Patterson and Jenny sought alternative map projections of equal areas for world maps, but could not find any that met their aesthetic criteria. Therefore, they created a new projection that had more visual appeal compared to existing projections of equal areas. [3] [4] [5] [6] They claim that they need a world map that shows continents and countries in real size with each other. [2]

## Formulation

The projection is formulated as the equations

{\displaystyle {\begin{aligned}x&={\frac {2{\sqrt {3}}\,\lambda \cos {\theta }}{3\,(9\,A_{4}\,\theta ^{8}+7\,A_{3}\,\theta ^{6}+3\,A_{2}\,\theta ^{2}+A_{1})}}\\y&=A_{4}\,\theta ^{9}+A_{3}\,\theta ^{7}+A_{2}\,\theta ^{3}+A_{1}\,\theta \end{aligned}}}

where

{\displaystyle {\begin{aligned}&\sin {\theta }={\frac {\sqrt {3}}{2}}\sin {\varphi }\\&A_{1}=1.340264,\ A_{2}=-0.081106,\ A_{3}=0.000893,\ A_{4}=0.003796\end{aligned}}}

and ${\displaystyle \varphi }$ refers to latitude and ${\displaystyle \lambda }$ to longitude.

## Use

The first known thematic map published using the Equal Earth projection is a map of the global mean temperature anomaly for July 2018, produced by the NASA’s Goddard Institute for Space Studies. [7]

## Related Research Articles

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The Bottomley map projection is an equal area map projection defined as:

This is a table of orthonormalized spherical harmonics that employ the Condon-Shortley phase up to degree = 10. Some of these formulas give the "Cartesian" version. This assumes x, y, z, and r are related to and through the usual spherical-to-Cartesian coordinate transformation:

In cartography, a Tissot's indicatrix is a mathematical contrivance presented by French mathematician Nicolas Auguste Tissot in 1859 and 1871 in order to characterize local distortions due to map projection. It is the geometry that results from projecting a circle of infinitesimal radius from a curved geometric model, such as a globe, onto a map. Tissot proved that the resulting diagram is an ellipse whose axes indicate the two principal directions along which scale is maximal and minimal at that point on the map.

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The Hammer projection is an equal-area map projection described by Ernst Hammer in 1892. Using the same 2:1 elliptical outer shape as the Mollweide projection, Hammer intended to reduce distortion in the regions of the outer meridians, where it is extreme in the Mollweide.

In physics and mathematics, the solid harmonics are solutions of the Laplace equation in spherical polar coordinates. There are two kinds: the regular solid harmonics, which vanish at the origin and the irregular solid harmonics, which are singular at the origin. Both sets of functions play an important role in potential theory, and are obtained by rescaling spherical harmonics appropriately:

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The Eckert IV projection is an equal-area pseudocylindrical map projection. The length of the polar lines is half that of the equator, and lines of longitude are semiellipses, or portions of ellipses. It was first described by Max Eckert in 1906 as one of a series of three pairs of pseudocylindrical projections. Within each pair, meridians are the same whereas parallels differ. Odd-numbered projections have parallels spaced equally, whereas even-numbered projections have parallels spaced to preserve area. Eckert IV is paired with Eckert III.

The Boggs eumorphic projection is a pseudocylindrical, equal-area map projection used for world maps. Normally it is presented with multiple interruptions. Its equal-area property makes it useful for presenting spatial distribution of phenomena. The projection was developed in 1929 by Samuel Whittemore Boggs (1889–1954) to provide an alternative to the Mercator projection for portraying global areal relationships. Boggs was geographer for the United States Department of State from 1924 until his death. The Boggs eumorphic projection has been used occasionally in textbooks and atlases.

The Strebe 1995 projection, Strebe projection, Strebe lenticular equal-area projection, or Strebe equal-area polyconic projection is an equal-area map projection presented by Daniel "daan" Strebe in 1994. Strebe designed the projection to keep all areas proportionally correct in size; to push as much of the inevitable distortion as feasible away from the continental masses and into the Pacific Ocean; to keep a familiar equatorial orientation; and to do all this without slicing up the map.

The Eckert-Greifendorff projection is an equal-area map projection described by Max Eckert-Greifendorff in 1935. Unlike his previous six projections, It is not pseudocylindrical.

## References

1. Šavrič, Bojan; Patterson, Tom; Jenny, Bernhard (2018-08-07). "The Equal Earth map projection". International Journal of Geographical Information Science . 33 (3): 454–465. doi:10.1080/13658816.2018.1504949.
2. "Equal Earth projection". shadedrelief.com. Retrieved 2018-08-23.
3. Morales, Aurelio. "La nueva proyección Equal Earth: todo lo que debes saber" (in Spanish). Valladolid: MappingGIS. Retrieved January 24, 2020.
4. "Equal Earth: un mapamundi más preciso que muestra el tamaño real de África" (in Spanish). N+1. August 22, 2018. Retrieved January 24, 2020.
5. "Equal Earth: Idean un nuevo mapa del mundo basado en un mapa del 1569" (in Spanish). Código Oculto. Retrieved January 24, 2020.
6. "Colección cartográfica - La proyección Equal-Earth". visionscarto (in Spanish). Retrieved January 24, 2020.