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The Miller cylindrical projection is a modified Mercator projection, proposed by Osborn Maitland Miller in 1942. The latitude is scaled by a factor of 4⁄5, projected according to Mercator, and then the result is multiplied by 5⁄4 to retain scale along the equator. Hence:

$${\displaystyle {\begin{aligned}x&=\lambda \\y&={\frac {5}{4}}\ln \left={\frac {5}{4}}\sinh ^{-1}\left(\tan {\frac {4\varphi }{5}}\right)\end{aligned}}}$$

or inversely,

$${\displaystyle {\begin{aligned}\lambda &=x\\\varphi &={\frac {5}{2}}\tan ^{-1}e^{\frac {4y}{5}}-{\frac {5\pi }{8}}={\frac {5}{4}}\tan ^{-1}\left(\sinh {\frac {4y}{5}}\right)\end{aligned}}}$$

where λ is the longitude from the central meridian of the projection, and φ is the latitude. Meridians are thus about 0.733 the length of the equator.

In GIS applications, this projection is known as: "ESRI:54003" and "+proj=mill".

Compact Miller projection is similar to Miller but spacing between parallels stops growing after 55 degrees.

In GIS applications, this projection is known as: "ESRI:54080" and "+proj=comill".

See also

• List of map projections

References

1. Flattening the Earth: Two Thousand Years of Map Projections, John P. Snyder, 1993, pp. 179, 183, ISBN 0-226-76747-7.
2. "Miller Cylindrical Projection". Wolfram MathWorld. Retrieved 25 March 2015.
3. "Projected coordinate systems". ArcGIS Resources: ArcGIS Rest API. ESRI. Retrieved 16 June 2017.
4. Open-source software PROJ
5. Patterson, Tom; Šavrič, Bojan; Jenny, Bernhard (2015). "Introducing the Patterson Cylindrical Projection". Cartographic Perspectives (78): 77–81. doi:10.14714/CP78.1270.
6. Open-source software PROJ

External links

• Math formulae information
• Historical information
• Miller projection in proj4

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