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# Mercator Projection

The Mercator projection is a map projection that was widely used for navigation since loxodromes are straight lines (although great circles are curved). The following equations place the x-axis of the projection on the equator and the y-axis at longitude , where is the longitude and is the latitude.

 (1) (2) (3) (4) (5) (6)

The inverse formulas are

 (7) (8) (9) (10)

where is the Gudermannian.

An oblique form of the Mercator projection is illustrated above. It has equations

 (11) (12) (13)

where

 (14) (15) (16)

The inverse formulas are

 (17) (18)

There is also a transverse form of the Mercator projection, illustrated above (Deetz and Adams 1934, Snyder 1987). It is given by the equations

 (19) (20) (21) (22) (23)

where

 (24) (25)

Finally, the "universal transverse Mercator projection" is a map projection which maps the sphere into 60 zones of each, with each zone mapped by a transverse Mercator projection with central meridian in the center of the zone. The zones extend from S to N (Dana).

Gudermannian, Spherical Spiral

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## References

Dana, P. H. "Map Projections." http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj_f.html.Deetz, C. H. and Adams, O. S. Elements of Map Projection with Applications to Map and Chart Construction, 4th ed. Washington, DC: U. S. Coast and Geodetic Survey Special Pub. 68, 1934.Pearson, F. Map Projections: Theory and Applications. Boca Raton, FL: CRC Press, p. 195, 1990.Snyder, J. P. Map Projections--A Working Manual. U. S. Geological Survey Professional Paper 1395. Washington, DC: U. S. Government Printing Office, pp. 38-75, 1987.

## Referenced on Wolfram|Alpha

Mercator Projection

## Cite this as:

Weisstein, Eric W. "Mercator Projection." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MercatorProjection.html