﻿ Van der Grinten Projection

# Van der Grinten Projection

A curved modification of the Mercator projection that is neither equal-area nor conformal. Although it is usually classed with the various pseudocylindrical projections it is not really a pseudocylindrical projection.

###### Scale

Only the Equator is true to scale.

###### Distortion

The central meridian and Equator are straight lines. All other meridians and parallels are arcs of circles. Great distortion in polar regions. Most maps using this projection do not extend past Greenland and the outer rim of Antarctica.

###### Usage

Used for world maps. Used by the National Geographic Society for their standard world map until 1988, which resulted in adoption of this projection by many other groups.

###### Origin

Presented in 1904 by Alphons J. van der Grinten of Chicago writing in a German geographical journal and patented in the United States in 1904. Van der Grinten originally invented two projections, the first of which is known as the " Van der Grinten I" or simply the "Van der Grinten" and the second of which is (confusingly) known as the "Van der Grinten IV." See the Van der Grinten IV topic for that second projection.

Van der Grinten's second projection is known as "IV" because after van der Grinten's original publication Alois Bludau in 1912 presented a variation of the first van der Grinten projection that became known as the "Van der Grinten II," as well as a second variation in 1912 based upon the second of van der Grinten's original projections and given the name of "Van der Grinten III."

Thus the original two projections are known as Van der Grinten I and IV, while Bludau's two variations are known as II (based upon the first original) and III (based upon the second original).

The Van der Grinten projection used within Manifold is the first of the series and was invented in 1898. It is the best known as the result of wide use by the National Geographic Society and the one commonly used. Van der Grinten published the projection using a geometric construction. Manifold uses the 1979 formulae published by John Parr Snyder.

###### Limiting Forms

Used only in the spherical form.