Van der Grinten projection
Encyclopedia
The van der Grinten projection is a compromise map projection
that is neither equal-area nor conformal. It projects the entire Earth into a circle, though the polar regions are subject to extreme distortion. The projection was the first of four proposed by Alphons J. van der Grinten in 1904, and, unlike most projections, is an arbitrary geometric construction on the plane. It was made famous when the National Geographic Society
adopted it as their reference map of the world from 1922 until 1988.
The geometric construction given by van der Grinten can be written algebraically:
where
takes the sign of 
, 
takes the sign of 
and
Should it occur that
, then
Similarly, if
or 
, then
In all cases,
is the latitude, 
is the longitude, and 
is the central meridian of the projection.
Map projection
A map projection is any method of representing the surface of a sphere or other three-dimensional body on a plane. Map projections are necessary for creating maps. All map projections distort the surface in some fashion...
that is neither equal-area nor conformal. It projects the entire Earth into a circle, though the polar regions are subject to extreme distortion. The projection was the first of four proposed by Alphons J. van der Grinten in 1904, and, unlike most projections, is an arbitrary geometric construction on the plane. It was made famous when the National Geographic Society
National Geographic Society
The National Geographic Society , headquartered in Washington, D.C. in the United States, is one of the largest non-profit scientific and educational institutions in the world. Its interests include geography, archaeology and natural science, the promotion of environmental and historical...
adopted it as their reference map of the world from 1922 until 1988.
The geometric construction given by van der Grinten can be written algebraically:
where
takes the sign of , takes the sign of andShould it occur that
, thenSimilarly, if
or , thenIn all cases,
is the latitude, is the longitude, and is the central meridian of the projection.