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.
Famous quotes containing the words van, der and/or projection:
““Mr. Van Buren, your friends may be leaving you—but my friends never leave me.””
—Andrew Jackson (1767–1845)
“Under the lindens on the heather,
There was our double resting-place.”
—Walther Von Der Vogelweide (1170?–1230?)
“In the case of our main stock of well-worn predicates, I submit that the judgment of projectibility has derived from the habitual projection, rather than the habitual projection from the judgment of projectibility. The reason why only the right predicates happen so luckily to have become well entrenched is just that the well entrenched predicates have thereby become the right ones.”
—Nelson Goodman (b. 1906)