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The world on Van der Grinten projection (2011)
(upload.wikimedia.org)
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 proposed by Alphons J. van der Grinten in 1904, and, unlike perspective projections, is an arbitrary geometric construction on the plane. It was adopted as the National Geographic Society's reference map of the world from 1922 until 1988.
15° graticule. Imagery is a derivative of NASA’s Blue Marble summer month composite with oceans lightened to enhance legibility and contrast. Image created with the Geocart map projection software.
Author: Strebe
A conformal projection makes straight lines appear on the map with the same relative direction they appear on the surface.
An equal-area projection makes the areas of parts of the map proportional to the area of the surface they represent.
That map on the post is neither. The most useful maps are normally neither.
Doesn't "useful" depend a lot on application and that's why we have more than one map type?