Hammer projection

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A Hammer projection of the Earth

The Hammer projection is an equal-area map projection, described by Ernst Hammer in 1892. Directly inspired by the Aitoff projection, Hammer suggested the use of the equatorial form of the Lambert azimuthal equal-area projection instead of Aitoff's use of the azimuthal equidistant projection:

$(\lambda, \phi)\mapsto\left(laeq_x(\lambda/2, \phi), laea_y(\lambda/2, \phi)/2\right)$

where $laea_x\,$ and $laea_y\,$ are the x and y components of the equatorial Lambert azimuthal equal-area projection. Substituting:

$(\lambda, \phi)\mapsto\frac{\sqrt 2\left(2 \cos \phi \sin(\lambda /2), \sin \phi\right)}{\sqrt{1 + \cos \phi \cos(\lambda /2)}}$

where $\lambda\,$ is the longitude from the central meridian and $\phi\,$ is the latitude.^[1]

Visually, the Aitoff and Hammer projections are very similar. The Hammer has seen more use because of it's equal-area property. The Mollweide projection is another equal-area projection of similar aspect, though with straight parallels of latitude, unlike the Hammer's curved parallels.