Hammer-Aitoff Equal-Area Projection

A Map Projection whose inverse is defined using the intermediate variable

$\begin{displaymath} z \equiv \sqrt{1-({\textstyle{1\over 4}}x)^2-({\textstyle{1\over 2}}y)^2}\,. \end{displaymath}$

Then the longitude and latitude are given by

$\displaystyle \lambda$	$\textstyle =$	$\displaystyle 2\tan^{-1}\left[{zx\over 2(2z^2 - 1)}\right]$
$\displaystyle \phi$	$\textstyle =$	$\displaystyle \sin^{-1}(yz).$