Wagner VI projection

Wagner VI is a pseudocylindrical whole Earth map projection. Like the Robinson projection, it is a compromise projection, not having any special attributes other than a pleasing, low distortion appearance. Wagner VI is equivalent to the Kavrayskiy VII horizontally elongated by a factor of ${\displaystyle 2}$⁄${\displaystyle {\sqrt {3}}}$. This elongation results in proper preservation of shapes near the equator but slightly more distortion overall. The aspect ratio of this projection is 2:1, as formed by the ratio of the equator to the central meridian. This matches the ratio of Earth’s equator to any meridian.

The Wagner VI is defined by: ^{[1] [2]}

$${\displaystyle {\begin{aligned}x&=\lambda {\sqrt {1-3\left({\frac {\varphi }{\pi }}\right)^{2}}}\\y&=\varphi \end{aligned}}}$$

where ${\displaystyle \lambda }$ is the longitude and ${\displaystyle \varphi }$ is the latitude.

Inverse formula:

$${\displaystyle {\begin{aligned}\psi &=\arcsin \left({\frac {\sqrt {3}}{\pi }}y\right)\\\lambda &={\frac {x}{\cos {\psi }}}\\\varphi &=y\end{aligned}}}$$