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.

Wagner VI projection of the world

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:

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