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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 $2$ ⁄ ${\sqrt {3}}$ . 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]

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

where $\lambda$ is the longitude and $\varphi$ is the latitude.

Inverse formula:

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

References

^ Wagner, Karlheinz (1949). Kartographische Netzentwürfe. Bibliographisches Institut, Leipzig. p. 197.
^ Snyder, John P. (1993). Flattening the Earth: Two Thousand Years of Map Projections. p. 205. ISBN 0-226-76747-7.