Wagner VI projection

Wagner VI projection of the world

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:

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

See also

• List of map projections
• Cartography
• Kavrayskiy VII projection
• Robinson projection

References

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