# Wagner VI projection

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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 ${\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]

{\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.

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## References

1. Snyder, John P. (1993). Flattening the Earth: Two Thousand Years of Map Projections. p. 205. ISBN   0-226-76747-7.