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 $2$⁄$\sqrt{3}$. 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:

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

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

Inverse formula:

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

See also

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