Eckert VI projection

Eckert VI projection is one of six map projections, the Max Eckert Access Dorff developed and published in 1906. As the projections Eckert and Eckert II -IV is equal area. The lengths of the polar lines are only half as large as that of the equator, and the longitude are sine curves.

Formulas

To describe the mathematical projection, we look at the earth's surface as a sphere of radius and describe points to it by the spherical coordinates. The image of this point, we describe by its coordinates, where the x - axis is the image of the equator, and the y- axis, the image of the meridian to the angle:

As for the Eckert IV projection of the value is given only implicitly and can only be approximated, for example, by Newton's method, are calculated.