Eckert IV projection

The Eckert IV projection is developed by Max Eckert Access Dorff and 1906 published pseudo cylindrical equal-area map.

Properties

The pole points are stretched to the half of the length of the equator. The meridians are represented as semi-ellipses or parts thereof. The two extreme meridians thereby become semicircles.

The advantage of this projection over the Peters projection is the low distortion of land with simultaneous surface fidelity.

Formulas

Is the radius of a sphere ( the surface of which serves as a model for the Earth's surface ), the central meridian, and a point with polar coordinates is given, and the coordinates of the pixel can be calculated on the map with the following formulas:

The equation can be solved for example by Newton's Method.

Are reversed, where the coordinates in the map, then the corresponding point on the sphere can be computed as follows:

Use

The Eckert IV projection is one of the most widely used of Eckert's card designs. Between 1940 and 1960 it was the third most frequently used in textbooks from the United States card design.