Lambert cylindrical equal-area projection

This projection is undistorted along the equator, which is its standard parallel, but distortion increases rapidly towards the poles.

The poles accrue infinite distortion, becoming lines instead of points.

The projection was invented by the Swiss mathematician Johann Heinrich Lambert and described in his 1772 treatise, Beiträge zum Gebrauche der Mathematik und deren Anwendung, part III, section 6: Anmerkungen und Zusätze zur Entwerfung der Land- und Himmelscharten, translated as, Notes and Comments on the Composition of Terrestrial and Celestial Maps.

[2] By multiplying the projection's height by some factor and dividing the width by the same factor, the regions of no distortion can be moved to any desired pair of parallels north and south of the equator.

[1] where φ is the latitude, λ is the longitude and λ0 is the central meridian.