Lagrange

Parameters: Parallel shown straight, Circular longitude pair

Classifications

polyconic
conformal

Graticule

Meridians: Central meridian is straight. Other meridians are circular arcs, concave toward the central meridian.
Parallels: One parallel, often the equator, is straight. Other parallels are circular arcs, concave toward the pole which is on the same side of the straight parallel.
Poles: Points.
Symmetry: About the central meridian. Also about the equator, if the equator is straight.

Scale

Increases rapidly with distance from the center.

Distortion

Great distortion of area and scale when the center is compared with poles or other outer limits. Conformality fails at the poles.

Other features

The general formula can be used to create a variety of conformal maps.

Usage

Whole-world maps and conformal maps within a circle of smaller portions of the world.

Similar projections

Van der Grinten I is not conformal.

Specializations

Stereographic projection.
Littrow projection.

Origin

Johann Heinrich Lambert (1728–1777) of Alsace presented the world conformally in a circle in 1772. This projection is usually called the Lagrange projection, however, after Joseph Louis Lagrange (1736–1813) of France, who generalized Lambert’s concept in 1779.

Description adapted from J.P. Snyder and P.M. Voxland, An Album of Map Projections, U.S. Geological Survey Professional Paper 1453. United States Government Printing Office: 1989.