## Geocart Projections

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Lambert equal-area cylindric

Classifications

Cylindrical
Equal area
Perspective

Graticule

Meridians: Equally spaced straight parallel lines 0.32 as long as the Equator.
Parallels: Unequally spaced straight parallel lines, farthest apart near the Equator, perpendicular to meridians
Poles: Straight lines equal in length to the Equator
Symmetry: About any meridian or the Equator

Scale

True along the Equator
Increases with distance from the Equator in the direction of parallels and decreases in the direction of meridians to maintain equal area
Same scale at the parallel of opposite sign

Distortion

Infinitesimally small circles (indicatrices) of equal size on the globe are ellipses except at the Equator, where they are circles. The areas of all the indicatrices are the same. Thus, there is shape distortion but no area distortion. Shape distortion in polar regions is extreme.

Other features

Simple graticule, perspectively projected in lines perpendicular to the axis onto a cylinder wrapped around the globe tangent to the Equator

Usage

Minimal except to describe basic principles in map projection texts
Prototype for Behrmann and other modified cylindrical equal-area projections
Recommended for equal-area mapping of regions predominantly bordering the Equator

Origin

Presented by Johann Heinrich Lambert (1728–77) of Alsace in 1772

Aspects

Normal is described here. Transverse and oblique aspects are rarely used but are recommended for equal area mapping of predominantly north-south regions or regions extending obliquely.

Other names

Cylindrical Equal-Area

Similar projections

If meridians are compressed relative to parallels and if the spacing of parallels is increased in inverse proportion, other cylindrical equal-area projections result, and the standard parallel changes. The extreme case, in which the poles are standard parallels, consists of a single vertical line, infinitely long.
Named examples are as follows:
Behrmann
Gall Orthographic
Trystan Edwards
Peters
(See Behrmann Cylindrical Equal-Area projection for the differences.)

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.