Cylindrical equal-area projection

In cartography, the cylindrical equal-area projection is a family of cylindrical, equal-area map projections.

The term "normal cylindrical projection" is used to refer to any projection in which meridians are mapped to equally spaced vertical lines and circles of latitude are mapped to horizontal lines (or, mutatis mutandis, more generally, radial lines from a fixed point are mapped to equally spaced parallel lines and concentric circles around it are mapped to perpendicular lines).

The mapping of meridians to vertical lines can be visualized by imagining a cylinder (of which the axis coincides with the Earth's axis of rotation) wrapped around the Earth and then projecting onto the cylinder, and subsequently unfolding the cylinder.

By the geometry of their construction, cylindrical projections stretch distances east-west. The amount of stretch is the same at any chosen latitude on all cylindrical projections, and is given by the secant of the latitude as a multiple of the equator's scale. The various cylindrical projections are distinguished from each other solely by their north-south stretching (where latitude is given by φ):

The only cylindrical projections that preserve area have a north-south compression precisely the reciprocal of east-west stretching (cos φ): equal-area cylindrical (with many named specializations such as Gall–Peters or Gall orthographic, Behrmann, and Lambert cylindrical equal-area). This divides north-south distances by a factor equal to the secant of the latitude, preserving area but heavily distorting shapes.

Any particular cylindrical equal-area map has a pair of identical latitudes of opposite sign (or else the equator) at which the east–west scale matches the north–south scale.

All cylindrical equal-area projections use the formula:

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