cylindrical projections/cylindrical equal-area map projection

A cylindrical map projection onto a cylinder tangent to a sphere, showing the geographic meridians as a family of equal-spaced parallel straight lines perpendicular to a second family of parallel straight lines. They represent the geographic parallels and are so spaced as to produce an equal-area map projection. The equal-area condition preserves a constant ratio between corresponding ground and map areas. This projection must not be confused with the Mercator projection, to which it bears some general resemblance. True or correct scale will obtain along the great circle of tangency or the two homothetic small circles of intersection. If the axis of the cylinder is parallel to the axis of the earth, the parallels and meridians will appear as right, perpendicular lines. Points on the earth equally distant from the tangent great circle (equator) or small circles of intersection (parallels equally spaced on either side of the equator) will have equal scale departure. The pattern of deformation will therefore be parallel to the parallels, as a change in scale occurs in a direction perpendicular to the parallels. If the cylinder is turned 90° with respect to the earth’s axis, the projection is said to be transverse, and the pattern of deformation will be symmetric with respect to a great circle through the poles. If the turn of the cylinder is less than 90°, an oblique projection results.

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