Editing Map projection (section)

====Normal cylindrical====
[[File:Usgs map mercator.svg|frame|right|The Mercator projection shows [[rhumbs]] as straight lines. A rhumb is a course of constant bearing. Bearing is the compass direction of movement.]]
A normal cylindrical projection is any projection in which [[Meridian (geography)|meridians]] are mapped to equally spaced vertical lines and [[circles of latitude]] (parallels) 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 whose axis coincides with the Earth's axis of rotation. This cylinder is wrapped around the Earth, projected onto, and then unrolled.

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 [[Trigonometric function|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):
* North-south stretching equals east-west stretching ([[Secant (trigonometry)|sec]] ''φ''): The east-west scale matches the north-south scale: conformal cylindrical or [[Mercator projection|Mercator]]; this distorts areas excessively in high latitudes.
* North-south stretching grows with latitude  faster than east-west stretching (sec{{sup|2}} ''φ''): The cylindric perspective (or [[central cylindrical projection|central cylindrical]]) projection; unsuitable because distortion is even worse than in the Mercator projection.
* North-south stretching grows with latitude, but less quickly than the east-west stretching: such as the [[Miller cylindrical projection]] (sec {{sfrac|4|5}}''φ'').
* North-south distances neither stretched nor compressed (1): [[equirectangular projection]] or "plate carrée".
* North-south compression equals the cosine of the latitude (the reciprocal of east-west stretching): [[cylindrical equal-area projection|equal-area cylindrical]].  This projection has many named specializations differing only in the scaling constant, such as the [[Gall–Peters projection|Gall–Peters]] or Gall orthographic (undistorted at the 45° parallels), [[Behrmann projection|Behrmann]] (undistorted at the 30° parallels), and [[Lambert cylindrical equal-area projection|Lambert cylindrical equal-area]] (undistorted at the equator). Since this projection scales north-south distances by the reciprocal of east-west stretching, it preserves area at the expense of shapes.

In the first case (Mercator), the east-west scale always equals the north-south scale. In the second case (central cylindrical), the north-south scale exceeds the east-west scale everywhere away from the equator. Each remaining case has a pair of [[secant line]]s—a pair of identical latitudes of opposite sign (or else the equator) at which the east-west scale matches the north-south-scale.

Normal cylindrical projections map the whole Earth as a finite rectangle, except in the first two cases, where the rectangle stretches infinitely tall while retaining constant width.