A map projection is a mathematical set of equations for taking a position on the three dimensional earth onto a flat map. For the Mercator projection, this keeps parallels and meridians perpendicular. The only way to do this is to increase the scale in north-south direction because the meridians should be converging toward the poles. To keep the angles and local distances on the map correct, the east-west dimensions increase by the same amount. This scaling factor increases from 1 at the equator to ¥ at the poles (which can thus never appear on a Mercator map).
The x and y coordinates on the map can be plotted like a regular graph. They may or may not actually appear on the map?for ground maps used by the Army and Marines they are the preferred way to report positions, although with a UTM projection and not with a Mercator projection. The actual equations, especially for an elliptical earth, can be quite messy.
Projection(lat, long, earth radius) à Map(x,y)
InverseProjection(Map x,y) à Earth(lat, long, earth radius)
last revision 1/11/2017