Editing Mercator projection (section)

==== Truncation and aspect ratio ====
The ordinate ''y'' of the Mercator projection becomes infinite at the poles and the map must be truncated at some latitude less than ninety degrees. This need not be done symmetrically. Mercator's original map is truncated at 80°N and 66°S with the result that European countries were moved toward the centre of the map. The [[aspect ratio (image)|aspect ratio]] of his map is {{sfrac|198|120}} = 1.65. Even more extreme truncations have been used: a [[:File:Pieni 2 0791.jpg|Finnish school atlas]] was truncated at approximately 76°N and 56°S, an aspect ratio of 1.97.

Much Web-based mapping uses a zoomable version of the Mercator projection with an aspect ratio of one. In this case the maximum latitude attained must correspond to ''y''&nbsp;=&nbsp;±{{sfrac|''W''|2}}, or equivalently {{sfrac|''y''|''R''}}&nbsp;=&nbsp;{{pi}}. Any of the inverse transformation formulae may be used to calculate the corresponding latitudes:
:<math>
\varphi = \tan^{-1}\left[\sinh\left(\frac{y}{R}\right)\right]
= \tan^{-1}\left[\sinh\pi\right]
= \tan^{-1}\left[11.5487\right]
= 85.05113^\circ.
</math>