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Gall's Stereographic Projection

Since the Mercator projection causes considerable distortion of size at latitudes approaching the poles, many attempts have been made to create map projections which, although similar to it, improve upon it in this respect.

One such projection, which has appeared in a number of British atlases, is Gall's projection. This projection uses the stereographic projection, which we will encounter later:

and which is the conformal azimuthal projection, as the guide for how rapidly the parallels should spread apart in it. Since it is cylindrical, and not azimuthal, of course, this does not yield a conformal projection.

Gall's projection looks like this:

Note that because the northern and southern parts of the map are stretched horizontally, the map as a whole was stretched vertically; in this way, while tropical countries are stretched vertically, the map's standard parallels, where the stretching is balanced, are at 45 degrees north and south, allowing the temperate countries to be shown well.

If we don't stretch the map, we get Braun's projection:

and I must admit I generally prefer projections not to be stretched overall in the fashion of Gall's projection. Thus, I will be showing the Plate Carré and Cylindrical Equal-Area projections with the Equator as their standard parallel in forthcoming pages. Some projections with such an overall stretch, though, were too notable to exclude, and do not have an alternate form without it, specifically the Mollweide projection and the Eckert IV projection.

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