Map projections are two dimensional representations of a three dimensional globe. Conceptually, projections are created by inserting a light source inside of a semi-transparent globe and wrapping the globe in a sheet of paper. The features of the globe will be “projected” on the surface of the 2D sheet. Depending on the orientation of the sheet, different projections are produced.
There are issues inherent within the translation process that can distort everything from angles and distances, to shapes and areas. These problems become apparent when trying to measure any of the aforementioned quantities. For example, in the maps above, I attempted to measure the distance between Washington D.C. and Kabul, Afghanistan. For this I used a straight line measurement tool in the ArcMap program. As one can see the distances vary greatly from map to map, even on those maps that are “equidistant,” (more about this later).
Luckily, certain projections can preserve certain measurements. Conformational projections such as the Mercator and Gall Stereographic projections preserve angles. Equidistant projections preserve the distance between points. Equal Area projections preserve the area of polygons. There is an important caveat to this however. Notice how on the equidistant projections, the distance between Kabul and D.C. still differ between the Equidistant Conic and Equidistant Cylindrical projections. This is because within projection categories, maps can preserve different aspects of distance, or angles, or areas etc. For example, in the conformational projections, the Mercator projection preserves the angles of rhumb lines, or lines of constant course; however, the Gall Stereographic projection preserves the shapes of circles.
The specific qualities of projections, if known, can prove to be useful. Mercator projections for example were ideal for navigators on sailing ships because straight lines drawn on the map correspond to real-world courses. If you were to draw a straight line on an Equidistant Cylindrical projection, the line would not correspond to your real-world course. Again, this is because moving over a 3D surface is different from moving over a 2D surface.