Distances between Washington D.C. and Kabul, Afghanistan by projection:

Conformal:
                GCS WGS 1984- 7,000 miles
                Mercator- 10,100 miles

Equal Area:
                Goode Homolosine- 10,000 miles
                Mollweide- 7,920 miles
                             
Equidistant:
                Plate Carree- 10,100 miles              
                Equidistant conic- 6,950 miles

            A map projection is a representation of the three dimensional globe on a two-dimensional surface, such as a piece of paper or a computer screen. Because of the difference in the number of dimensions, it would be impossible to copy the globe onto a two-dimensional surface completely accurately. There are many different types of projections that can be used, preserving some certain geographic properties while allow distortions in others, depending on the purpose of the map.
            One type of map projection is equal-area, in which the area of objects on the map is preserved, making these types of maps ideal for projecting continuous raster data. The equal-area projections I used were the Goode Homolosine projection and the Mollweide projection. Goode Homolosine is pseudocylindrical and interrupted, whereas Mollweide is pseudocylindrical and uninterrupted.
            Another type of map projection is equidistant, in which, a distance from some specific point or line on the map is preserved. The equidistant projections I chose to use were Plate Carree and Equidistant Conic. In Plate Carree, distance is preserved at the equator, whereas Equidistant conic is centered on the North Pole.
          One more type of projection I did was conformal, which preserves angles. For this I did GCS WGS 1984 and Mercator. GCS WGS 1984 is the standard coordinate system used for GPS, and Mercator is a cylindrical projection, useful for navigation because of its ability to chart courses without them becoming distorted.
          Clearly there are many different ways to project maps, and we can see why we may want to choose one projection over another, depending on what we want to map. It is also clear that we must be careful with the maps we look at, and we need to consciously take into consideration the amount of distortion present. The distance between Washington D.C. and Kabul, Afghanistan varies by over 3,000 miles depending on which projection is used. Even looking from map to map, we can see how drastic these distortions are. The representation of Antarctica is by for the most various and most profound throughout the different projections.