This assignment revealed many interesting aspects of the map projection process.  The first piece of information I learned was that there are several different ways to measure distance between two points on a map.  In addition, different map projections represent these distances with different values.  For example, using the planar measurement, Kabul to Washington DC was 10,141 miles in the Mercator Projection, 8,329 miles in the Hammer-Aitoff Projection, 9,919 miles in the Stereographic Projection, 8,341 miles in the Azimuthal Equidistant Projection, 8,763 miles in the Behrman Cyinder Projection, and 6,919 miles in the Two-Point Equidistant Projection.  Overall, the Great Elliptic and Geodesic measurements were the most consistent (and always identical to each other) while the Planar measurement was the least consistent.  The rest of the data is stored in the table below.

                While no map was perfect, each projection had strengths and weaknesses.  The Hammer-Aitoff Projection and the Behrman Cylinder Projection were both very good at preserving areas; Greenland was not bloated like it is on most maps, and Africa took up its due space.  However, in the Hammer-Aitoff Projection, the shapes of the Pacific Rim nations (such as China and the United States) are heavily bent.  In the Behrman Projection, Africa is stretched vertically and Greenland is squished vertically.  Both maps, in this sense, fail to convey the shapes of the world.

                The Stereographic Projection and the Mercator Projection both preserved the shapes of individual countries nicely.  In both projections, the United States looks like it does on the globe.  The same is true with Greenland and with China.  However, the relative areas of these countries differ greatly from reality.  In the Mercator Projection, Greenland looks bigger than the continent of Africa.  Even more peculiar is the Stereographic Projection, in which the United States was rotated on its side about seventy degrees and Australia appears several times the size of South America.  The planar distances in these two maps between Washington DC and Kabul also differ the most from the actual distance.  Likewise, the equidistant maps had shortcomings.  Both the Azimuthal Projection and the Two-Point Equidistant Projection reported relatively accurate planar distances between the two cities, but distances between more Pacific cities came out distorted and the shapes of countries were very inaccurate.

                For most applications, it seems a hybrid map style is most suitable to depict the world.  An equal area map will distort angles and distances.  A conformal map will distort distances and areas and an equidistant map will distort angles and areas.  In a few applications—such as examining the missile range of North Korea—one of these three partially perfect styles may be needed.  But in most cases, one must compromise in order to get a good depiction of the globe’s geography.  For most applications, the best map will have slightly inaccurate angles, distances and shapes.  That way, none of the three elements is too distorted.

Projection Type:	Hammer-Aitoff	Behrman	Stereographic	Mercator	Azimuthal	Two-Point
Planar Distance	8,329 miles	8,763	9,919	10,141	8,341	6,919
Geodesic Distance	6,934 miles	6,934	6,934	6,934	6,934	6,919
Loxodrome Distance	8,112 miles	8,112	8,112	8,112	8,112	8,093
Great Elliptic Distance	6,934 miles	6,934	6,934	6,934	6,934	6,919