Above, left: cylindrical "normal": Above right: cylindrical transverse; lower left: cylindrical oblique.
Then, to complicate matters even further, the "developable surface" can be "tangent," considered to have points or lines of tangency where it is touching the globe, or it can be "secant," which means the developable surface seems to be slicing through the globe. Secant projects have the advantage of additional points of tangency, and therefore more areas on the map that are "true."
And, then, we have projection classification by method of light source: from where, in our imaginary transfer of data from the face of the globe to the projection surface, is the light coming? There’s Gnomonic (light projected from the center of the globe to projection surface); Stereographic (light projected from the antipode of point of tangency); or Orthographic (light projected from infinity).
And, here are some tres cool maps that use unusual projections which I found when poking around on the Internet:
This is a map of Human Migration, using the Dymaxion Projection. The choice of this particular projection highlights the interconnectedness of the land masses of the world, and makes it easy to see the flow of humankind over the centuries.
Another one based on the Dymaxion Projection! and I suspect for the same reason as the Human Migration map. This one portrays a prediction of the energy grid of the future, with various types of energy sources named.
And, just for kicks, here is the Cassini Projection, developed by César-François Cassini de Thury in 1745. This is the son of the guy for whom the Cassini spacecraft was named (Giovani-Domenico Cassini), even though NASA is not using his projection to map the data, but rather an oblique conformal projection. But Cassini (the elder) was the first to observe and document Saturn’s moons, and that’s probably why they named the spacecraft after him. He also began the work to create a comprehensive topographic map of France, work that was completed by his son and grandson over a century later. He used the then-new method of triangulation and his own method of determining longitude, which meant that this was the first truly accurate map of France. Unfortunately, this accuracy resulted in a much smaller France than the Sun King Louis XIV (who commissioned the survey) was expecting. Apparently the King joked that Cassini had taken more of France from him than he had won in all his wars. It was the first topo map of an entire country.
An application of theCassini Projection - Present and fossil teeth suggest several migration waves in the past, when reduced sea levels created bridges between now isolated Japanese and Aleutian islands. From:
And to end up on a humorous note, here is a part of a poem about, of all things, maps! and their use (or not!) in navigation
Fit the First - The Landing
Undertaking another as well
Fit the Second - The Bellman's Speech
UPDATE - September 10, 2011: Map Monkey has instituted a map projection identification contest! For details, see http://geographer-at-large.blogspot.com/2011/09/name-that-map-projection.html