This is a remarkable projection, for a couple of reasons. First, it was invented by a highly influential 19th-Century American philosopher. Second, it's a con

This is a remarkable projection, for a couple of reasons. First, it was invented by a highly influential 19th-Century American philosopher. Second, it's a conformal† projection that can be infinitely tiled in every direction. Third, some really crazy things occur at four points on the equator. At these points, if you're traveling straight along the equator in the real world, you make a sudden 90-degree turn on the map. If you travel straight ahead on the map, you've actually done a sharp 180-degree turn in real life. If you make one circle on the map around one of these points, you've actually gone around the point twice in real life. All this strange behavior has to do with the fact that at these four precise points, the map is actually not conformal. † Conformal projections preserve shapes locally. That means that in any small region of the map, a shape drawn on the ground will retain its shape when projected onto the map. It will be scaled up or down in size, but it won't be stretched along only one axis or sheared.