In spherical geometry, the shortest-length curve between two points on the surface of the sphere turns out to be part of a Great Circle – an equator-line circle that cuts the sphere in half. So lines are circles, which is fun to share with philosophers. (Note – taxicab geometry provides that same amusement, where circles are squares.)

So a natural question, where “natural” means I never actually thought of it but wish I had, is What is the longest line along the surface of the earth that goes entirely through water? This would be the longest possible straight-line sailing distance, if you ignored all the physical aspects of sailing like wind and water currents. Fortunately, before I even thought of the question, someone had answered it. Behold!

This gif appears to be from a youtube video by Patrick Anderson of 2012 (here) which has the advantage of being a little slower.

So that raises the question of the longest straight-line distance through land. And here’s a guess at it: http://i.imgur.com/nbNfl.jpg and then another one https://sites.google.com/site/guybruneau/fun-stuff/longest-distance-on-land, although that second one it doesn’t quite look like part of a Great Circle so possibly the projection imposed a different geometry. Or possibly I have trouble visualizing projections of Great Circles, which is also possible because they are weird. (The cool kind of weird, of course.)

*Thanks CJ for sending me that gif, although now that I’m finding myself asking questions like “What line passes through the most countries?” I can tell that it’s going to keep me from my grading for longer than it should.*