This is a section of Giovanni Maria Cassini’s globe, a very beautiful object, which you can view in great detail at David Rumsey’s map site. You can see that Cassini knew something I was just guessing at, how to find the radius of the curve of map gores. Dr. Math tried to explain it to me, but he’s a mathematician and I’m a dilletante and we have trouble communicating. Every time I read the term “radians,” a wee pixie comes in through the cat door and blows out my pilot light. The eyes glaze over and the frontal lobes grow cold and I wake up eight hours later, surrounded by empty 40 ounce malt liquor bottles and professional wrestling, blaring on the television.
This is not the royal road to geometry. This is not even the on-ramp.
I kept thinking it was a spherical triangle thing. It probably is, but since I can’t manage to get the concept into my head, I tried doing it with good old Pythagoras and a piece of paper. (Well, actually, I was sketching madly on my tablet pc, amusing the other bus passengers no end.) It is not beautiful, but I think it works. Feel free to disagree; I won’t argue.
(For our foreign readers, I will mention that a pixie is a small, semi-mythical being, very like a leprechaun, but with a post-punk sensibility.)
Hey, speaking of Pythagoras, are any of our South Asian readers familiar with the medieval mathematician, Bhaskara II? Came across a reference to his having done a proof of the Pythagorean theorem by folding paper, but I can’t find any details on this.