Update on Archimedes.

Back in October, I mentioned a Nova program on a Medieval copy of a manuscript from Archimedes. A recent article describes one of the findings from that manuscript. Part of the manuscript is called the Stomachion, which a Stanford historian of mathematics says is a treatise on combinatorics, a field that did not come into its own until the rise of computer science. The goal of combinatorics is to determine how many ways a given problem can be solved. And finding the number of ways that the problem posed in the Stomachion can be solved is so difficult that it took a team of four combinatorics experts six weeks to solve it.

Part of the problem was that most of the introduction to the Stomachion was illegible, so it appeared to be a children's entertainment, taking fourteen shapes and trying to put them together to make shapes, like elephants. Although this seemed to be beneath Archimedes' talent, there was no clearer explanation. It now appears, though, that Archimedes was interested in seeing how many different ways there were to put the shapes together to form a square, the essence of combinatorics. And the historian believes that Archimedes must have had a solution to the question, although that solution doesn't appear in the manuscript.

And how many different ways are there to put these irregular shapes together to form a square? 17, 152. This site has a graphic showing all of them, not counting reflections and rotations, which brings it down to 536. (Bring a magnifying glass.)