25 March 2011
du Sautoy on symmetry
An interesting TED talk: Marcus du Sautoy on symmetry -- interesting to watch, lots of pictures; ignore the fact that it starts with the standard slightly overwrought version of Galois' story. If you want a more accurate version, I recommend Amir Alexander's Duel at Dawn: Heroes, Martyrs, and the Rise of Modern Mathematics . About halfway through he gives a presentation of a proof that the two groups of order 6 are different. (One, the cyclic group of order six, is abelian; the other, the symmetric group on three elements, is not.) I particularly like the pictures of the Alhambra, on which du Sautoy has overlaid animations showing the effect of rotating them. Presumably they won't let you do this if you actually go there.