Magic squares
This blackboard comes from the website Blackboard of the Day or BBOTD. If you click on ‘Mathematics’ at the top of the page you get taken to loads of wonderful mathematics blackboard photos, and from time to time I will post my favourite pictures on this blog too.
This board was the result of a conversation between the Fields medallist Cédric Villani and an unnamed audience at the University of Lyon. Cédric started by showing them the magic square in the bottom right corner, where every row, column and diagonal adds to 65. This can be better understood by joining the top edge to the bottom edge and the left edge to the right edge to form a torus, as drawn in the top left corner. The audience weren’t so impressed because this sort of magic square is well known and understood. Thereupon Cédric drew a magic hexagon (top right) in which the sum of every vertical and diagonal line added up to 38. Moreover, he claimed that this was the only such magic hexagon. Attempts to draw this hexagon on a torus did not provide further understanding and the audience was left frustrated.
Finally, the discussion became topological and the group realised that they could draw the Borromean rings by folding sides of a cube in half, as shown in the middle drawing.
That cube is topologically a dodecahedron too:
http://homepages.warwick.ac.uk/~maaac/notknot.html
November 19, 2012 at 9:51 pm