Tuesday, July 20, 2010

pi day down under

My maths by mail subscription just notified me that this Thursday is considered pi day in Australia (22/7 rather than 3.14). I am used to celebrating in March, but I am glad to hear that we can justify celebrating twice a year.

Unfortunately, there seems to be only one day that we can celebrate as tau day, and only one day for celebrating e.

Wednesday, July 7, 2010

eschering and coxetering

Much has been written about how the work of M.C. Escher was inspired by mathematics and has inspired mathematicians in turn. The relationship between math and art in the work of Escher is still the subject of analysis and discussion: in this month's Notices of the AMS, there is a very interesting article on the mathematical aspects of M.C. Escher's work by Doris Schattschneider.

As Schattschneider describes, the mathematician that alternately inspired and frustrated Escher in much of his work was Donald Coxeter. If you haven't read it yet, you should check out Siobhan Roberts's King of Infinite Space, a popular biography of Coxeter, which also discusses his relationship with Escher.

Way back in 2003, the hyperbolic tilings that Escher and Coxeter corresponded about were used for the Mathematical Awareness Month poster, and Douglas Dunham wrote an accompanying essay to explain how the image for the poster was created.

My own meager contribution: here are two little GSP activities (one here, the other here) inspired by some of Escher's plane tilings.

Monday, July 5, 2010

de Morgan's magic square

In The Elements of Arithmetic (1830), Augustus De Morgan (noted in Wikipedia for his peculiarities) has a little fun after explaining how to add multi-digit numbers. On page 20, De Morgan presents this exercise:

Not the most gentle exercise for someone who just learned how to add.

If you divide all the entries by 36, you'll see that this is a magic square of order 11 (magic constant 671).

The Wolfram Mathworld article on magic squares explains various ways of generating magic squares. It looks like  De Morgan used what came to be known as the "Siamese method" starting in the cell (6,7) with an order vector of (1,1) (shown in blue below) and a break vector of (0,2) (shown in red below).