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Saturday, September 8, 2012

Theorem-lovers: Take Your Pick

(via Tosha at Wikimedia Commons)
                    A = i + \frac{b}{2} - 1.

Richard Elwes (@RichardElwes) recently tweeted a link to his latest article on "Pick's theorem," a beautifully simple, comprehensible, almost quirky piece of geometry, dealing with the area of a polygon in a lattice grid:

http://education.lms.ac.uk/2012/09/in-praise-of-pick%E2%80%99s-theorem/

In a sentiment that is echoed by many others, Cliff Pickover says in his "The Math Book," "Pick's theorem is delightful for its simplicity, and it can be experimented with using a pencil and graph paper."

Another treatment of the theorem here:

http://simomaths.wordpress.com/2011/12/08/picks-theorem-and-some-interesting-applications/

Interestingly, Pick's theorem works in the geometric plane, but NOT in 3-dimensional space.

Austrian mathematician Georg Pick originally proposed the theorem in 1899, but it wasn't popularized until 1969, long after Pick himself had died in a Nazi concentration camp in 1942.


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