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on Friday, May 25th, 2007 at 9:16 pm and is filed under Math, Riddles.
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[no spoilers, but points to spoilers]
This is indeed a great riddle, because one can solve it in so many ways: using graph-theory, using complex integration (the ‘standard’ proof), etc.
For a few simple proofs, see http://www.inference.phy.cam.ac.uk/mackay/rectangles/ (also inside: a link to an article from 1987, that proves the theorem in 14 *different* ways).
By the way, the same theorem holds even if you define a ‘whole’ rectangle as one having at least one *rational* side, or even one *algebraic* side.
May 26th, 2007 at 4:13 pm
[no spoilers, but points to spoilers]
This is indeed a great riddle, because one can solve it in so many ways: using graph-theory, using complex integration (the ‘standard’ proof), etc.
For a few simple proofs, see http://www.inference.phy.cam.ac.uk/mackay/rectangles/ (also inside: a link to an article from 1987, that proves the theorem in 14 *different* ways).
By the way, the same theorem holds even if you define a ‘whole’ rectangle as one having at least one *rational* side, or even one *algebraic* side.