Comments on: Whole Rectangles http://yaniv.leviathanonline.com/blog/riddles/whole-rectangles/ Strain your Brain Tue, 13 Sep 2011 13:21:47 -0700 hourly 1 http://wordpress.org/?v=3.1 By: Danny http://yaniv.leviathanonline.com/blog/riddles/whole-rectangles/comment-page-1/#comment-22 Danny Sat, 26 May 2007 13:13:58 +0000 http://yaniv.leviathanonline.com/blog/riddles/whole-rectangles/#comment-22 [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. [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.

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