Bogomoly's site doesn't mention it, but proof #69 can be thought of as
an infinite double tiling of the plane.
Furthermore, an infinite number of new proofs can be generated by
sliding the square an increment in any direction and adding up the
areas.
So the number of proofs is not just 78.
-Roger
On Jul 4, 2008, at 12:52 PM, Robert Holmes wrote:
Re today's discussion about proofs of the Pythagorean theorem -
here's a link to a page with ~80 proofs: http://www.cut-the-knot.org/pythagoras/index.shtml
Proof #4 is the one that Frank & I were so impressed with; #1 is the
one that Nick (along with anyone who graduated St Johns) failed to
reproduce; #5 is the one due to Pres. Garfield (an intelligent
president! those were the days...). And you can get an "extra-
geometric" proof that relies on Newton's 2nd law at http://www.cut-the-knot.org/pythagoras/mech.shtml
Robert
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