Subject: Re: [HM] "President Garfield's Proof"
From: Ed Sandifer (SANDIFER@wcsub.ctstateu.edu)
Date: Mon Jan 17 2000 - 16:19:23 EST
Allow me to make a case that disagrees somewhat with Michael Lambrou, who
wrote of President Garfield's proof:
"Well, to criticize the proof, I feel that it does not have enough new
ideas to qualify it as a genuinely new proof: ..."
Some people are "splitters", and find differences between things.
Loomis, who collected over 300 "different" proofs of the Pythagorean
theorem was such a style of thinker. Among those, there are many pairs that
seem to me more closely related than the Garfield proof and the Chinese
proof, though, indeed, these two are very similar.
Other people ar "lumpers", and find similarities among things. A
determined lumper might find as few as three really different central ideas
among the 300 proofs Loomis collected, though most of us would divide them
into two main families, similarity proofs and dissection proofs, and perhaps
6 to 10 smaller families.
If I were trying to demonstrate that the Pythagorean theorem has a
variety of different proofs, I would certainly not choose the Garfield/Chinese
pair to support my contention.
On the other hand, if I were trying to demonstrate that diverse
cultures solve the same problems and discover very similar solutions, despite
their separation in time, space and culture, then I might choose this pair.
That said, let me paraphrase two Williams, Gates and Clinton, and say
"It depends on what you mean by 'different.'"
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* Ed Sandifer * sandifer@wcsu.ctstateu.edu *
* Professor of Mathematics * *
* Western Connecticut State University* www.wcsu.ctstateu.edu/~SANDIFER/*
* Danbury, CT 06810 * *
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