How Was the Pythagorean Thoerem Proved?

Date: 06/05/2006 at 12:09:12
From: Phyllis
Subject: Pythagorean Theorem

How did Pythagoras derive the Pythagorean Theorem?

Date: 06/05/2006 at 14:53:13
From: Doctor Peterson
Subject: Re: Pythagorean Theorem

Hi, Phyllis.

According to my books, we know so little about Pythagoras that the
best we can say is that "the Pythagorean theorem is ascribed to the
Pythagoreans" (him and his followers); we don't know how, or even
whether, he or they actually proved it. They were not the first to
know it, though; the Chinese, the Babylonians, and perhaps the
Egyptians, also were aware of it.

Here is a quotation from D. E. Smith's History of Mathematics:

  The proof of the proposition is attributed to Pythagoras (c. 540
  B.C.) by various writers, including Proclus (c. 460), Plutarch
  (1st century), Cicero (c. 50 B.C.), Diogenes Laertius (2nd
  century), and Athenaeus (c. 300). No one of these lived within,
  say, five centuries of Pythagoras, so that we have only a weak
  tradition on which to rest the general belief that Pythagoras was
  the first to prove the theorem. It would seem as if such an
  important piece of history would have some mention in the works
  of a man like Aristotle; but, on the other hand, it is difficult
  to see how such a tradition should be so generally received unless
  it were well founded. Not only are we not positive that the proof
  is due to Pythagoras at all, but we are still more in doubt as to
  the line of demonstration that he may have followed.

You can see Euclid's proof in the Elements; but there's a good chance
that that is not what Pythagoras would have done!

If you have any further questions, feel free to write back.


- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/