This is the talk page for discussing improvements to the Pythagorean theorem page.

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Arbitrary square?

I should recommend that the proof start out with an arbitrary right triangle, and then construct the square from that, instead of beginning with an arbitrary square.

Localhost00 03:38, 22 March 2008 (UTC)localhost00

I don't disagree with your logic. I've seen similar proofs elsewhere. While not stated in the proof, it is nonetheless obvious that an arbitrary right triangle can be constructed with proper choice of square side length c, rotating the inner (green) square suitably, and finally shrinking or expanding the outer square (blue) such that each side is tangent to exactly one vertex of the inner square. There's more than one way to skin a cat. In fact, after having written up this proof, I checked the web site cut-the-knot.org, which lists no less than 77 proofs of the Pythagorean Theorem. The method you describe is listed somewhere near the top and, by my admission, is conceptually more straightforward. What I recommend is separating multiple proofs into subpages (formed simply by adding a slash and some additional text to the title). In such an arrangement, the most conceptually straightforward proof can be listed first, with less straightforward proofs subsequently catalogued. I would defend the deliberate inclusion of multiple proofs by this reasoning: it illustrates the connectedness of mathematics and promotes lateral thinking. Fermat's Last Theorem wasn't proven using elementary number theory, for example. It was proven by drawing from the theory of elliptic curves (of which I know virtually nothing). If you sift through the 77 proofs, you'll notice several standouts which, at first glance, appear to have nothing whatsoever to do with the Pythagorean Theorem. Their full-text proofs are shockingly complex. Nevertheless, they vividly demonstrate the power of "outside-the-box" thinking. Would you agree to exhibiting multiple proofs?
Whikiker 05:29, 22 March 2008 (UTC)
I don't see any problem with hosting multiple proofs. I would prefer having a main page for one proof, and then an extra page for other proofs. Also, I might want to move proof pages to something like "Pythagorean Theorem/proof"
Localhost00 21:06, 22 March 2008 (UTC)localhost00

caps

Capital "T" in "Theorem"? —こいする 06:46, 13 June 2008 (UTC)

No, the word theorem shouldn't be capitalized. A user did a cut-and-paste page move of the contents of the article at Pythagorean theorem (18 September 2006 version by Braindrain0000) to the title Pythagorean Theorem (29 November 2007 version by LindySoul), overwriting a redirect left there when I did a real page move to the non-capitalized version of the title back in June 2006. Such cut-and-paste "moves" are discouraged (to put it nicely) because they break the continuity of the article history. Accordingly, this page has been reverted back to the version just before the move, and then updated to the last version of the article at the other title. Unfortunately, this "reconstruction" also breaks the history, so see [1] for the edits made by LindySoul and myself while the article was at the other (capitalized) title. I did it this way because I believe if I had forced a page move back to the current (non-trivial-history) page title, it would have deleted the original page history. I wanted to keep both. - dcljr 01:53, 14 June 2008 (UTC)
BTW, note that if page moves are always done using "Special:Movepage" — i.e., the "move" tab at the top of the article — then they can be done any number of times to an article without worrying about losing any of the edit history. If a user finds that they can't move a page that way (because of a non-trivial edit history at the destination title), then they should consult an administrator about the issue. They should not simply cut-and-paste the contents to the new title. - dcljr 02:14, 14 June 2008 (UTC)
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