Talk:Geometry/Chapter 14

How about including some more diagrams which can serve as proof of the theorem, perhaps the one with the three squares on the outside of the center triangle, or the one with three circles. Perhaps I will upload some myself. --Navaburo 01:48, 24 September 2006 (UTC)

There was a time when a certain French mathematics journal (I forget the name) actually banned the use of diagrams in proofs in their articles. Why? Because they found too many authors were drawing figures that were special cases or otherwise fooled the author (and reader) into thinking something not yet proved was proved because "it is obvious from the diagram".

So here, too. Even the first diagram used in the main text of chapter 14 for 'proving' the Pythagorean Theorem obscures the fact that the author of the proof did not prove that the figure formed by all four instances of the hypotenuse c really IS a square. By the time you dot all your i's and cross all your t's, the proof is not that simple after all, even though the symmetry is so highly suggestive. This is one of several reasons Euclid did not do it this way, choosing a proof that at first glance appears more obscure and complicated.

Now if the author had first proved that the only quadrilateral with C4 symmetry is the square, then fixing his proof (of the PT) would have been much easier, so the diagram based proof would still be useful. But as it is...

24.4.133.80 (discuss) 01:59, 24 April 2014 (UTC)