Talk:Pythagorean theorem

Dijkstra generalization as subsection 9.10 of main article

In Euclidean geometry, Pythagoras' Theorem holds for any three points A, B and C such that through A and C a straight line can be drawn orthogonal to a straight line through B and C. How many mathematicians appreciate that the theorem remains applicable when some or all of the points A, B and C coincide? it is widely used all over the world.also ,it is a good tool to help with the problems about Shortest Path!

Yet this seems largely responsible for the convenience with which Pythagoras theorem can be used:

Edsger W. DIJKSTRA. "Notes on Structured Programming". p. 3 month = apr, year = "1970", note = "circulated privately", url = "http://www.cs.utexas.edu/users/EWD/ewd02xx/EWD249.PDF". 

— Preceding unsigned comment added by NumoNF (talk • contribs) 05:11, 9 October 2011

Making this article readable for non-experts - i.e. as if it were a sort of encylcopedia

The following sentence "the theorem is about both areas and lengths, or can be said to have both areal and metric interpretations" is gratuitously obscure. No one not versed in mathematics knows what "areal" means or for that matter what is meant by "metric." An encyclopedia should explain things for a motivated, intelligent and reasonably educated reader - this sentence puts me on the hunt for a textbook which will explain to me the difference (in mathematical terms" between "areal" and "metric." So please someone who understands the difference could you either rewrite this article without this jargon - or tell us what these words mean. — Preceding unsigned comment added by 208.124.226.27 (talk) 22:12, 16 October 2011 (UTC)

You are right. It's not at all clear what they mean or what their significance is, and I can't read the reference to find out. Even if I could adding detail about the significance of 'areal' and 'metric' proofs would I think be a lengthy digression. The proofs are already organised in ways we recognise today, i.e. broadly into geometric and non-geometric, then within the geometric proofs there are proofs by rearrangement and others, and so on. So I've removed all mentions of them, adding a couple of sentences about the proofs to summarise them in a more general way.--JohnBlackburne^words_deeds 22:38, 16 October 2011 (UTC)

That sentence was very helpful! Once I was trying to find a proof and did not succeed until I was given the tip to think in terms of areas! Because you can state the Pythagorean theorem without talking about areas: "the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides", here square refers not to the polygon but to the exponentiation operation. Weimer (talk) 12:04, 27 November 2011 (UTC)

I would say 'square' can be thought of both ways, as both an arithmetic or algebraic operation of multiplying a number by itself and a geometric one of forming a square with side equal to a length to get the area. So the statement can be interpreted two ways, but these are algebraic and geometric, not 'areal' and 'metric'. These are not terms commonly used today, so would need explanation as to their significance. It seems odd to try and categorise the proofs as 'areal' or 'metric' as all of them are about lengths, and how the lengths are related through the areas. And as they are already organised into geometric and other proofs it's redundant.--JohnBlackburne^words_deeds 13:19, 27 November 2011 (UTC)

History of the Theorem in the introduction

Right now the paragraph on the history of the theorem in the Introduction reads:

Indented line The Pythagorean theorem is named after the Greek mathematician Pythagoras, who by tradition is credited with its discovery and proof,[2][3] although it is often argued that knowledge of the theorem predates him. There is evidence that Babylonian mathematicians understood the formula, although there is little surviving evidence that they fitted it into a mathematical framework.[4][5]

I suggest that we change it to:

Indented line The Pythagorean theorem is named after the Greek mathematician Pythagoras, who by tradition is credited with its discovery and proof,[2][3] although it is often argued that knowledge of the theorem predates him. References to Pythagorean triples, and to the theorem, have been found in ancient texts from Babylon, China and India.

In its current form, the introductions seems to go into the detail of only one of the other possible sources of the theorem, though all three sources listed in the History section (Babylonian list of triples, Zhou Bi Suan Jing, and the Apastamba Shulba Sutras) are claimed to predate Pythagoras. Mentioning only Pythagoras and Babylon therefore sounds (at least to me) mildly POV (unless of course the claims in the History section can be challenged, but they appear to be properly sourced). Piyush (talk) 23:43, 4 December 2011 (UTC)

It's not clear that the others predate Pythagoras: the dates for each is much vaguer, raging from before to after his dates, so there's no evidence for them actually predating him. Even if they were there's no evidence that knowledge spread to Greece. The Babylonian tablets are much earlier and there's evidence that much of their maths was preserved through the Greeks: for example we are thought to have 360 degrees in a full turn and 60 minutes in the hour because of them. The article does suggest the theory reached India from Babylon (there's a lengthy quote in the ref), but I don't know how likely that is.--JohnBlackburne^words_deeds 01:33, 5 December 2011 (UTC)

The lengthy quote also does not give any evidence for why it is more likely that it would have reached India from Babylon, or if indeed it is likely at all. On the other hand, the article on Shulba Sutras includes a citation to Plofker, which attributes the appearance to the Baudhayana Shulba Sutras, and dates them to 800-600BC (which is before the time of Pythagoras), supposedly on linguistic evidence. I am not an expert, so I wouldn't know which to give more weight. What I find puzzling is the lack of primary sources: both of the above two quotes (Boyer and Plofker) seem to pulling data out if thin air (Mesopotamian influence on Shulba Sutras for Boyer and dates for the Shulba Sutras in the latter). Tongue firmly in cheek, I would like to suggest they might have their own opposing POVs. Piyush (talk) 05:52, 6 December 2011 (UTC)

I just notied another curious (but referenced) statement in the article: "According to Albert Bŭrk, this is the original proof of the theorem; he further theorizes that Pythagoras visited Arakonam, India, and copied it." Looks like there is a lot of assertion without evidence (or on lousy evidence) going on in the field of the history of Pythagoras theorem, so I guess I had better leave it alone till the historians figure out whether the Indians copied it from the Mesopotamians, or the Greeks copied it from the Indians and the Mesopotamians. Piyush (talk) 06:00, 6 December 2011 (UTC)

Why do you say it's referenced? Finding no source, I removed it. Dicklyon (talk) 06:06, 6 December 2011 (UTC)

Yes, I just noticed the statement was not sourced. However, a quick Google search reveals this reference. That reference also dates the statements in both the Baudhayan and Apastamba Sulba Sutras to 800BCE and 600BCE respectively. I am not adding these in now, but I think some restructuring of the treatment of the history of the theorem seems warranted, especially in light of the fact that all sources seem to date both Baudhayan and Apatamba before Pythagoras, contrary to the claims that these dates are "disputed". Piyush (talk) 15:29, 6 December 2011 (UTC)

Also, there seems to be some confusion about Shulba Sutras: my reading of the references seems to be that there are many of them, dated between 800BCE and 200CE, but the ones most relevant to this article (Baudhayana and Apastamba) are among the oldest and date between 800BCE and 600BCE. Piyush (talk) 15:31, 6 December 2011 (UTC)

One more point: I thing in spite of the reference being available, we should leave out Albert Burk's statement, since it seems to be not well accepted. I am also not sure about Boyer's claim of Mesopotamian origin though: that seems disputed too, and the only reason Boyer gives is that the triplets are the same as those given in Babylonian texts. That doesn't look like a reason to impute origin at all, since it is equally likely that the writers of the Shulba Sutras and the Babylonians hit upon the same rule. But before deciding on removing it, we probably need reference which either raise these objections or give support for Boyer's claim of Babylonian origin. Piyush (talk) 15:39, 6 December 2011 (UTC)

copyright issue

From the link posted above it seems the history section was in large part copied from that source with minor rearrangements (possibly done by editors since). The problem is too large to be easily fixed so I've blanked the section. It can be reintroduced if someone spends the time rewriting pretty much all of it to avoid the copyright violations, though even then it would suffer from being based on a single source.--JohnBlackburne^words_deeds 15:43, 6 December 2011 (UTC)

mea culpa, it seems there's not a copyright problem. The book was published in 2007, I've checked the page history and the history section is at least that old. The book is copied from Wikipedia, i.e. it used this article as a very close source. So it is certainly not a valuable source here, per WP:CIRCULAR. First time I've had to write that about a print publication !--JohnBlackburne^words_deeds 15:54, 6 December 2011 (UTC)

Wow!Piyush (talk) 22:23, 11 December 2011 (UTC)