Talk:Pythagorean theorem

Deletion of animation

This animation was deleted with the reason Wikipedia:External links. Can a specific reason be selected from the several pages of this article? Brews ohare (talk) 19:41, 4 August 2010 (UTC)

I removed it per wp:ELNO #1, #8 (Flash), #11, #13, and specially per wp:PROMO (personal webpage, selling CD with all the animations). See Peetvanschalkwyk (talk · contribs). User was spamming his own work using various IP's and later using this username. See warnings and relevant links to IP-talk pages with similar warnings on this revision of his talk page. Furthermore, during the animation some of the squares grow and shrink again, which looks odd, if not suspicious. Fancy graphics, but poorly conceived. DVdm (talk) 20:08, 4 August 2010 (UTC)

By the way, when you check the history of this article, you can see that these reasons were selected and stated 3 times in the edit summaries: [1], [2], [3]. DVdm (talk) 20:16, 4 August 2010 (UTC)

Terrible source

How is it possible that in an ecyclopedic article we use material from a book called Pride of India: a glimpse into India's scientific heritage, which tells us how the speed of the light is mentioned in the vedas and how Ayharbata developed an heliocentric theory? It´s a shame for wikipedia to use pseudoscientific book written by indian nationalists.--Knight1993 (talk) 18:44, 9 August 2010 (UTC)

Animation

Hi, recently I found a very didactic animation that I think would be very suitable in this article, but I'm not good at making animations, maybe someone can make something similar to that? (I think we need to credit the author of the original animation, saying our animation is based in it). What do you think? Thanks. AmigoDoPaulo (talk) 03:09, 26 August 2010 (UTC)

I personally don't think this animation has much didactic value. On the contrary: two of the "squares" aren't even square to begin with. With that corrected, I don't think it would add something valuable to the (already heavily overloaded) article that isn't already there. DVdm (talk) 07:40, 26 August 2010 (UTC)

"Already heavily overloaded" is right. I think the 40 KB article that we had in April was better than the 95 KB that Brews bloated it into. Dicklyon (talk) 04:51, 27 August 2010 (UTC)

Converse?

The first statement in the converse section is not quite right:

For any three positive numbers a, b, and c such that $a^{2}+b^{2}=c^{2}$, there exists a triangle with sides a, b and c, and every such triangle has a right angle between the sides of lengths a and b.

The first part of this statement is not the converse to the Pythagorean theorem. It actually follows directly from the Pythagorean theorem. Simply take a right triangle with side lengths a and b. By Pythagoras' theorem, the hypotenuse must be c. Showing that any triangle with side lengths a,b, and c satisfying $a^{2}+b^{2}=c^{2}$ has a right angle is the converse. This is stated a few lines down, but I wonder why the section on the converse does not start with this. I will change if no one objects. Paul Laroque (talk) 03:02, 28 September 2010 (UTC)

You have a point and the cited reference doesn't support the addition either. Euclid's version of the converse is noteworthy simply because it's Euclid's, and another one using modern notation is useful, but it seems a bit redundant to have three versions of it.--RDBury (talk) 08:27, 28 September 2010 (UTC)

Dimensional analysis

I have added a dimensional proof of the Pythagorean theorem. I believe it, at least for me (a physicist), much more convincing than all those complicated triangle rearrangements which are used in most other proofs. Unfortunately, though I have given an academic reference, I don't know who originally proposed it. If someone knows, please add the reference.--GianniG46 (talk) 12:50, 13 October 2010 (UTC)

The proof is very interesting, but I'm afraid that it isn't actually a proof. The issue is that you have assumed that the form of the area is $c^{2}f(\alpha ,\beta )$ where f is dimensionless. Ignoring the question of whether dimensional analysis is a valid proof technique at all (which I would say it is not), the assumption about the form of the area is far from obvious. It would be equally possible for the area to be of the form $cg(\alpha ,\beta )$ where g has units of length (for example, if g includes some constant that has units of length). It would even be possible, in principle, for the area to be of the form $c^{3/2}h(\alpha ,\beta )$ where h has units of (length)^4/3. The deeper issue is that dimensional analysis is not a valid proof technique, but even if it was there is no reason that the area would need to be in the form specified in that argument. In general all that can be said is that the area can be written as some function of c, α, and β – the form of the function cannot be known ahead of time. — Carl (CBM · talk) 14:34, 13 October 2010 (UTC)

I don't quite understand why it's called "dimensional analysis", but it is a general property of the n-dimensional Lebesgue (or Hausdorff) measure that if A and B are similar objects with coefficient of similarity r, then λB = rⁿλA. Triangles with the same angles are similar, and the coefficient is the ratio of their longest sides, which indeed implies that the area is c²f(α,β) for some f.—Emil J. 14:51, 13 October 2010 (UTC)

Yes; I was commenting only on the proof as it was written, which seemed to claim that the form of the area function follows solely from its units.

If we rewrite the proof in terms of similarity, it has the same essence as the "similarity proof" that the article already includes. I think it would be nice to expand out that proof sketch to something more detailed, since this is a very pretty proof. I'll see what I can do. — Carl (CBM · talk) 17:03, 13 October 2010 (UTC)

So, now the proof is correct, provided that you change the words "dimensions of a length squared" with "scales by a factor of s^2". Now I ask: this is the same concept or not? And, if the question was only the language, it was not possible to correct my text, rather than deleting it, keep its concepts, and rewrite it again? I think it is incorrect: a) to delete without a previous discussion a contribution with citations and not obviously wrong . b) to use the material to write another contribution instead of trying to amend the original contribution. --GianniG46 (talk) 20:45, 13 October 2010 (UTC)

I thought that, modulo the issue with dimensional analysis, the idea behind the proof was nice. At first, I was somewhat blinded by the dimensional analysis issue and didn't I realize that the text could be transformed into a better proof of the "similarity" method that was already sketched obliquely in the article. The invocation of dimensional analysis was a red herring for me.

Once EmilJ pointed out how the proof method could be salvaged, I went right back and did that. I apologize for not taking the most direct route to the current state of the article. However, I think that the outcome is good so far: we have a more clear version of what you wrote, merged with a previously less clear section on similarity. — Carl (CBM · talk) 21:09, 13 October 2010 (UTC)

This proof is not as well described as it might be. For example, when the hypotenuse is scaled by c, it is assumed, but not pointed out, that all the angles (not just the right angle) are held fixed, and that this implies the other two sides are also scaled in the same proportion. That is tantamount to a theorem that the sine of an angle is a function of the angle only, and not the lengths of the sides, an observation tantamount to Pythagoras' theorem, and the reason the proof works. This article in general is unclear about the difference between equivalence of statements and proofs strictly based upon the fundamental axioms themselves. That failure unfortunately undermines the notion of a deductive system. Brews ohare (talk) 17:31, 14 October 2010 (UTC)

Proof by area vs. proof by rotation

Perhaps the interested parties can bring this discussion to the talk page instead of brewing an edit war? Orange Suede Sofa (talk) 18:13, 3 November 2010 (UTC)

I don't think we're anywhere near an edit war, but for the record here's my reason for restoring Hgilbert's change, expanded from the edit summary. The proof has little to do with rotation. The only things that need to be rotated are the triangles, but that is true of many of the proofs that involve triangles, such as the one immediately above. The square does not need to be rotated as it is clear it is a square, with sides length c and right angled corners, even inclined.--JohnBlackburne^words_deeds 18:31, 3 November 2010 (UTC)

FWIW, I agree with your reasoning.—Emil J. 18:41, 3 November 2010 (UTC)