Talk:Lagrange's formula

How could Lagrange know the cross and dot product?

When I see Lagrange, I immediately associate that name with the great master Joseph Louis Lagrange. He died in 1813, about thirty years before Hamilton defined his "quaternion product", from which Gibbs extracted his "cross product" and "dot product".

Paradox. However, I see in this article that some Lagrange paradoxically was dealing with the triple cross product and the squared magnitude of the cross product. If that Lagrange is the famous Joseph Louis Lagrange, he defined the triple cross product two generations earlier than the simple cross product was defined by Gibbs and one generation before Hamilton used it as a component of his quaternion product!

Reference. I have searched "Vector Analysis", a book published in 1901 by Wilson (Gibbs's student). The entire book is available on line here. The triple product expansion is explained, but Wilson doesn't attribute it to Lagrange.

Questions.

• Was there some other Lagrange in the history of mathematics (I doubt it)? Or were both Hamilton and Gibbs just using a "product" or set of operations which was already known and studied by Joseph Louis Lagrange, one generation earlier?
• If you live or work in a university campus, or you have old math textbooks, would you mind to check what is the oldest book which calls "Lagrange's formula" the triple product expansion, and see if the book explains why?

Please see the history section in the article about cross product, and the relevant discussion.

Paolo.dL 16:15, 3 August 2007 (UTC)

He did know about determinants, though.--Lionelbrits 18:37, 6 October 2007 (UTC)

Drats, I was thinking of the other triple product.--Lionelbrits 18:38, 6 October 2007 (UTC)

Deletion

I endorse a redirect of this page to triple product#Vector triple product for reasons in prod. But I would think some discussion of how Lagrange is/is not associated with the expansion could be useful on that page. I .. must have created the page, but I forget my source. Musta been a book. Fresheneesz (talk) 23:37, 11 January 2008 (UTC)

This page has been already duplicated in triple product#Vector triple product (except for a sentence about the true identity, which I moved to Lagrange's identity.

Also, there has been already a long discussion on cross product about the association of Lagrange's name to this formula. Notice that there's another article in Wikipedia about Lagrange's identity, and there's no mention to the triple product expansion there.

We cannot attribute the formula to Lagrange unless somebody can prove that some Lagrange (possibly not Joseph Louis) is the author of that formula. This is a questionable fact that Wilson, Gibb's pulil, didn't acknowledge in his book about vector analysis, where he described this formula together with other kinds of triple and quadruple products (please see Talk:Cross product#Did Joseph Louis Lagrange know the cross product before it was invented? (Part 2)).

This is the strategy I suggest: now, let's just delete this article. Later, we can add a redirect from "Lagrange's formula" to triple product, provided that someone will find a reliable reference proving that some Lagrange is related to this triple product expansion. Paolo.dL (talk) 23:46, 11 January 2008 (UTC)

By the way, Fresheneesz, I discovered what was your source. You created this page by just copying a section of Cross product (see your own edit summary in the history page). The name "Lagrange's formula" is used in that article since 2002, when it was created (see Earlest contribution in History of Cross product). Wikipedia is not reliable enough as a bibliographic source. We need a reliable book or paper, explaining why the triple product expansion is called "Lagrange's formula". Paolo.dL (talk) 00:49, 12 January 2008 (UTC)

I would prefer to make a redirect to keep the edit history available. Redirects are cheap and free of nasty side effects, whereas deletions destroy histories. The redirect could possibly be to Lagrange's identity, cross product#Triple_product_expansion, or triple product#Vector triple product. - Neparis (talk) 15:42, 13 January 2008 (UTC)

Since we discovered (see Talk:Cross product) that the name "Lagrange's formula" is used in a book that mathematicians accept as a reliable source to indicate triple product expansion, and since Silly Rabbit explained that the attribution to Lagrange is plausible (but infrequent), we might redirect to triple product#Vector triple product (which is the main for this topic). However, there's nothing interesting in the brief history of this article. It is just a copy of a section of cross product (which is now more up to date than this article). Even this discussion is just repeated or summarized elsewhere. But if you really want to keep history and discussion in Wikipedia's servers, feel free to do it. Paolo.dL (talk) 18:31, 13 January 2008 (UTC)

Summary

• I proposed deletion of this article.
• Fresheneesz and Neparis both suggested redirection.
• Silly rabbit supported deletion since he doubts this term is sufficiently widely used to deserve a separate article (see Talk:Cross product).
• Salix alba removed my proposal of deletion, because he believes the problem is too complex to be decided that way.

I think the best compromise is to redirect. I did it. Paolo.dL (talk) 20:25, 13 January 2008 (UTC)

Woot. Sorry i was being lazy. Fresheneesz (talk) 00:00, 14 January 2008 (UTC)

multiple formula, disambig?

In trying to find some google references to the formula it seems there are a number of other thing which have been referred to by this name:

• Lagrange polynomial see Lagrange Formula
• Lagrange inversion theorem see [1]

Maybe a disambig page might be more suitable. --Salix alba (talk) 20:50, 13 January 2008 (UTC)

Yes, I agree it should be a disambiguation page. In any case, the current redirect seems inappropriate, as the Lagrange interpolation formula appears to be a more common meaning. --Zundark (talk) 20:59, 13 January 2008 (UTC)

Good job. However, I suspect that the author of Lagrange formula may use "Lagrange formula" in lieu of the more common (polynomial interpolation in) "Lagrange form". I would not trust an internet page as a reliable source (even a book may contain mistakes...) I agree about the disambiguation page. Paolo.dL (talk) 21:05, 13 January 2008 (UTC)

In McGraw-Hill Dictionary of Scientific and Technical Terms, McGraw-Hill, New york, 1994:

• "Mean value theorem [MAT]" ... "Also known as first law of the mean; Lagrange's formula; law of the mean."

Salix alba was right, we need a disambiguation. Paolo.dL (talk) 16:59, 15 January 2008 (UTC)