Talk:Rule of three (mathematics)

Complete rewrite
Dear Heron:

Thank you to your contributions to this article, especially the references and the expansion of the article with subsections. However, I reverted your edit. What previously existed in the article was more clearly written than some of what you changed or added. For example:
 * The words extremes and means become meaningless when separated from the wiki-linked word proportion.
 * The rule of three still works and is still used. It is not an historical artifact, or obsolete, as your edit suggests.
 * You refer to the "Rule Direct" (your capitalization). What is that? Do you mean what you call the direct rule rather than what you call the inverse? That is not a real distinction, and is part of the confusion that your rewrite introduces. The rule, properly defined and used, applies when any three values of a proportion are known to solve for the fourth.
 * Your use of old principle implies obsolescence. Perhaps you intended to say long known principle.
 * In my opinion, your distinction of the algebraic method is not genuine. Using the rule of three is algebra, regardless of whether the user knows it. This article should explain the algebra in explaining why the method works.
 * The proportionality notation that you replaced is correct and is the more modern notation. On the other hand, the old proportionality notation, which you use, may be more familiar to non-mathematicians (I am not sure of this; I have not been in touch with what is being taught in junior high school for over a decade). In any event, it would be a very useful improvement in the article for you to show how the old and new proportionality notation and fractional notation are related.
 * Please don't use math tags in lines that also have normal text; it throws off the line spacing. Put the mathematical expressions with math tags on separate lines, with appropriate punctuation. Likewise, your inline proportions would stand out better on separate lines formatted with math tags.

I am sure that of what you wrote that can be worked into the article as it exists, rather than by such a radical reorganization and rewrite, and hope you will try to do so. It might be useful to add section headings as you did, although the article may be too short to warrant headings. Certainly additional references would be welcome.

It would also help the article to explain the entire method, in terms of a, b, c, and d, and then to give one or two examples. One of the weaknesses of the article as now written is that it introduces an example too soon, which forces it to use x in place of d.

Frankly, I would try to work your material into the article myself, and attempt to make some other improvements, but I do not have the time right now.

Thanks again for your efforts to improve the article. I hope you will try again. Finell (Talk) 03:24, 21 May 2007 (UTC)


 * Hi Finell. Much as I dislike your reversion of my edit, I can see that you did it in a constructive spirit, so I will be happy to cooperate with you on improving the article.  I agree with most of your points, with some reservations, but not at all with the one about algebra.


 * The word 'algebra' is not defined narrowly enough to allow you to state whether the rule of three 'is algebra' or is not. What matters is that the rule is taught to students who do not know how to do elementary algebra in its general sense: that of manipulating symbols, instead of numbers, in equations.  This is the reason for the existence of the rule in the first place.  The problem with the article is that it uses algebra to explain a rule to readers who cannot be assumed to understand algebra.  My new version was an attempt to put the cart after the horse, rather than before it.  The article should begin by explaining the rule as it is taught, in words, without using any mathematical symbols.  In fact, the article doesn't even say what the rule of three is.  There is a beautiful example of the rule stated in words by Piero della Francesca in De abaco here (under the heading Proportion and the Rule of Three), but you might feel that a more modern version is appropriate.  Regardless of our differing opinions on the meaning of 'algebra', can we at least agree that the order of presentation needs to be changed? --Heron 21:15, 21 May 2007 (UTC)

Dear Heron:

Thanks for your very constructive response. If you wish to begin with how the rule is taught today, please do document that with with a source (i.e., a secondary school text book, perhaps one that can also be found online); the lack of sources is a weakness in the current version that should be corrected. If you have the time and access to materials, you might want to consult a few modern texts to get a broader picture of how it is actually taught.

I certainly hope that modern teaching does NOT begin with an example and then back into the rule, like the Renaissance example of Piero della Francesca that your comment linked. I have seen this example-first (or only) approach in a lot of very old texts, including ancient Egyptian and the first algebra codified in the Muslim world. In my opinion, teaching should begin with the method, followed by examples. If the "rule" is taught without algebraic symbolism, so be it. I would hope that anyone who would look to Wikipedia for information on the "rule of three" could handle simple algebraic notation, but who knows?

You say that the present article does not actually state the "rule of three", but neither does your rewrite. How exactly does one state the "rule of three" as a rule? It isn't on Mathworld (too bad). My quick look today at your linked sources appear to state the rule only by example. 'Until your response, I thought, apparently mistakenly, that the first two sentences of the existing article stated the rule, that is, that the rule was that where a/b = c/d'' (i.e., in any proportion), one can solve by simple algebra for any 1 unknown if the other 3 are given. According to your linked sources, it appears that the rule (or at least the "Single Rule of Three Direct") solves only for an unknown d. So I agree with you that a statement of the rule is necessary.''' I also think that a section on the history of the rule would be a wonderful addition, but not as a source of the rule or its teaching today.

I disagree with the article being categorized as Elementary arithmetic.

If you are willing, please do try another revision along the lines we are discussing. But please try also to conserve so much of the existing text as is correct and works, such as the first two sentences as far as they go.

I still quibble about the algebra point, but it needn't affect how the article is written. I would rejoin that the definition of algebra is necessarily broad enough to embrace the "rule of three" as an instance of solving a/b = c/d for one unknown. Algebra as a well developed system dates back to around the 9th century. Modern symbolic notation, on the other hand, dates back only to around the 18th century. See History of algebra.

Thanks again.

Finell (Talk) 18:44, 22 May 2007 (UTC)


 * Let me take things one step at a time. You said "The rule, properly defined and used, applies when any three values of a proportion are known to solve for the fourth."  I'd like to ask on what authority you base that statement.  According to all the examples I've seen on the web, including online versions of printed dictionaries, and my trusty Brewer's, the three known quantities in the proportion are always stated in a fixed order and the rule tells you how to find the fourth.  Can you prove otherwise? --Heron 19:16, 25 May 2007 (UTC)


 * Dear Heron: Did you read my last post? I acknowledged that I was initially mistaken and that what I found on the Web supported you on this point. I have put that language in boldface, and underscored two words, so you can find it more easily. Finell (Talk) 01:37, 26 May 2007 (UTC)


 * It was your use of 'apparently' and 'it appears that' that put me off. Those terms implied to me a conditional agreement based on limited evidence, and so I was reluctant to act on your statement.  As you have now removed all doubt, I shall go ahead and edit the relevant bits of the article. --Heron 10:50, 26 May 2007 (UTC)


 * I don't know where any of that came from... there doesn't need to be a "fixed" order; you could solve a / x = c / d or something like that; you could also rearrange that to be a / b = c / d but no "rule" states that it must be a / b = c / x. This is simply how it is written often. Metsfanmax (talk) 17:47, 27 March 2008 (UTC)

Merge proposal

 * (see also Talk:Cross multiply)

Hi, the article for cross multiply is the same thing, and so I'm proposing a merge. Rhetth (talk) 01:13, 17 April 2008 (UTC)

Please do not merge. I found "the rule of three" when searching for just that - as I didn't know that the phrase meant to cross-multiply. —Preceding unsigned comment added by 71.58.14.253 (talk) 07:54, 11 May 2008 (UTC)


 * Don't worry. If the articles are merged, a search for "rule of three" would lead to the Cross multiply article, and the full explanation would be there. Finell (Talk) 06:56, 12 May 2008 (UTC)


 * No. Rule of three is much more significant in itself than cross multiply. --Rumping (talk) 20:44, 16 May 2008 (UTC)


 * No. Instead, some historical information should be added to the Rule of Three article, since this was the term used all through the 19th century and tends to puzzle people today. DGG (talk) 15:46, 23 May 2008 (UTC)