Talk:Closed-form expression/Archive 1

Archive 1

Fluid dynamics

In Fluid dynamics, the closure form of the governing equations is called for the boundary layer approximation or the parabolic approximation.

I'd thought that closed-form solutions were possible for quintic equations, although there is no general formula for them? Could someone more knowledgeable edit this article?

You can of course find closed form solutions to quintics such as $x^{5}-1=0$ (the five roots of one). There is even a general process to solve quintics by introducing a new radical (The Bring radical). --njh 12:12, 12 July 2006 (UTC)

Opposite of closed form

Should the opposite of a closed form expression be defined on (or linked from) this page? It would seem to be a useful addition to the article. Alchemeleon 21:12, 7 June 2007 (UTC)

This article title is not so good

Why the word "solution"?? Some cases of closed-form expressions in mathematics are in some sense "solutions", and others are not. This seems to me like one of those cases where someone picks a word like "equation" or "solution" as a sort of catch-all term to be used when they don't know the right nomenclature. This happens frequently in math, when, for example, lay persons promiscuously use the word "equation" to denote anything at all that is written in mathematical notation.

Since closed form seems to be a disambiguation page, I propose that this article be moved to closed-form expression. Michael Hardy 00:05, 26 November 2005 (UTC)

I agree with your basic point. I have a general problem with the notion of "closed form", as I think it's a bit difficult to define "closed form" in the abstract, or to differentiate "expressed in closed form" from "expressed analytically". For example, one can often solve (in)equalities by using inverse functions, but whether or not the resulting expression would be said to be "in closed form" depends on what the basic inventory of functions and expressions is. I'm not sure if e.g. Lambert's W function would be considered part of that inventory, but it's obviously very convenient for expressing solutions of certain equations in a form that can easily be evaluated by numerical software. I have the feeling that large aspects of this notion of "closed form" are very much a remnant of a past time when only a small number of expressions could be conveniently evaluated by hand or looked up in a table. --MarkSweep (call me collect) 01:27, 26 November 2005 (UTC)

I am inclined to suspect that the concept does admit some precise definition, but I am skeptical of the claims even of some fairly sophisticated mathematicians to have done that definitively. But the fact that it is not yet fully precise doesn't mean there should be no article on it. Michael Hardy 22:33, 26 November 2005 (UTC)

So, let's move it, shall we? Regarding the content, here are some external links, which may or may not shed further light on the meaning of "closed form":

• http://mathworld.wolfram.com/Closed-FormSolution.html
• http://planetmath.org/encyclopedia/ClosedForm.html
• http://www.riskglossary.com/link/closed_form_solution.htm

Also note that these articles all talk about solutions (though I agree with you now that that's too limited). --MarkSweep (call me collect) 10:58, 29 November 2005 (UTC)

1. Are there any expressions that are not closed-form expressions? Can someone give examples?
2. Are there indeed contexts in which people call certain expressions "closed-form expressions" in which these expressions are not the solutions of equations discussed in that context? Can someone give examples?
3. The Google search term [closed-form-solution -wikipedia] gets almost twice the number of hits of [closed-form-expression -wikipedia]. In general the recommendation is to use the most common form for the article's title.

 --Lambiam 14:31, 26 December 2007 (UTC)

The Fibonacci numbers as an example

Perhaps the Fibonacci numbers provide a good example of a closed-form solution in contrast to a definition that does not use a closed-form expression. By the way, I don't think there is a single term with the opposite meaning. —141.150.24.182 (talk) 04:36, 15 February 2010 (UTC)

Closed-form number

The first paragraph of that section needs to be clarified:

"...in increasing order of size, these are the EL numbers, Liouville numbers, and elementary numbers."

"The first, denoted L for Liouville numbers..."

what?

I might be able to work out the correct interpretation on my own, were it not for the fact that three sets are mentioned, and I see four labels in the paragraph: E, L, EL and C. —Preceding unsigned comment added by 24.28.74.115 (talk) 02:52, 16 March 2010 (UTC)

Clarification needed

@CRGreathouse: Please try to be constructive here. I found the relevance of the sentence to what precedes it in the paragraph to be unclear, so I took a shot at stating what the point was. You reverted, saying the addition was invalid. Then I put in a clarification-needed tag, which you reverted, saying the point was already pretty clear and giving an informally worded version of the point in the edit box but not in the relevant place in the article. Then I tried to give a more carefully worded version of your edit-box explanation in the article, saying in my edit summary "If you don't like this version, put in something better." You responded by reverting without replacing, with the edit summary "I don't mind a clarification if it's correct, but this one is not". This is not constructive in the absence of a replacement clarification.

I'm trying to get this passage in the lede improved to a point where people who know enough math to read the article can understand the point of the sentence. If the point is not what I put in in either of my two edits, then its point is not clear to me, and if it's not clear to me then it's not clear to others as well.

Please just put in an addendum to the sentence clarifying it in a way that's satisfactory to you. Duoduoduo (talk) 20:02, 12 January 2012 (UTC)