Talk:Square root of 5

message: A creation of square root of 5 must come before a property of \,\sqrt{5},\,  like its irrationality exposed now in the first section.   If \,k\, denotes the ratio of a given similarity,   or its coefficient,  then this transformation multiplies areas by k^{\,2}.\;  Therefore here are two direct similarities  that multiply areas by 5.   Arthur Baelde (talk) 13:19, 20 November 2021 (UTC)
replies: text: I agree that the decomposition of one triangle into five is not necessary to illustrate \sqrt{5}, but not that the busy image shown here would be better.  What would really be nice would be just a simple 1, 2, sqrt(5) right triangle, but I don't see one on commons. Also note that new sections should be placed at the bottom of talk pages.  Cheers. Danstronger (talk) 13:42, 21 December 2021 (UTC)
replies: text: I have not written on Wikipedia for a long time,  excuse me for the wrong position of this section on the talk page.I will propose soon a better image.      Arthur Baelde (talk) 09:51, 23 December 2021 (UTC)
thread_title:  Existence of the square root 

message: Quite possibly the most difficult to follow, most unorganized and most back-and-forth nonsense I have ever read.  How about a proof that actually constitutes a proof?  — Preceding unsigned comment added by 75.172.60.221 (talk) 10:59, 13 July 2012 (UTC)
thread_title:  The So-called Proof 

message: Thanks for adding a few refs.  I beefed them up with more info, like a url to the book page for the first one.  However, I don't yet feel that these refs establish notability of the topic.  The first might support notability for the series of root rectangles, but does not distinguis root 5.  The second is self-published and therefore not qualified as a reliable source.  The third is pure fiction, somewhat admittedly fiction, and not very useful, but might possibly verify something; not sure what, though, since it is so in contradiction with all scholarly analysis of golden ratio and the Greeks; and it's a children's book; in any case, it's more about the root 5 rect than about the square root of five itself.  How about some refs that talk about the square root of five as if it's notable? Dicklyon 04:31, 4 August 2007 (UTC)
replies: text: Firstly, I repeat that I consider it unreasonable that you claim all the info that is already provided about the important connection of this measure to the most elemental geometry, including the square and 1:2 rectangle, the cube, the pentagon and pentagram and the golden ratio (you will have a hard time finding something about the golden ratio which doesn't mention the square root of 5, and that alone is more than enough to make this number notable), as well as its importance for trigonometry, supposedly is not enough by itself to establish the notability of this number. If that is not notable enough, then what is? Why don't you ask for references to be convinced of the notability of the numbers 1 and 2 as well, since their articles do not cite any source to "establish the notability" of those numbers either? Secondly, the first reference, and other references on root rectangles, does specifically single out the root rectangles of √2, √3 and √5 (as well as, of course, the √1 and √4 ones, which are the square and the 1:2 rectangle) as those root rectangles that are most important and most relevant for geometry and design. The second source was merely intended to provide a diagram that shows how the root-5 rectangle can be split into a square and two golden rectangles, and that reference is "self published" by someone who holds M.Sc and Ph.D. degrees and whose site is hosted by the Department of Mathematics at Surrey University, and which has been awarded, among others, the Britannica Internet Guide Award and selected for the Scout Report for Science & Engineering by the Internet Scout Project. Lastly, I find it a bit odd that Diggins' supposed "book of fiction" was recommended by Lauretta J. Fox of Yale-New Haven Teachers Institute  to be used by teachers in introducing their students to the use of basic geometry in architecture, and that the reproduction of chapter 15 of that book which is referenced in the article, is hosted at the servers of the Saint Anselm College. And I don't see where on earth is the supposed "contradiction with all scholarly analysis of golden ratio and the Greeks"; a simple check at the dimensions of the Parthenon (which rests on a plinth of 30.9 by 69.5 metres) shows that its base fits a root-5 rectangle (30.9 × 2.236 = 69.1, a deviation of only a few centimetres or about 0.5% from a perfect root-5 rectangle), its front façades being the ones that approximately fit golden rectangles (in any case, both kinds of rectangles are inextricably linked to the square root of 5, and both are generated geometrically from a square in a few easy steps). Uaxuctum 13:50, 4 August 2007 (UTC)
replies: text: The things that make it notable just need to be evidenced by citation of verifiable independent reliable sources.  A children's book that gets the history of Greek use of golden ratio wrong is not what I'd call reliable, but maybe that's just me. Dicklyon 17:52, 4 August 2007 (UTC)
replies: text: Exactly what does it get wrong? And if it is so "wrong" and "unreliable", how on earth did it manage to get recommended by a Yale professor and end up hosted in the servers of the Saint Anselm College? And in any case, how would that affect the fact that the dimensions of the plan of the Parthenon fit the proportions of a root-5 rectangle? And for God's sake, we're talking about a number, it is absurd to suggest that simple mathematical facts associated with it, like that it is the diagonal of the double square, that it forms the base for the geometric construction of the golden ratio or that it appears in some two dozen formulae for exact trigonometric functions, need to be "evidenced by citation". Learn a bit about basic geometry and do the elementary math yourself, if you insist in unreasonably calling into question such utterly simple statements of fact. What will be next, asking for a citation to "evidence" that the sky is blue? Uaxuctum 20:41, 4 August 2007 (UTC)
replies: text: Many things get recommended, for various reasons.  It's probably a good for teaching geometric concepts.  But there's no evidence that these particular irrational length/width ratios played any role in the design of Greek structures.  On the contrary, that would have been outside the scope of their mathematical knowledge and practice.  Only in retrospect have people found structures with dimensions in interesting ratios.  The golden ratio, or any other ratio, is very easy to find once you know what you're looking for, but that doesn't mean it was used in the design. Dicklyon 22:05, 4 August 2007 (UTC)

text: The recognised Pythagorean ratios are (from memory) mathematical (2:3:4) geometric (1:2:4) and harmonic (2:3:5), the latter being the golden ratio which was used by classical architects. They didn't know (or refused to accept, maybe) that the root of 5 was the same thing, nor any other mathematical abstraction or irrational number was involved, they just used those relations and proportions. The article gets no help from the Greeks, I'm afraid. mikaultalk 01:28, 5 August 2007 (UTC)
thread_title: References

message: There doesn't seem to be anything here that's not already covered at square root or golden ratio, with the exception of the root 5 rectangle, which is just the fifth in an infinite sequence of root n rectangles, with no apparent reason to think it's notable in itself.  I'd recommend an article on root rectangles, since there seems to be a lot written about those.  Dicklyon 06:08, 5 August 2007 (UTC)
replies: text: I think so, it just needs to be carefully sourced and properly integrated. WP:NUMBER is the relevant guideline for notability and it seems to me it lacks only the third of the three main criteria there. I might be persuaded to support a merge or redirect to root rectangles if such an article existed, but it doesn't. This one does, and it seems to me to be (almost) notable enough. mikaultalk 11:19, 5 August 2007 (UTC)
replies: text: I would have thought the first criterion there would be plenty (Have professional mathematicians published papers on this topic?).  So how come nobody gives us such a citation? Dicklyon 15:46, 5 August 2007 (UTC)
replies: text: We're looking... I'm looking in the Fibonacci Quarterly. Please give me a couple of days. Knotslip12 21:26, 6 August 2007 (UTC)

text: That new article by mathnerd at PlanetMath (his only contribution, it appears) does make it clear way paying attention to a wiki as a source is unworkable.  It's really unfortunate that this math cite has now been crapped up with the statistics nonsense that someone found where the number 5 in a problem (for 5 work days in a week) leads to sqrt(5) in the answer; this is unbelievably lame nonsense; anyone mind if I take it out again?  Dicklyon 22:02, 11 August 2007 (UTC)

text: The problem is that we need sources for that.  If you know any, please suggest or be bold.  Brusegadi (talk) 05:18, 27 February 2008 (UTC)
thread_title: Do we need this article?

message: I do not think the page should be deleted.  At least not speedly, I think it deserves some discussion since the number appears in many things.Brusegadi 22:37, 3 August 2007 (UTC)
replies: text: I do not understand the nomination either, and I actually think the claim that "notability is not asserted" is plainly false, since the article does mention several algebraic and geometric aspects that make this number notable. Together with √2, √3, φ, π and e, this is one of the most elemental and important irrationals, being intimately related to the golden ratio and to several of the most geometrically simple shapes (square, cube), as well as appearing in lots of important formulae such as those for the exact trigonometric constants. If this number is not considered notable, then on what grounds are the square root of 2 and the square root of 3 considered so? Besides, an "unreferenced" tag has also been placed, but everything that is currently stated in the article can be verified immediately simply from knowledge of elemental geometry and using well-known mathematical formulae such as the Pythagorean theorem. Sure the addition of more info and references would be very nice, but the "unreferenced" tag makes it seem as if what the article currently says is dubious or disputed, which most definitely is not but is the mere pointing out of very elemental algebraic and geometric relations. Uaxuctum 22:56, 3 August 2007 (UTC)
replies: text: What's hard to understand?  The article doesn't include evidence of notability, and such articles are subject to deletion.  Please read WP:Notability.  The edit summary "just the fact that it appears in the golden ration makes it notable enough. I recall this number is important" completely misses the point; it's not your opinon or recollection that matter, but what evidence is cited in the article.  Mere frequent appearance is not relevant.  You need to cite reliable secondary sources that talk about the square root of five as an important topic of its own. Dicklyon 23:20, 3 August 2007 (UTC)
replies: text: I was not using my recollection of the importance of the number as a reason for it to stay, I was using it as a reason for it to not be speedly deleted; which is different.  The difference is that one of them gives us time to discuss without just throwing a potentially useful article away.  Basically, I thought that the article should be discussed, like we are doing now.  When I get back home I will look for my number theory books and see if this number is any more important than say, the sqrt of 223 (both irrational by the way...) Brusegadi 23:55, 3 August 2007 (UTC)

text: It doesn't look like WP:NOTE is going to be taken seriously, so I guess the article stays;  so I've been working on improving it.  For example, the stuff on golden ratio, one of the original reasons for the article, I think, had grown to horrendous proportions, as golden ratio stuff tends to do.  So I pruned it.  And I fixed the ref styles into one consistent style.  And a few other things.  Dicklyon 17:42, 12 August 2007 (UTC)
thread_title:  Should this article be deleted? 

message: Please see immediately above where I said "the stuff on golden ratio, one of the original reasons for the article, I think, had grown to horrendous proportions, as golden ratio stuff tends to do.  So I pruned it."  If you disagree with a topic that active in a talk page, bring up your objections here, instead of just reverting and objecting in the edit summary.  That way, we can work toward a consensus. Dicklyon 20:14, 12 August 2007 (UTC)
replies: text: I don't see why letting readers clearly see the interrelations between this quantity and the golden ration and its conjugate qualifies as unnecessary trivia, and I fail to see where this section has "grown to horrendous proportions" when in fact it was almost telegraphic and your edits have further reduced it to the absolute minimal expression. Those formulae are useful, especially to understand their geometric relations (such as the very clarifying one that sqrt(5) = phi + Phi); sure, the readers could work them out for themselves from the only one provided in your version, but the purpose of an encyclopedia article is to be informative, not to conceal or leave potentially useful or clarifying information unstated. Uaxuctum 20:39, 12 August 2007 (UTC)
replies: text: Thanks for responding.  My objection was of course not to "letting readers clearly see" something, but rather to what appeared to be a typical golden ratio algebra fest.  The golden ratio has a ton of fun relationships, which are pretty much discussed in hundreds of articles about the golden ratio, and hence are repeated in the wikipedia article on it.  I don't think those same manipulations are needed in an article on the square root of 5, but if you can find a source for saying that the square root of 5 can be written in terms of the golden ratio in all those ways, then by all means include them and reference it.  The present version is just too much original research, that is, algebra that one can do oneself but has not been pubished, as far as I can tell. Dicklyon 22:32, 12 August 2007 (UTC)
thread_title: Golden ratio trivia

message: Is it the case that 5 is the smallest integer n such that the integral domain Z[√-n] fails to be a unique factorization domain?  Certainly Z[√-5] is a common example of a domain for which unique factorization fails to hold, and this might be worth mentioning in the article.  -- Dominus 23:12, 14 August 2007 (UTC)
replies: text: No. Z[√-3] is not a UFD: 2*2=(1+√-3)(1-√-3). Algebraist 19:44, 24 May 2008 (UTC)
thread_title:  Unique factorization domains 

message: Could someone please explain, or better yet clarify in the article, the following:
*"He then applied the square root of five within the golden ratio ... as a way to select the relative length of the two parts of his piece." More specifically, what does "the square root of five within the golden ratio" mean? How did Wuorinen "apply" it to proportion the length(s) of "the two parts of his piece"? What "two parts of his piece"? (E.g., 1st and 2nd movement of a 2-movement work? Theme A and theme B of a sonata form?)
*"In doing so, he took the bite and harsh dissonance normally accompanying of 12-tone music." Does took in this statement mean he eliminated or reduced "the bite and harsh dissonance"? How did applying some proportion to the lengths of 2 subdivisions of the piece affect its harmonic character?
*Since the article is discussing a particular composition by Wuorinen, it is essential to name the piece.
If someone can send me a copy of the review, I can try to make some sense of it. Thanks. Finell (Talk) 00:46, 15 August 2007 (UTC)
replies: text: I had asked here for the guy who posted that to let me know what it says; or just leave it out.  He didn't respond, so I take it that leave it out is OK for now.  I'll  take it out and we can see if he cares. Dicklyon 00:56, 15 August 2007 (UTC)
replies: text: From the context, it sounds like a review of a performance of a composition by Wuorinen. There is probably something worthwhile there, but it was not well summarized in the article. If there is something, it probably relates as much or more to φ than to √5. If I had easy access to the source, I would get it myself--but I don't. Finell (Talk) 02:26, 15 August 2007 (UTC)
thread_title:  Music 

message: Since the Golden ratio is known to billions of digits (at least 17 billion per that article though the Mathematical constant article suggests it's actually 100 billion), shouldn't the Square root of 5 also be known to the same billions of digits? After all:
 \sqrt 5 = 2 \varphi - 1 
Glenn L (talk) 19:46, 25 May 2009 (UTC)
replies: text: Seems plausible, since multiplying by 2 seems pretty simple, and the subtraction of 1 effects only the one digit before the decimal point. Michael Hardy (talk) 20:09, 25 May 2009 (UTC)
replies: text: Indeed, it would be trivial to take 17 billion digits of phi and make 17 billion digits of root 5. And if someone would report doing so, in a reliable source, there's no reason we wouldn't include that fact. Dicklyon (talk) 04:21, 26 May 2009 (UTC)
thread_title:  Only "one million digits"? 

message: Based upon a discussion at Wikipedia talk:WikiProject Mathematics#"Infoboxes" on number articles, I've removed the infobox from the article. If anyone disagrees, could you please join the discussion there. Thanks, Paul August ☎ 14:58, 18 October 2009 (UTC)
replies: text: I have suggested centralizing this discussion to Wikipedia_talk:WikiProject_Mathematics#Irrational_numbers_infobox and Wikipedia_talk:WikiProject_Mathematics#Infobox_with_various_expansions as it refers to an infobox occurring in several articles. Please go there to build consensus on this edit. RobHar (talk) 19:34, 18 October 2009 (UTC)
thread_title: Removal of infobox