Talk:Golden ratio/Archive 4

The Graph Theory relation
I think it's important to provide accurate, and relevant knowledge on the topic of $$ \varphi$$.

It's my understanding that, other than personal articles from publications, I may contribute to the knowledge base as long as I submit the relevant citations. I can provide the text book citations on the matter and the details of the basic contribution and note that in writing any material on the subject outside of rewriting from a text requires knowledge of the topic as learned from the text.

Anyone that is maintaining the article should already know the simplified ratio of Fibonacci numbers and that that contribution is well founded. I do not know why it is not shown anywhere in this article that the limit converges to the value. I am attempting to make the connection from $$ \varphi$$ to Fibonacci Numbers to Graph Theory in a manner that allows the knowledge base to grow.

That being said I want to make certain that the limit and its convergence dependence are shown in any event, and I would like to include the relevance to graph theory as either a proof of the convergence or as an alternate form of derivation. —Preceding unsigned comment added by CWDURAND (talk • contribs) 22:48, 30 August 2009 (UTC)


 * The fact that the ratio of successive Fibonacci numbers converges to the golden ratio is already mentioned in the section Relationship to Fibonacci sequence. The limits in the section that you added seem to be simply a re-statement of this fact. If you do not provide references then the new section will be assumed to be your original research. If you do provide references, the section is more relevant to the Fibonacci number article rather than this article. Gandalf61 (talk) 23:25, 30 August 2009 (UTC)


 * I think this comment makes clear that it is, in fact, original research. At the very least our suggestions on conflicts of interest should apply: although it is not forbidden to add one's own research to articles, it often works better to bring it up on the talk page and try to convince the other editors of the article to add it. —David Eppstein (talk) 23:29, 30 August 2009 (UTC)


 * I have to say that the point is missed here, although I am happy that a discussion is taking place rather than conflicts of interest. I understand that there is a form of protection here just because of the long history in the number. --CWDURAND (talk) 16:48, 31 August 2009 (UTC)
 * According to what I posted the convergence is even-odd, and that is not allowed in convergence theory. By stating that the convergence was so dependent I am making a larger statement about the nature of $$ \varphi $$. I would appreciate some help is posting the result because of the significance in the relationship or at least some personal help in discussing weather the conflict is existent. —Preceding unsigned comment added by CWDURAND (talk • contribs) 16:12, 31 August 2009 (UTC)


 * If you believe you have discovered something entirely new then you need to publish it in a reputable journal before it can be included in Wikipedia. Wikipedia does not publish original research or original thought, no matter how significant it might be - see this Wikipedia policy. Questions about how to add content to Wikipedia can be asked at Wikipedia Help Desk. If you have questions about mathematics you could try the Mathematics Reference Desk. Gandalf61 (talk) 17:50, 31 August 2009 (UTC)


 * Ok, I'm going to be frank right away here, $$\lim_{n\to\infty}\frac{F(n+1)}{F(n)}=\varphi$$ is not fact or even cited. I've clearly shown that it doesn't converge in the strict sense of convergence. So unless someone can put the original source of its claim I'm going to remove it as weasel and status quo nonsense.
 * There is one person saying original can go up, another saying it can't. So post the original source for $$\lim_{n\to\infty}\frac{F(n+1)}{F(n)}=\varphi$$ or it's nothing more than a weasel.  --CWDURAND (talk) 22:56, 31 August 2009 (UTC)


 * Ok, now you're getting into WP:FRINGE territory. What definition of convergence are you using that excludes even such a simple case? In any case, see this Google book search for plenty of sources. —David Eppstein (talk) 23:33, 31 August 2009 (UTC)
 * I wouldn't say Fringe David, since it's a topic of importance, but I hear you telling me to be careful of trying to post an opinion.
 * On the matter of convergence though I hope to clear something up. First, the limit has to be unique. That part seems obvious in $$\lim_{n\to\infty}\frac{F(n+1)}{F(n)}=\varphi$$. I get that easy, but in the derivation of the sequence under the matrix mechanics it is based upon path length. Those lengths are size 1. Each even power produces a term in the sequence at some column-row but for that same column-row an odd power produces zero. This alternation cause the sequence to have more than one limit. My query follows from the sequence $$\lim_{n\to\infty}\frac{F(n+1)}{F(n)}=\varphi$$ as is a superset of the sequences I produced.
 * Since :$$\lim_{n \to \infty} \frac{F_{n} + F_{n-1}}{F_{n}}= \varphi^2 $$ is a subsequence in $$\lim_{n\to\infty}\frac{F(n+1)}{F(n)}=\varphi$$ for every other term, and it converges to a different limit. I have to pose this question.
 * Bear with me Dr Eppstein because it's been years since my real analysis or abstract algebra, but I believe I am right in saying that the subsequence must converge to the same limit. I'm open to your correction.--CWDURAND (talk) 02:10, 1 September 2009 (UTC)
 * I'm rethinking the subsequence comment and now I see my confusion.--CWDURAND (talk) 02:17, 1 September 2009 (UTC)
 * Here is my error :$$\lim_{n \to \infty} \frac{F_{n} + F_{n-1}}{F_{n-1}}= \varphi^2 $$. Note the n-1 in the denominator. It's my original error but it allowed me to see that my sequence is not a subset. Now I'm disappointed.--CWDURAND (talk) 02:24, 1 September 2009 (UTC)
 * It's just not what I thought. It's a completely different sequence. --CWDURAND (talk) 02:38, 1 September 2009 (UTC)

Strange recent addition about Pyramids
This recent edit added a rather long and strange-seeming excursion about the Pyramids and their relationship to something that might not be completely unconnected with the golden ratio. But the new section seems incoherent at best, and is perhaps a fringe theory. For example:


 * both the Khufu and the Khafre pyramids are in complete mathematical and geometrical agreement with … the Pythagorean Theorem

It is not really clear what it means for a pyramid to be "in agreement with" a theorem, or what it would mean for a pyramid to disagree with the theorem.

The new section appears to cite the following sources:


 * The Museum of Harmony and the Golden Section
 * "Russian Architect Igor Shmelev in his Brochure Phenomenon of Ancient Egypt"
 * "Ukrainian scientist Nikolai Vasutinski in his book titled The Golden Proportion"
 * Biographic dictionary of persons in the field of mathematics

The "Museum of Harmony and the Golden Section" is not actually a museum, but a web site; it is not a reliable source. There is no work in WorldCat with title "Phenomenon of Ancient Egypt" and no similar-sounding title, either in English or in Russian, by anyone named Shmelev; in any case the new section calls this source a "brochure" without mentioning a reputable publisher. There is no listing in WorldCat for any author named "Vasutinski". There is no work in WorldCat with the title "Biographic dictionary of persons in the field of mathematics".

If it were clear that the content of the new section was important, it might be worth the effort to identify the sources and fix the writing. But since it is unclearly written and effectively unsourced, I would like to delete it entirely. I will do this unless there is an effort made to address the many problems of this new section. —Dominus (talk) 19:02, 3 September 2009 (UTC)

1/89
i am really sorry that i can't write this out myself because of the need to learn wikipedia things and formatting equations--weighed down with too much--but there is that neat little expansion of 1/89 i seem to recall. perhaps someone else knows. for each new decimal place, put the next fibonacci number, but then the number (after a few iterations) is more than two digits long, so earlier decimal places have to be revisited.

1       1         2          3           5            8            13             21              33               55                89              *  144 1/89=.01123595505617...

ok, it doesn't look like it's going to make it at the *, but there are higher terms. here is reference to a proof that this is true.

http://library.thinkquest.org/27890/applications3p.html

(the math is good.)

this really is a trivial contribution, but is kind of funny or intriguing, in a ridiculous way. again, someone might want to include this, or not. i just thought i'd mention it. (and apologies if this has been covered; i've decided to learn wikipedia. writing something in an talk page is baby steps.)

thanks, see you around, peter w--66.31.29.49 (talk) 18:39, 24 September 2009 (UTC)


 * Umm, shouldn't this be in Talk:Fibonacci number instead?&mdash;Tetracube (talk) 19:42, 24 September 2009 (UTC)

nautilus shells
the nautilus shells and other nature spirals should be added to the "in nature" paragraph as that shell clearly has the golden rule logarithmic spiral from the golden rule, etc see also http://www.sacredarch.com/sacred_geo_exer_shell.htm, pythagoras del vado 69.121.221.97 (talk) —Preceding undated comment added 18:13, 12 October 2009 (UTC).

Should this page be protected?
should this article have protected status? I've been following this article for a while.. and it seems to have a high rate of vandalism, especially pornographic vandalism. Since it is an article about a mathematical formula.. the only thing I can figure out is perhaps the name attracts the flies. I think the protected status just keeps IPs from editing the article. If you look at the history, about half the edits are IPs and they are almost all vandalism, as far as I can see. Any comments from people that watch this article?

--stmrlbs | talk 01:19, 30 April 2009 (UTC)


 * Anyone? Comment?
 * --stmrlbs | talk 19:13, 10 May 2009 (UTC)


 * I don't think the rate of vandalism is high enough for this to be a problem. It's only averaging a little over 1 edit per day, not an excessive rate. And most of the activity on this article involves good-faith but misguided edits, of a type that should be reverted but not preempted, per WP:BITE. And I don't consider inserting the word "penis" to be pornographic, or requiring any extra vigilance to protect our readers' virginal eyes; it's just standard boring vandalism. —David Eppstein (talk) 20:01, 10 May 2009 (UTC)


 * LOL.. no, the word "penis" is not pornographic. Just not used to seeing it in the middle of an article about a mathematical formula.
 * But, I understand what you are saying. WP:Bite is a very good reason.  Thanks.
 * --stmrlbs | talk 20:29, 10 May 2009 (UTC)

I think that this article should have some protection since information about a mathematical constant isn't prone to change.

--Humanist Geek (talk) 21:21, 22 November 2009 (UTC)

Removal of infobox
Based upon a discussion at Wikipedia talk:WikiProject Mathematics, I've removed the infobox from the article. If anyone disagrees, could you please join the discussion there. Thanks, Paul August &#9742; 15:01, 18 October 2009 (UTC)


 * I have suggested centralizing this discussion to Wikipedia_talk:WikiProject_Mathematics and Wikipedia_talk:WikiProject_Mathematics as it refers to an infobox occurring in several articles. Please go there to build consensus on this edit. RobHar (talk) 19:35, 18 October 2009 (UTC)

Why is it "Golden"?
Why is this called the "Golden" ratio? Is there any rationale for that, or explanation? Hires an editor (talk) 20:10, 3 November 2009 (UTC)


 * The Golden Ratio is considered by many to be the most beautiful ratio.--Humanist Geek (talk) 21:27, 22 November 2009 (UTC)

Golden ratio of the earth
I watched this on youtube and thought to be interesting...

http://www.youtube.com/watch?v=-laIgBYCYVk

but the response (by another author, see below) to the video above created some doubt...I am looking into different religions and thus your professional response to this is important to me.

The response to the above, by another author, is below;

http://www.youtube.com/watch?v=-gN70IPogGc&feature=related

Please do respond with your comments... —Preceding unsigned comment added by 92.40.78.24 (talk) 13:35, 22 December 2009 (UTC)

New series form
The new series form is a trivial application of the Taylor series for sqrt(1+x) at Square_root; but it's sourced to a personal web page with long detailed derivations. If we don't find it in a WP:RS, we probably shouldn't include it. But I'm on break... Dicklyon (talk) 05:35, 6 January 2010 (UTC)

Hi Dicklyon, I was the one entering the infinite series info. Thanks for taking the time to look at and comment on this. There are some reliable sources on this, such as Weisstein, Eric W. "Golden Ratio." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/GoldenRatio.html however, for transparancy, the citing in MathWorld also came indirectly from me via some earlier work with Steven Finch from MathSoft. Here is the background. Around 1997 I was looking to determine an infinite series to describe phi. This was to look at computer calculations for various famous math constants. As you noted, I derived the series here by applying a standard Taylor series approach, or alternately a binomial series. To validate the series for publishing I took two independent approaches from 1997-1999. 1) Conduct a math/proof check and separtely 2) conduct a numerical/computational check of the series against other calculation methods. For 1) I did a Internet peer review and a prof at Macquarie University checked the Taylor series, and confirmed it with the binomial series. For 2) A computational check was conducted with S. Finch from MathSoft using Mathcad symbolics. After that, the series was subsequently run with Wolframs Mathematica program to match published values. It was matched thru tens of thousands of deciamal places at that time to confirm the math. After conducting these checks the series was added to Wolframs published sites. It has also been checked running Maple. Net, it has been validated computationally using a couple of derivation approaches and numerically with multiple programs. The series has seen some use over the past decade, from use in school to research on the fractal properties of mathematical constants (from series representations). I will understand if this needs to be removed from the site because of the reference protocol, but it is accurate and may have other uses that make it worth sharing. Thanks, Brian —Preceding unsigned comment added by Broselle (talk • contribs) 00:52, 8 January 2010 (UTC)

Golden Ration Found in the Quantum World
"By tuning the system and artificially introducing more quantum uncertainty the researchers observed that the chain of atoms acts like a nanoscale guitar string. ... 'The first two notes show a perfect relationship with each other. Their frequencies (pitch) are in the ratio of 1.618…, which is the golden ratio famous from art and architecture.'"

I don't know if anyone wants to add something about this but I found the article interesting: http://www.sciencedaily.com/releases/2010/01/100107143909.htm 4.225.88.175 (talk) 11:15, 8 January 2010 (UTC)

Psuedoscientific nature of many claims
Most assertions about this mathematically interesting ratio are wrong, even the oft-cited Pantheon example. What we seem to have is confirmation bias leaping upon any examples where ratios close to ~1.6 appear. I'd invite you all to read the excellent debunking (by an academic) here about Phi and the Fibonacci Sequence: http://www.lhup.edu/~dsimanek/pseudo/fibonacc.htm —Preceding unsigned comment added by 86.44.107.201 (talk) 02:06, 18 January 2010 (UTC)


 * You are welcome to edit the article constructively yourself. Bear in mind that a professor's web site page may or may not qualify as a Reliable source under our standards, depending on the author and other circumstances.—Finell 03:42, 18 January 2010 (UTC)

May be totally and utterly silly, but possibly worth mentioning
The length between two opposite corners of a golden rectangle is equal to 1.902113033... multiplied by the length of the shorter side. That number comes from Pythagoras' theorem, something like a^2+b^2=c^2 where c= the length of the hypotenuse of a right angled triangle. adjkfhsdfk (AAAAAAA) (cuntributions) 04:06, 6 February 2010 (UTC)

That constant (≈ 1.9021130325903) would be equal to $$ \sqrt{2.5+\sqrt{1.25}} = \frac{\sqrt{10+\sqrt{20}}}{2} $$. --Glenn L (talk) 08:42, 21 February 2010 (UTC)

(New)The Fibonacci Golden Rule, might apply to another mystery: the inhale-exhale motion in nasal breathing. If 1 is the duration of the inhaling :6.18 is the corresponding lapse of exhaling. So, for experimenting with normal breathing of adult male-female subjects. There must be a relationship between the amount of O2 that is needed by the blood and the amount of the CO2 sent out by the system. The consideration are many about the energy consumption, the air amount and so on. I suppose that there is a similar motion with mouth breathing, but we all know that the last is not the most natural way of breathing and this is proved by issues created by such practice ( dry mouth,snoring,winter cold,more exposure to bacterial and viral infections).MERosati (talk) 17:53, 10 April 2010 (UTC)

Math
Somebody should check the math in this article, it's a disaster in some places... - anon:P —Preceding unsigned comment added by 87.206.137.149 (talk) 21:08, 15 April 2010 (UTC)


 * It's a large article, so a pointer to where or what you think the "disaster" is would be a big help. Gandalf61 (talk) 08:38, 16 April 2010 (UTC)

New big mathy section
The recently added big section "The side and diagonal of the regular pentagon" was previously rejected from another article here. I think the same objections apply here: not very relevant, sourced to just a web page, redundant and overly complicated, busy ugly complicated figures, etc. But I'm on break, so I'll leave it to others to evaluate. Dicklyon (talk) 02:02, 13 May 2010 (UTC)


 * This section was not "rejected" because it was "big and mathy", but because it was too great a digression from Pythagoras' theorem, as most of it was devoted to golden ratio. However, it is more appropriate here. There is very little in the way of actual derivation of the properties of golden ratio as applied to the pentagon on WP. So this is a possible way to do that. It is sourced, and it is not too long. Brews ohare (talk) 02:51, 13 May 2010 (UTC)


 * I agree with Dicklyon. If we had an article about compass-and-straightedge construction of pentagons, it might belong there, but it is too detailed and specific to fit in to the article on the golden ratio. Basically, the same reason as for Pythagoras: it's too big a digression. Contra what you say, most of it is not about the golden ratio, but about a specific compass-and-straightedge construction. I'm not worried about it being OR, but I don't think it fits, so I'll remove it. —David Eppstein (talk) 02:53, 13 May 2010 (UTC)

Obviously, I disagree with you on this one. I hope you are not simply supporting Dick Lyon, but are actually expressing your own thoughtful opinion. This section does not require the construction you object to, as that is incidental to the derivation of the golden ratio, and is included only to provide the length of the side. That preliminary could be omitted. There appears to be no other demonstration of the golden ratio for the pentagon in WP. If you are interested, I can rewrite this section to leave out the derivation of the side, but I am unwilling to redo the diagram and discussion if you are simply going to delete it again. What is your decision? Brews ohare (talk) 16:58, 13 May 2010 (UTC)


 * The fact that the golden ratio is the ratio of the side to the diagonal of the pentagon definitely needs to be in Wikipedia, and in this article. A tedious derivation of that fact does not. My general feeling about proofs in Wikipedia is that they should included only when (1) the proof itself is notable (e.g. included in Proofs from THE BOOK), or (2) they are short and they convey some essential idea that would not be conveyed by not giving a proof (e.g. the proofs in double counting (proof technique), where it's necessary to include some examples to show off the technique but it would not be necessary to use those specific examples). Otherwise, a short summary of the main ideas of the proof, or a reference to a source containing the proof, should be good enough. In the case of the Pythagorean theorem article, the search for different proofs is a big part of the history of the subject, so I can see a rationale for including some of them (although I think as it is now the article is a bit too proof-heavy). But in this case it's less clear: why is this specific proof important? —David Eppstein (talk) 17:05, 13 May 2010 (UTC)


 * The role of proofs is an interesting topic. Apparently that philosophical issue must be decided before we can proceed. Then it must be established that this particular effort conveys some essential idea. My own view is that proofs are used for the same reasons that any argument is used: to show the connection between a result and some premises, to demonstrate a mode of reasoning, and to provide some instruction in the art. Whether it is long or short is immaterial. Whether it is educational is often conjectural. Whether a proof is "tedious" is in the eye of the beholder. I don't see much likelihood of my efforts being accepted by you or by Dick Lyon. Brews ohare (talk) 17:37, 13 May 2010 (UTC)
 * I fear that this is cargo cult mathematics: putting on a show of the forms of mathematics without an understanding of the reasons behind them. The primary purpose of proof in mathematics is to provide verifiability: another mathematician can read the proof and be convinced that the claim is true. But in Wikipedia, we provide verifiability through sources; if sources cannot be found, and we must resort to mathematical proofs instead, we are committing original research. Proofs do have uses other than verifiability, some of which remain important as rationales for providing proof in Wikipedia, as I've attempted to outline above. But to say "this is mathematics, therefore we must write it with proofs" is misguided and incorrect. —David Eppstein (talk) 17:42, 13 May 2010 (UTC)


 * Yes, proofs are to demonstrate how one arrives at a result from a given set of premises. I don't think that's in dispute. What is in dispute here is whether proofs belong on Wikipedia. Remember that Wikipedia is an encyclopedia, not a mathematics textbook. As such, the audience is different. You are not targeting mathematicians and mathematics students, but the populace in general. Therefore, proofs (especially full proofs) should not be presented except where the subject matter itself requires them. (And even then, it is questionable whether presenting a mathematical proof adds value to an encyclopedia.) It has nothing to do with whether we agree on the philosophical meaning of proofs. The issue here is whether this overly lengthy section on the relationship between the pentagon and the golden ratio deserves so much attention. The fact itself should definitely be mentioned, but the proof need not be. And I say that it should not be, because its length makes the article imbalanced and gives this particular proof undue weight.&mdash;Tetracube (talk) 17:55, 13 May 2010 (UTC)

David and Tetracube: I agree with Eppstein that verifiability is not the point of a proof on WP. The conclusions and the premises can be sourced, and supply "proof" that the conclusions generally are accepted to follow from the premises.

The role of the proof is therefore to assist the reader to join the dots between premises and conclusions. Eppstein has said there are some reasons for including a proof, such as conveyance of points not otherwise explicable.

I'd go further than that to say that the proof itself explains how the whole thing works. Many proofs convey the subject matter better than any other exposition, and say more than any individual "point" or "conclusion".

A statement like “it is questionable whether presenting a mathematical proof adds value to an encyclopedia” is simply intolerance brooking no discussion.

Aside from such generalities, in this specific case of deriving how the golden ratio applies to the pentagon, I've said that the part of the discussion concerning the size of the side is not pertinent. However, what about the part that is directly related to the golden rule? Brews ohare (talk) 21:16, 13 May 2010 (UTC)


 * Brews, it's already in there. You have stated that "There appears to be no other demonstration of the golden ratio for the pentagon in WP."  But what about the description under the section Ptolemy's theorem?  It could be expressed more clearly, but it's there, with a very simple derivation using an elegant and well-known theorem; much more direct that trying to work from Pythagoras.  Dicklyon (talk) 23:40, 13 May 2010 (UTC)


 * And also the Example section in Ptolemy's theorem, which even has a diagram by which the derivation of the Golden Ratio is visually clear.&mdash;Tetracube (talk) 00:28, 14 May 2010 (UTC)

Great. This discussion would have been much easier if these treatments were pointed out at the outset. The material removed that you object to was simply a proof of Ptolemy's theorem for the case of the pentagon, a topic on WP I wasn't aware of at the time. Diatribes about "big mathy section" and various claims that "questionable whether presenting a mathematical proof adds value", were "undue weight", blah, blah, were contentious baloney. What works is that the material can be found elsewhere on WP, and that fact should be made clear in this article. Brews ohare (talk) 03:35, 14 May 2010 (UTC)


 * Right, good point. Reset to yesterday.  What I should have said was, "Brews, your new big mathy section is immediately adjacent to a small concise section that demonstrates the golden ratio in the pentagon.  Are you thinking we don't have such a demonstration right there already?  Or are you sure we need another demonstration of this?  Or just looking for a place to dump this stuff you wrote that got rejected elsewhere?  Or what?  Tell me, because I can't read your intentions from your edits or your edit summaries."  Dicklyon (talk) 04:58, 14 May 2010 (UTC)


 * You should have said: "Brews, your new section is redundant because there already is a section that demonstrates the golden ratio in the pentagon. There's a brief version in Pentagon and an extended proof in Ptolemy's theorem." No need to tear a strip off me. Brews ohare (talk) 05:57, 14 May 2010 (UTC)


 * I should explore WP to find all the things that you contributions are redundant with, when the problem is more local and immediate than that? Are you purposely ignoring the point that you placed it immediately adjacent to a short section that showed the golden ratio in the pentagon in the article at hand?  And I was supposed to guess that the problem was that you hadn't read anything in the immediate context of your edit?  Sorry, my intuition was not that good.  Dicklyon (talk) 15:26, 14 May 2010 (UTC)

Language
In the top descrition it says "In mathematics and the arts,". It's not called THE arts, just arts. Please change it ConferAll (talk) 19:30, 13 June 2010 (UTC)


 * Although you may not have come across it before, the usage is correct - see our article on The arts. Gandalf61 (talk) 19:40, 13 June 2010 (UTC)

Found a golden section software tool
Hello. I found a software for detection and application of the golden section: Golden Ratio.

Do you think this is worth an external link?

I tested several screen measuring programs, because I wanted to detect golden ratio proportions in paintings and photos on my screen. This was the only one that was really useful. Other programs were only able to measure horizontally or vertically, but not in any angle, as the circle compass feature in this program does. I think this might be useful for anyone who is interested in the golden ratio. Unfortunately it is not freeware, but cheap. After 30 days you have to pay 15$. 93.135.56.71 (talk) 19:46, 15 June 2010 (UTC)


 * Earlier today I removed the link per WP:ELNO (points 5, 6, 11) and of course per WP:PROMO. I'm afraid that this is not the place to sell a home written software. DVdm (talk) 20:20, 15 June 2010 (UTC)


 * I see (except point 11). It seems I did "spam Wikipedia without meaning to". On the other hand, I find a high relevance of this software in the context of the article. Although the program is not globally important (as for example Microsoft Office), it is important in the context of the golden section. And therefore a link might be OK.


 * But maybe an encyclopedia is only collecting knowledge, but not tools to help gathering that knowledge. Any opinions about that? 93.135.109.203 (talk) 20:36, 16 June 2010 (UTC)


 * DVdm, there is another link you should remove for the same reasons if this discussion concludes that commercial software must not be linked.
 * The "goldennumber.net" site's main purpose is to promote the Phimatrix and Phidental software programs made by the author of the site. This is obvious, even if the author manages to hide that fact between some general information about the golden section and between many links to commercial products. 93.135.109.203 (talk) 20:54, 16 June 2010 (UTC)


 * Yes, this link was added with this edit. This site seems to offer a lot more about the subject of this article than what is already covered by it, so perhaps it can stay per WP:ELYES point 3. To me it doesn't look like selling software is the primary purpose of the site. Let's see what the other contributors think about it. DVdm (talk) 21:36, 16 June 2010 (UTC)


 * Um, while I was writing this, it looks like something was already set in motion :-) - DVdm (talk) 21:40, 16 June 2010 (UTC)
 * I'm the one that upon reading this section decided to pare the external links section down. The ones I left don't seem necessary.  On a philosophical note, since a google search already turns up thousands of hits for the golden ratio, why do we need to add any more here?  At best we're duplicating what a google search would turn up, at worst we (the wikipedia community) will appear to be endorsing those links we include here as somehow better than the ones we don't.  A mere link does not actually improve the content of the article.  Adding links for this article is a no win situation.  Although I won't object if someone wants to put back in several of the ones I deleted (though I think the specific one in question in this section is unnecessary).TheRingess (talk) 22:41, 16 June 2010 (UTC)

Parthenon
"Parthenon's facade as well as elements of its facade and elsewhere are said to be circumscribed by golden rectangles" This is a notion that will not die despite it being patently nonsense. Firstly the Parthenon's stylobate is curved, i.e. it doesn't form a rectangle with anything. Secondly where do these rectangle get measured from? Do they include the arcolith, the stylobate, the projecting geisons? In other words these are inevitably measurements edited to suit a thesis, in other other words - crap. But we all learnt it at mother's knee so it must be true. Twospoonfuls (ειπέ) 17:33, 11 July 2010 (UTC)


 * The only reasonable thing to do is to attribute the observation to those who published it (preferably first, or early at least), as well as report the analyses of those who have debunked it. And get rid of the misleading image/caption.  Go for it.  Dicklyon (talk) 21:03, 11 July 2010 (UTC)

In fact, it seems to me that the entire section on architecture belongs in the "disputed observations" subsection. (This would also have the advantages of bringing the mathematical portions of the article more closely together and de-emphasizing the nonsense parts of the article.) I'm not going to make such a change myself (I don't understand how to make image placement work out right, for one thing), but I hope someone else will! --18.87.1.234 (talk) 21:49, 10 September 2010 (UTC)


 * It should be pointed out that the standard references books on Greek architecture, Anderson Spiers Dinsmoor, DS Robertson, Banister-Fletcher, AW Lawrence, none of them mention phi in relation to the Parthenon. This theory that it was used really ought to be placed under the rubric WP:FRINGE. Twospoonfuls (ειπέ) 13:43, 16 September 2010 (UTC)

Remove reference to light switch plate?
The section on "Disputed observations" contains a ridiculous reference to light switch plates. For something to belong in the section on disputed observations of the golden ratio, there should be some claim that the thing being observed exhibits the golden ratio somehow. In the case of the light switch, there is no evidence for such a claim, and indeed any such claim would be inherently unreasonable (since in fact there is an exact known ratio of the sides of a light switch plate, and this ratio is not equal to phi). I attempted to remove this yesterday but my change was reverted; rather than changing it again, I'm posting this here in the hope that someone else will deal with it. Thanks! --18.87.1.234 (talk) 21:43, 10 September 2010 (UTC)


 * I'm all for removing unsourced observations of the golden ratio, but that one can actually be found in two different 1999 books, and it's as good as most. Dicklyon (talk) 04:25, 11 September 2010 (UTC)


 * No books (from 1999 or otherwise) are referenced in the sentences in question. Right now, the comment there is, in its entirety, an observation that a particular rational number (4.5/2.75) is not very far away from phi.  This is not an observation of phi, disputed or otherwise.  (Incidentally, I'm the same person as 18.87.1.234.) --71.233.44.242 (talk) 13:29, 11 September 2010 (UTC)


 * See your own comments here: Talk:Golden_rectangle. They apply in full force (except that in this case, there is not even an advertising blurb using the word "golden"). --71.233.44.242 (talk) 14:54, 11 September 2010 (UTC)


 * I'm just saying that in Google book search, I see two sources; if someone wants to source it or remove it, I don't care either way. Dicklyon (talk) 15:40, 11 September 2010 (UTC)


 * I will oppose its removal. It is included under the heading "Disputed observations", which, as the original poster has shown, is indeed disputed. It is not however, "ridiculous". Wall switch plates were obviously designed for aesthetic attractiveness, and it's a good bet that these professional designers were well aware of the aesthetic reputation of the golden ratio. It's therefore a good bet that the fact that the closeness (one percent) of the ratio of the sides of a wall switch plate to the golden ratio is not coincidental. Furthermore, when the dimensions of these wall switch plates are listed in millimeters, they are listed as 114 x 70 mm (e.g. http://www.homedecorhardware.com/baldwin-4764.html), which yields the golden ratio to within less than seven tenths of one percent. To prove that the design was in fact based on the golden ratio would simply remove this example from the "disputed observations" section to an "undisputed observation" section or some such thing. The fact that it is within about one percent of the golden ratio (or less!) is sourced. This fact should not be suppressed. PAR (talk) 16:49, 11 September 2010 (UTC)


 * PAR, as I said, just add a source. But also note that what you're saying is not correct.  It is not sourced that the switch plate is within one percent of the golden ratio.  The same page that lists the metric dimensions also lists English dimensions that are NOT within 1% of golden ratio, and that source does not mention the golden ratio.  You can use it as a source of approximate dimensions, but not as a source of how close it is to golden ratio.  And your assumption that they "were obviously designed for aesthetic attractiveness" and that "it's a good bet that these professional designers were well aware of the aesthetic reputation of the golden ratio" are just guesses; I'd guess that it's just a coincidence.  Let's just stick with sources and calling it disputed.  Dicklyon (talk) 04:13, 12 September 2010 (UTC)


 * This is, in fact, ridiculous, and your argument, as stated, rests on the unverifiable mental state of the people who decided on 4.75 by 2.5 inches. So far, no one has claimed that the golden ratio is present here, and any such claim would be self-evidently false, since the number in question is by definition not equal to the golden ratio.  "Numbers that are close but known to be not equal to the golden ratio" are not, and cannot be, instances of the golden ratio, by definition.  There are uncountably many real numbers within 1% or 2% of the golden ratio (that the ratio in millimeters is closer is due to rounding when converting inches to the metric system and has exactly 0 significance); they don't all deserve mention here.  Unless there is some specific claim that the light switches *actually exhibit the golden ratio*, it should not be in this section; since any claim in this case is false by definition, it should be removed.  --71.233.44.242 (talk) 18:58, 11 September 2010 (UTC)
 * Ridiculous or not, this claim is actually made in published books about the golden ratio. And in fact most of the claims in this section are ridiculous; that's why they're "disputed claims" rather than something more substantial, so being ridiculous is hardly an argument for excluding it. —David Eppstein (talk) 19:06, 11 September 2010 (UTC)
 * Perhaps we could rename the section to Ridiculous claims. Sorry, couldn't resist. DVdm (talk) 20:40, 11 September 2010 (UTC)
 * Anyone who wants to keep should go ahead and look up at least one of the book sources, and add a ref. Otherwise, anyone is free to remove it.  Dicklyon (talk) 04:00, 12 September 2010 (UTC)

DickLyon - I'm not sure I understand what you mean when you say the metric dimensions are not within 1% of the golden ratio. The metric dimensions are given as 114mm and 70mm. $$(114/70-\varphi)/\varphi$$ = 0.00651... or about 0.65 percent. Are you saying that this trivial calculation must be referenced?

To anonymous and DVdm, ok, let me see if I understand the rules. Any reference to a supposed golden ratio which is not precisely equal to the golden ratio must be expunged. That means we have to expunge reference to any phsical object (biological, architectural, artistic, etc.) that is supposed to exhibit a golden ratio, since measurements are not precise and cannot reproduce the golden ratio exactly, unless we can prove that mechanism or mental state which produced it is explicitly derived from the mathematical golden ratio. For biological specimens that will require DNA analysis and biomolecular mechanics and biochemical analysis beyond present technology, so that's gone.

That also means, under the Timeline section we must eliminate Phidias and Charles Bonnet. We can remove the entire Architecture section, since there are no references which prove that any architecture was purposefully designed using the golden ratio, only that the architect praised the golden ratio as an ideal, and then that certain ratios in their architecture have been found to approximate the golden ratio. In the Art section, we can keep Salvadore Dali, purge everything else. Purge Book design, Perceptual studies and if you actually read the sources in the music section, that must be purged too. The section on Nature - gone, Egyptian pyramids - gone, and of course, all disputed observations. What we are left with is essentially a mathematical description of the square root of five minus one divided by two. Is that what we want?

I say no.

To David Eppstein, you say the claim is made in published books about the golden ratio - good, can you provide such a source and maybe put an end to this? PAR (talk) 19:44, 12 September 2010 (UTC)
 * ✅. —David Eppstein (talk) 21:07, 12 September 2010 (UTC)
 * The rules say that, in the section Disputed observations, any observation that is not properly sourced as being disputed should be removed. That implies that some of these (i.m.o.) ridiculous claims only have a place here if they are properly sourced as being disputed. Simple rule. DVdm (talk) 20:20, 12 September 2010 (UTC)


 * Ok, that rule makes more sense than that other nonsense, although I still think it is too strict. Thanks, David, for the source information. PAR (talk) 23:16, 12 September 2010 (UTC)


 * I reduced it to what the sources support. I see nothing in sources claiming a relation to Lucas number, to 11:18, or to any other integer ratio.  The metric dimensions argue against interpreting the approximate standard size as exact; no source does so, as far as I can see.  Dicklyon (talk) 05:19, 10 October 2010 (UTC)
 * The reliability of the statement is still questionable to me. One source mentions posters and credit cards in the same sentence, but my credit cards are not golden rectangles and posters dimensions vary from poster to poster. Popular writing in mathematics can be unreliable since the people checking the facts may know little about the subject and that appears to be the case here. It seems more reasonable to me that the dimensions of a plates come from the dimensions of an electrical box plus a margin than a deliberate attempt to form a golden rectangle. The plates designed to cover multiple switches are definitely not golden rectangles. There is no source for the "4.5 by 2.75 inches" statement as well; this can probably be easily fixed but it smacks of WP:SYNTHESIS. Given the facts are questionable, it seems to me that the section does not add enough value to the article to justify its inclusion.


 * I tend to agree, now that it's not listed as a "disputed sighting". I think it may have been I who added the dimensions, from some online catalog, but I don't see them mentioned any place that talks about golden ratio, so it probably is WP:SYN.  Still, it might make sense to somehow acknowledge that authors do often find something close to golden ratio in lots of places when they go looking for it, so that we don't have people in the future adding those things back in one by one. Dicklyon (talk) 20:56, 10 October 2010 (UTC)
 * I like this change, de-emphasizing the specifics of the switchplate example and instead highlighting the supposed ubiquity of the ratio in design. —David Eppstein (talk) 21:16, 10 October 2010 (UTC)

Online publication
I have a question- does online publication in a blog count as published source for a Wiki entry? I run a blog about alternative periodic tables. It was discovered that when Fibonacci and Lucas numbers are mapped to the periodic table as atomic numbers the patterning was nonrandom. Up to atomic/fib number 89 ALL the odd fib numbers correspond to elements with a single electron in one orbital lobe (s1,p1,d1,f1), while ALL the even fib numbers here map to the first doublet electron in one lobe (the set (not all instantiated) of s2,p4,d6,f8). Lucas numbers map instead to the last singlet (half filled orbital) or doublet (full orbital), with exceptions, but these exceptions are behaviorally altered in terms of electronic configuration so they DO act as if they have full orbitals. This was all announced in the blog. Would this be enough to justify inclusion as an addition to this page or the pages on fib or lucas numbers, or is there still the issue of 'original research' unless somebody else reports on it? Thanks. JT —Preceding unsigned comment added by 108.5.120.161 (talk) 03:05, 10 October 2010 (UTC)
 * In general blogs are not considered acceptable sources. See WP:SPS. There are exceptions, but in the case of this article, when we are overwhelmed by potential sources that are more reliably published, I think the caution against using self-published sources should be taken especially strongly. —David Eppstein (talk) 04:03, 10 October 2010 (UTC)

Simple Cell division rate as explanation for Fibonacci numbers and for golden mean in nature.
Simple Cell division rate as explanation for Fibonacci numbers and for golden mean in nature.

http://deoxy.org/forum/showflat.pl?Cat=1&Board=vox&Number=55595&page=0&view=collapsed&sb=5 On the first topic thread there is the proposal, and linked simple diagram. Then follows open discussion, which at some point turns into computed tests to disprove or prove the explanation. Thus far no fault seems to have been found in it. Seems deceptively simple... In a nutshell: an organism, like cell (or even self replicating bubble ?) is born. Then it exists and grows. Then it divides, gives birth to another organism. While the new "child" organism is still gathering energy and growing, the original orgnism splits again. Then there is three. Next the elder child organism and parent organism split while youngest one still grows, and there is 5 of them, and it goes on and on and seems to give the fibonacci number each time, as well as the golden proportion in shapes and volumes, even if some of the organisms get wrecked at some generations, or starting amount of organisms is varied. Direct link to the cell division diagram only, without the discussions, commentary and testing: http://koti.mbnet.fi/maxt/oddsnends/fibo.gif My sources have been... I just started to calculate it as visual organic division, without numbers. I think I was trying to understand development of organic spatial forms. No other sources, except that I did not seem to find quite this simple explanation that gives reproducible results, in wikipedia or elsewhere in the Net. At least not for now. It is so very simple that it may be wondered why I post it... and the answer is, because I have not yet seen it elsewhere, only more complex models with more parameters, and things like rabbits and bee communities ratios of young queens.

Possible more complicated phenomena and versions: For extra variants and ratios, perhaps to gain insight to various precise cell division and growth processes at specific parts of specific living creatures and systems, the growth and division frequency ratios can be changed little (for example, considering units of dividing entities that divide 2 times or 1.1, times and so on times between new generations appering, and so forth. Also adding one or more types of "feeder" being units, that grow and divide into new, only by eating/absorbing amount of the first type ones, and calculating the fluctuations of populations and the shapes their existence creates. —Preceding unsigned comment added by MaxTperson (talk • contribs) 22:37, 11 October 2010 (UTC) MaxTperson (talk) 23:23, 11 October 2010 (UTC)
 * This is a talk page for discussing improvements to our article, not for discussing information generally related to the golden ratio. And postings on online forums are not generally considered acceptable sources for Wikipedia articles. —David Eppstein (talk) 03:14, 12 October 2010 (UTC)
 * Particularly when they are quite clearly bunk. Successive fibbonaci numbers grow exponentially. All exponential growth is "the same", in the sense that you can map then just by changing your baseline. If some "cells" increase their number by the golden ratio each time you sample them, simply by sampling them log(phi)/log(2) less frequently you will observe them doubling their number each time instead. —Preceding unsigned comment added by 124.178.225.104 (talk) 15:08, 4 December 2010 (UTC)

Incorrect Reference
I'm very new to Wikipedia so thought I'd mention something here instead of editing the text myself. Also, I need to figure out how you all do References.

The reference to Euclid's "Elements" (Reference #5) should point to Book 6 Definition 2; not Definition 3.

Kabuch (talk) 00:14, 13 November 2010 (UTC)
 * Reference 5 ("Euclid, Elements, Book 6, Definition 3") is used in four places; each can be seen by clicking the a, b, c, d links. Definition 3 (here) seems correct. What is the problem? Johnuniq (talk) 02:30, 13 November 2010 (UTC)


 * I'm looking at my copy of Euclid's Elements. Book 6:
 * Definition 2: A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less.
 * Definition 3: The height of any figure is the perpendicular drawn from the vertex to the base.
 * My copy does not have the definition listed as #2 in the link you supply. Kabuch (talk) 04:47, 13 November 2010 (UTC)


 * Euclid's Elements is outside my knowledge, and I'm hoping someone will explain the discrepancy. My guess is that different translators have arranged material rather differently. I refactored your comment to show how it would normally be entered (click "edit" to see the wikitext), but there is no need to worry about such things. Johnuniq (talk) 06:58, 13 November 2010 (UTC)

The golden section
The sentence "The golden section is a line segment divided according to the golden ratio: The total length a + b is to the longer segment a as a is to the shorter segment b." is very vague. What does this mean? —Preceding unsigned comment added by 84.202.70.29 (talk) 19:16, 28 December 2010 (UTC)


 * I added "the length of" in strategic places to make it more clear, I hope. The language "...is to...as...is to..." is about relationships, by which we mean ratios.  This language is common in geometry, but I agree that if you don't know, then it's not very helpful.  Maybe someone will want to make it more explicit.  Dicklyon (talk) 21:52, 28 December 2010 (UTC)

Use of Upper case VS lower case Phi
This article states that the upper case version of Phi is usually used to represent 1.618... and then proceeds to use the lower case version to represent it. The Wikipage on Phi states the following..

The lower-case letter $$\varphi \,$$ (or often its variant, $$\phi \,$$) is often used to represent the following:
 * The golden ratio $$\tfrac{1 + \sqrt{5}}{2} \approx 1.61803\ldots$$

If that's true then the sentence suggesting otherwise should be deleted. We have a contradiction here. Wolfram uses $$\phi \,$$ Dave3457 (talk) 12:04, 11 January 2011 (UTC)


 * Good catch. Our article does it the other way around. Since the statement is not sourced anyway, I guess nobody will mind if I bring it in line with the article and change it as follows:
 * In this article the golden ratio is denoted by the Greek lowercase letter phi ( $$\varphi \,$$), while its inverse, (1/phi), which is also equal to (phi-1), or 0.6180339887... is denoted by the uppercase variant Phi ($$\Phi \,$$).
 * DVdm (talk) 13:09, 11 January 2011 (UTC)

Citation needed
There's a "sitation needed" on the sentence: "The rhombic triacontahedron is a rhombohedron that has a very special property: all of its faces are golden rhombi".

Surely you don't need a citation for well-known immutable facts of geometry. The page for rhombic triacontahedron doesn't have "citiation needed" plastered all over it. —Preceding unsigned comment added by 124.178.225.104 (talk) 14:53, 4 December 2010 (UTC)


 * It's not so much about "immutable" facts as about conclusions and about what things are called. Probably someone actually felt that some of those statements might be incorrect, or not supported well by the linked articles.  In particular, "The rhombic triacontahedron is a rhombohedron" seems to be false, according to my read of those pages.  Since the rhombic triacontahedron doesn't cite its sources, it's hard to verify; I tagged it as needing inline citations.  Dicklyon (talk) 22:00, 28 December 2010 (UTC)
 * i agree with the above point, regardless how well-known it is or what immutable means in this sense, and will highlight the implicit point made thereafter (but apparently not acted on), that 'it' is about what things are 'called', or said to be known as; therefore an in-line link to another wiki page serves as a citation, where the assumption is that that further page will be cited, and further that discussion of that site, article or dilemma is best held within that context rather than this one. As stated, there doesn't seem to be any citations on the rhombic triacontahedron page, but there is an unbroken external link (Eric W. Weisstein, Rhombic triacontahedron (Catalan solid) at MathWorld) which seems (to me, upon a cursory examination) to serve or satisfy for the purposes of prior usage. As to whether the assumption is correct, please describe a rhombic triacontahedron with a face that is not a golden rhombus, and then remove all that is necessary. I will leave the citation marks, but these could certainly also be interpreted as verification marks, following the idea that geometry is logically self-evident, or can be defined within its own terms (ie without reference to anything else)124.150.56.235 (talk) 14:17, 23 February 2011 (UTC)


 * What you call "self evident", or via logical deduction, is what we call WP:OR. Why not just cite a source?  Here's one that might cover it.  Dicklyon (talk) 15:29, 23 February 2011 (UTC)

ruler & compass construction
There is no section regarding the common geometrical (ruler & compass) constructions of the golden section. Imho there should be a chapter for them, the required drawings arre already available in the German interwiki.--Kmhkmh (talk) 21:22, 19 February 2011 (UTC)

What "Body of Literature" in the Renaissance?
The article claims that "Beginning in the Renaissance, a body of literature on the aesthetics of the golden ratio was developed." Is this really true? Luca Pacioli's important book naming the "divine proportion" was certainly written, but where's the rest of the body? Texts and web sites I've seen tend to start with that, and then go to pictures of later artists with various pentagrams, lines, and spirals overlaid — with no actual body of literature referenced. Do we have any written record that any of these works were composed with that intention (in the cases where they do line up reliably and not just through selection bias and close-enough-must-mean-it-works)?

When we get to the early 20th century, there's a lot of interest and clear documentation. But that's hardly in the Renaissance!

Matthew Miller (talk) 03:37, 28 February 2011 (UTC)

In fact, looking at List of works designed with golden ratio, it seems that everything from Pacioli is speculation based on analysis of works, not the result of any literature at all! — Preceding unsigned comment added by Mattdm (talk • contribs)


 * It came in this diff and the next one by Finell. It used to say "A large corpus of written materials about the aesthetics of the golden ratio has developed over the last 500 years," which is in some sense more accurate, since most of it developed in the last N years, and very little of it in or near the Renaissance.   I agree on the list of works, but I got tired fighting that guy (User:20-dude); we need to make sure it's all attributed as retrospective analysis, if it's not. Dicklyon (talk) 04:20, 28 February 2011 (UTC)

Elevating Zeising as Contributing to Golden Ratio in Aesthetics
The article refers to Adolf Zeising under the heading "nature". But, his contribution seems more important that that — in fact, he may be the origin of the modern conception of the golden ratio as important to aesthetics and design!

For example, |The Psychology of Aesthetic Reaction to Rectangular Forms, Psychological Review, 1904, which says "Since the aesthetic value of the golden section was first developed by Zeising¹, all questions in the psychology of the aesthetics of form have centered around this one, the psychology of the golden section." (With the footnote referring to Zeising's Aesthetische Forschungen).

Or even more strongly, http://herz-fischler.ca/zeising.html, which says "Almost all of the statements that have been made concerning the appearance of the golden number (golden section, golden ratio, etc.) in man-made objects (art, architecture etc.) and in nature (human body, astronomy etc.) can be traced back to one person, the German intellectual Adolph Zeising." which is such an amazing statement I am forced to put it in bold here. :)

Matthew Miller (talk) 04:55, 28 February 2011 (UTC)

And from |The golden ratio by Mario Livio, "Numerous authors have claimed the Golden Rectangle is the most aesthetically pleasing of all rectangles. The more modern interest in this question was largely initiated by the German researcher Adolf Zeising, which started in 1854 with the publication of Neue Lehre von den Proportion des menschlichen Körper (The latest theory of proportions in the human body) and culminated in the publication (after Zeising's death) of a massive book, Der Goldne Schnitt (The golden section), in 1884."

It seems pretty clear that Zeising should at least be added to the timeline at the top of the page and to the section on aesthetics.

Matthew Miller (talk) 05:17, 28 February 2011 (UTC)


 * And one more: http://www.deepdyve.com/lp/de-gruyter/adolph-zeising-and-the-formalist-tradition-in-aesthetics-5fIqaRfpI9 (And now, bedtime for me.) Matthew Miller (talk) 05:30, 28 February 2011 (UTC)
 * Wait wait just one more: http://www.bachnetwork.co.uk/ub1/tatlow.pdf "The practice of searching for golden sections, or golden numberism, did not begin until the 1830s. The interest was initially confined to Germany, but gradually spread to the rest of Europe. The major events progress can be charted in the following chronology." Matthew Miller (talk) 05:46, 28 February 2011 (UTC)
 * More. :) Humorous skepticism from 1856. http://books.google.com/books?id=TBQXAAAAYAAJ&pg=PA125&lpg=PA125&dq=zeising+parthenon&source=bl&ots=3V09mGQTVt&sig=dbePAEmvfUiB2vVHlcxAr_vH6Iw&hl=en&ei=njZzTaTcHIGglAfhueVg&sa=X&oi=book_result&ct=result&resnum=2&ved=0CBUQ6AEwAQ#v=onepage&q=zeising%20parthenon&f=false Matthew Miller (talk) 07:28, 6 March 2011 (UTC)
 * Thank you for that quite wonderful review article. Dicklyon (talk) 07:36, 6 March 2011 (UTC)
 * And here's the work by David Hay referenced there. It also responds directly to Zeising: http://books.google.com/books?id=04ufAAAAMAAJ&pg=PA117&dq=zeising+parthenon&hl=en&ei=nztzTd2yLYKztwfFxoHzDQ&sa=X&oi=book_result&ct=result&resnum=5&ved=0CDwQ6AEwBA#v=onepage&q=zeising&f=false Matthew Miller (talk) 07:48, 6 March 2011 (UTC)

Binary
In binary, sqrt(5) and the golden ratio's bits look very similar. I just wanted to post this here because using decimal numbers often hides pretty simple things. Here they are in binary: sqrt(5): 10.00111100011011101111001101110010111111101001010011111... golden ratio: 1.100111100011011101111001101110010111111101001010011111... 92.107.251.225 (talk) 20:58, 30 April 2011 (UTC)


 * And in decimal, the digits of 1+pi/10 are lot like those of pi itself! Dicklyon (talk) 21:47, 30 April 2011 (UTC)

This edit by anonymous editor properly removed Copyrighted material
Material was pasted from pg 6 of cited source. Ward20 (talk) 19:20, 1 May 2011 (UTC)


 * Sorry didn't relaize it was in a quote. Ward20 (talk) 19:59, 1 May 2011 (UTC)

proof in Golden triangle section
At the end of the "Golden triangle" section it says "The proof is left to the reader". What is this, an encyclopedia or a math textbook? *sigh*134.147.194.112 (talk) 13:24, 9 May 2011 (UTC)
 * Indeed a rather unappropriate (and some what pointless) line, hence I removed it.--Kmhkmh (talk) 14:32, 9 May 2011 (UTC)

A minor point
Does it bother anyone that an irrational number bears the label "ratio"? I mean, the one thing an irrational number cannot be by definition is a ratio - else it would be rational.

PcGnome (talk) 06:18, 8 August 2011 (UTC)


 * The one thing an irrational number cannot be by definition is a ratio of integers. But it can certainly be, say, the ratio of the length of the diagonal of a regular pentagon to the length of the side of the pentagon, since there is no regular pentagon where both those lengths are integers.  —Mark Dominus (talk) 16:17, 8 August 2011 (UTC)

All fives
You can express the golden ratio using just the number five and exactly one use of each of the major arithmetical operations of exponentiation, multiplication and addition:

$$\varphi = 5^{.5} \times .5 + .5$$

--  Denelson83  23:54, 24 August 2011 (UTC)

an orphan wants you to help him
Dear authors of the "Golden ratio” Wikipedia entry: Concerning your article, may I cordially suggest you to read the text “The TK Theory of Visual Proportions” and, if necessary, link or cross-reference the latter article with the former. Please contact me in case you have any doubts or questions. Yours, espaisNT. --EspaisNT (talk) 10:00, 9 September 2011 (UTC) --EspaisNT (talk) 10:38, 9 September 2011 (UTC)

A Note
This article appears hesitant to present accurately the nature of the "golden ratio", in that it is a trivial construct and a simple geometric property whose only peculiarity is that it describes an approximately similar growth pattern to that of the Fibonacci sequence, which is itself a simple and related analytic construct, namely, increasing a population by summing the previous two terms in the sequence. Of course this creates a regularity of pattern! It is by definition and design a series of proportionate growth! This is not mystical, but is certainly of interest. I feel the esoteric tone of this article needs to be reduced, and that the endorsements of the subject's perceived profundity be relegated to headings lower on the page. All of the information is correct, only the strucure is imbalanced. Thank you. 150.135.210.78 (talk) 22:49, 13 September 2011 (UTC)

You're kidding, right?

Golden ratio, Traquair and TK


Dear authors of the "Golden ratio” Wikipedia entry, I wish you will study the possibility to include the attached article in the "perceptual studies".

I look forward to your response.

cordially "Harry Moss Traquair (1875-1954) was the pioneer of the study of the visuals fields. In "An Intoduction to clinical perimetry" (1927) defines our vision as "an island of vision surrounded by a sea of blindness." The blind spots are the elliptical boundaries of the "island of vision" in the horizontal plane. The angle from our eyes to the ends of our blind spot is approximately 34 degrees ; this angle is very approximately the same as covering a small side of the golden rectangle from the middle of the opposite side. There is a golden rectangle between the extremes of blind spots and the eyes of the observer of space. Kim Lloveras i Montserrat also uses it to define what is the horizontal section of the "Cone of Good Vision" in "The Theory TK of Visual Proportions" and in his "Theory TK and Laws of Positioning 2007" . The persons (with normal vision or with corrected myopia) perceive in a very different way the space inside and outside of the Cone of the Good Vision. There have been several publicly "Visual Experiences TK" in order to validate the Cone of Good Vision proposed in the the Theory TK: at the Barcelona School of Architecture (2002 - 2003-3008-2009), at the School of Architecture of Vallés (2008), and at  the Eduardo Torroja Institute (2008) of  Madrid, belonging to the National Research Council (CSIC). Arquiteturarevista summarizes what are the experiences TK of the cone of Good Person of the Person."

--EspaisNT (talk) 10:38, 13 October 2011 (UTC)


 * This material is only appropriate for the article about The Theory TK of Visual Proportions or a notional article about Harry Moss Traquair. Not mainstream, not influential in regard to the golden ratio. Binksternet (talk) 16:04, 13 October 2011 (UTC)

A number of problems
The assertion that "many artists and architects have proportioned their works to approximate the golden ratio" is misleading. If you search for actual examples, you will find that very few have. Try finding a major painting, for example, with a frame ratio of 1:1.612

There is no evidence supporting the use of the golden ratio in the Parthenon, or Pyramids of Giza.

Leonardo da Vinci's "Vitruvian Man" is not based on the golden ratio. It is based on a circle and a square, ratios of 1:1 not 1:1.612

The Illustration from Luca Pacioli's De Divina Proportione does not have anything to do with the golden mean.

You will find few postcards, playing cards, or posters with ratios of 1:1.612 as claimed by the article.

Wide-screen televisions (16:9) have a ratio of 1:1.77 not 1:1.612

http://www.maa.org/devlin/devlin_05_07.html — Preceding unsigned comment added by 24.214.204.222 (talk) 20:27, 28 November 2011 (UTC)
 * Thanks, that's another nice Devlin's Angle article. Please click "new section" to add a comment on a new topic to a talk page. That puts it at the bottom. Johnuniq (talk) 22:55, 28 November 2011 (UTC)

8"×10" and quarter-sized 4"×5" are popular formats in photography, and it would seem logical that the half-format 8"×5" would be particularly popular — conveniently derived from the others, and a decent approximation of the golden ratio. But, instead, 5"×7" became a standard size. In an 1891 magazine article, an author even writes: "I would recommend the 6½×8½ in preference to the 5×8, since for most work the latter is not so well proportioned." Matthew Miller (talk) 17:36, 19 December 2011 (UTC)

new link
In spite of the warning in the external links section I went ahead and added


 * Schneider, Robert P. A Golden Pair of Identities in the Theory of Numbers

to it. I had just recently added it to the article on Euler's totient, and thought it belonged here as well.

Virginia-American (talk) 17:34, 16 December 2011 (UTC)

negative reference for golden ratio
In researching photographic formats, I came across an interesting 1875 journal article. The article mentions that a certain in-vogue format is too narrow to meet "the best proportion, according to the golden mean", continuing "Unfortunately, but little attention has been given to the beauty standard, just as is the case in the cutting of our garments, and in the same way as it is impossible to argue down a new fashioned garment, no matter how foolish and ridiculous it may be, so we should be powerless to rob a picture of its popularity."

This makes the somewhat funny argument that while the golden mean provides the most beautiful portion, popular opinion seem to foolishly prefer others instead. And this continues with the relevant quote: "We may console ourselves with the thought that painters, on their part, trouble themselves very little about the golden mean."

The author, H. Vogel, appears to be reasonably notable. And his nationality (German) and the timing fit with the spread of the golden-ratio-as-beautiful meme. Matthew Miller (talk) 17:23, 19 December 2011 (UTC)


 * Good find! Binksternet (talk) 17:47, 19 December 2011 (UTC)

Blogs
Per WP:VERIFIABILITY and WP:BLOGS - Blogs especially this one, are not reliable sources. -- MST  ☆  R   (Merry Christmas!) 07:24, 20 December 2011 (UTC)
 * Also, regardless if the blog is reliable or not, common practise is actually discuss with an editor on the talk page, rather wp:edit warring, and the possibility of violating wp:3RR. Thank you, -- MST  ☆  R   (Merry Christmas!) 07:29, 20 December 2011 (UTC)

"Per WP:VERIFIABILITY and WP:BLOGS - Blogs *especially this one*" I think you are discriminating Google Blog Service which I find excellent (or which do you find "honorable"), plus, none of your references is mentioned this *blog* or blogs in general are not reliable sources. And I remind you that wp:3RR also applies to everyone, YOU included. Also, you should have started the talk request clarification before undoing it to explain in detail your IMO invalid reasons. Is there another instance or arbiter that can decide this besides you?
 * Don't know what point you are trying to prove, but an editor specifically told you they have issue with this blog being unreliable. I didn't warn you about the 3RR - another good-faithed user did - and you haven't broken 3RR anyway - that warning is to tell you, that you're a close to it. Don't tell me what I should and shouldn't have done, I did my job. Also, everyone's IMO is valid. Not just yours. -- MST  ☆  R   (Merry Christmas!) 08:00, 20 December 2011 (UTC)