Talk:Golden ratio/Archive 5

Mecca & co
That religious stuff is nonsensical enough and was removed in the past already. If anyone insist on including this under dipsuted claims, then to the very least you need to provide proper citations (no citation needed stuff). Furthermore a consent on the discussion page is needed as well.--Kmhkmh (talk) 23:55, 28 October 2011 (UTC)
 * I agree. —David Eppstein (talk) 00:07, 29 October 2011 (UTC)


 * I don't understand how these facts are nonsensical? Objectively, the values, actually, are very close to the golden ratio. Yes, they are coincidental, but isn't that exactly what adds to the aura of the golden ratio? About the citation, I am not sure whether the source that I have is applicable: It's not a journal, just an amateur website that has some calculations on it regarding this Mecca entry(which I have verified). The problem I found with the source, and the reason I hadn't posted it, is that it includes other claims that are, in fact, nonsensical: it claims that the Mecca is also longitudinally situated on the golden ratio (from east to west), which is completely arbitrary. The citation in question is: http://www.scribd.com/doc/9436715/THE-WORLDS-GOLDEN-RATIO-POINT


 * This is the entry in question:
 * In geography, the latitudinal position of the Islamic holy city of Makkah(Mecca) at N 21'42 corresponds closely to the golden ratio. That is the ratio of the latitudinal distance from the North Pole to the city to the latitudinal distance from the South Pole to the city equals 1/φ. In fact, any city situated near the N 21'42 line would have that same characteristic. In religious literature, the city of Makkah once again presents itself in a position of the golden ratio. In the Qur'an(Quran), the Islamic holy book, the word Makkah or Bakkah, referring to the city of Makkah, appears only twice. The word first appears in surah 3: verse 96, and it does so in a golden ratio position. There are 29 letters in the verse upto, and including, the word Bakkah; whereas the entire verse consists of 47 letters. This fraction, 29/47, is appoximately 1/φ.
 * 99.253.250.110 (talk) 09:00, 29 October 2011 (UTC)
 * This article is based on reliable sources discussing serious topics in mathematics and the arts. It is not the place to record every calculation that fringe groups may have performed. While it is mildly interesting to see how inventive minds can devise calculations to obtain some desired result, this is not the article to record such results, particularly without reliable sources. Johnuniq (talk) 09:25, 29 October 2011 (UTC)


 * I am asking for this entry to be placed in the Disputed Observations section. I think this entry adds to the aura of the golden ratio. It is an instance of the golden ratio appearing coincidentally, once again, in human history. Whether this is purely coincidence or not is up for debate or further research, which is why it is 'disputed'. For me, given the significance of Mecca in human history, this entry deserves a place in this article. 99.253.250.110 (talk) 09:34, 29 October 2011 (UTC)
 * Even disputed claims require reliable & reputable sources. If at all such a section is allowed at all it is to list well known claims published in reputable sources on which the academic community however does not agree. It is not meant as discussion forum or for including arbitrary fringe claims.--Kmhkmh (talk) 10:53, 29 October 2011 (UTC)
 * I can only find self-published, questionable(amateur) sources for this, although, the content seems easily verifiable. I hope we can leave this discussion up for others to see. It will save repetition of discourse. 99.253.250.110 (talk) 17:16, 29 October 2011 (UTC)
 * That's why it doesn't belong into in the article. Numerical verification is not the issue here rather notability.--Kmhkmh (talk) 18:49, 29 October 2011 (UTC)
 * I understand and agree. An entry's potential to generate interest in a topic does not compensate for a lack of notability. 99.253.250.110 (talk) 22:24, 29 October 2011 (UTC)

(indent pushed < thataways, sorry). For the proponents of the measurements of such cities: This is stepping away from mathematics and toward numerology. Given any number, you can look and find items that closely resemble it. If not a city, then a mountain range. If not that, then the trees. There is no point whatsoever in visiting each of these. IF A NEW ARTICLE ENTITLED (words to the effect of) "Matching items to the golden ratio", then perhaps. Tgm1024 (talk) 21:30, 7 February 2012 (UTC)

the arcticle's writer
who is the writer of this arcticle, im doing a work on the golden ratio in the pyramids so please help. — Preceding unsigned comment added by 192.115.130.253 (talk) 11:58, 9 February 2012 (UTC)

Amen break
From WP:RS, "Self-published material may be acceptable when produced by an established expert on the topic of the article whose work in the relevant field has previously been published by reliable third-party publications." That seems to fit the situation to a tee. He has a masters in Mathematics Education, and his book "A Beginner's Guide To Constructing The Universe: The Mathematical Archetypes Of Nature, Art and Science" has been published by a non-vanity press (HarperPerennial). Further, we are giving it as his POV, as with some of the other examples (e.g. Roy Howat). Superm401 - Talk 07:27, 14 February 2012 (UTC)
 * This concerns an edit which added text "The mathematician Michael Schneider analysed the waveform of the Amen break and found that the peaks are spaced at intervals in the golden ratio.ref"
 * The problem is that people have found the golden ratio in all sorts of things: looking hard enough often locates a pattern. The author's writings suggest a specialty in finding mathematical relationships, which is not what is needed in this article. Has the author analyzed other popular tunes looking for the golden ratio? If a significant proportion of such tunes fits a predefined pattern, a suitably qualified person might conclude something significant had been observed. Otherwise, it's just like noticing the decimal digits of the golden ratio in a car number plate. Johnuniq (talk) 07:55, 14 February 2012 (UTC)
 * [edit conflict] In an article for which we can find tens of thousands of actually-reliably-published sources, and on a subject on which many people have written and published many ridiculous things, I tend to think we should use stricter standards than He has a master's degree! In SCIENCE! Also, is a drum solo from the 1960's really central enough to the subject of this article to devote a whole paragraph to it? And finally, is it much of a surprise that you can take a sequence of 13 beats, break it up into 8 and 5, and find the golden ratio? It just looks like more numerology of a type we have too much of here already, to me. —David Eppstein (talk) 08:08, 14 February 2012 (UTC)
 * I agree. This is a topic with many dubious claims, but a wealth of (highly) reliable/reputable sources available, so we should stick to the latter and avoid any content that is somewhat dubious or of less or unclear notability to begin with.--Kmhkmh (talk) 10:12, 14 February 2012 (UTC)
 * I think we should try to base our discussion on actual policy. You haven't directly addressed WP:RS.  David Eppstein, it isn't a question of a master's degree "IN SCIENCE!".  It's a master's in Mathematics Education, which seems relevant to the topic at hand.  I don't think the fact that it's from the 1960's makes it less relevant.  It's been used in many notable songs since then, and there's no time limit on notability; that's why we have an article on it.  Johnuniq, I would be more concerned if the author found spurious golden ratios in every populuar song.  It seems relevant that it's specifically this break.  Quite unlike a car number plate, there is no suggestion that the Amen break was generated randomly or automatically.


 * Finally, the point of the mention is not to say definitely that the song uses the golden ratio. It is to relay his POV that it does.  If we have to tweak the wording, that's fine.  Superm401 - Talk 04:01, 20 February 2012 (UTC)
 * If you want argue from the point of WP:RS is kinda simple, as there are enough "high quality" source on subject hence there is no need to relax the criteria on sources. So if it is not published in a reputable (academic) journal, a book from a reputable academic publisher and/or by an particularly reputable academic/scholar then it stays out as in that case it is neither reliable nor notable enough for inclusion.--Kmhkmh (talk) 04:23, 20 February 2012 (UTC)
 * I'm certainly not arguing that Amen Break is a bad subject for an encyclopedia article. It might even be reasonable to mention its mathematical analysis within the Amen Break article itself. I just don't think it is sufficiently important to the topic of the Golden ratio to mention it in this article, and that the quality of sourcing (relative to the total volume and quality of sources for topics related to the golden ratio) is low. —David Eppstein (talk) 05:45, 20 February 2012 (UTC)
 * I agree with David Eppstein. If this isn't important enough to mention in the Amen break article, why is it important enough to mention here? —Mark Dominus (talk) 17:24, 20 February 2012 (UTC)

Reversion of edit without adequate explanation
I made an edit which made several improvements to this article. The edit was reverted with an enigmatic edit summary of "An edit that removes the numeric value from the lede is unacceptable," I'm putting the improvements back in. If anyone would like to make additional improvements, please feel free to do so, but don't simply revert a major, good-faith edit containing several changes without discussing it here first. (If that edit summary comment was about moving the equations from the introduction, please read WP:MOSINTRO before making any further edits.)  Sparkie82 ( t • c )  05:01, 2 March 2012 (UTC)
 * You are seriously mischaracterizing my edit summary, which invited you to discuss this here per WP:BRD rather than as you say didn't discuss it. And, WP:BRD is not about redoing your edits until the other editors give up in frustration: it's about actually discussing it *before* trying it again, which you haven't done. As for MOSINTRO: it says not to have unnecessary formulas in the intro, a very different thing than having no formulas at all. In a math article such as this one, some amount of math may be necessary to satisfy the other requirements of the MOS, that the lead section actually summarize the article and provide a concise description of the subject. In this particular case, it is absolutely essential that the approximate numeric value 1.618 be included in the lead, and that's not possible without a little bit of math to explain how that value relates to the English-language description. —David Eppstein (talk) 05:12, 2 March 2012 (UTC)
 * PS I just realized that until about a month ago what MOSINTRO actually said was "Mathematical equations and formulas should not be used except in mathematics articles." So you are edit-warring based on a change to MOSINTRO that has barely had time to have the ink dry and that has never been discussed with WP:WTM. And if you go back to the edit to MOSINTRO that is leading to this interpretation, and read the edit summary, you will see that the intent of the change was not to restrict the use of mathematical formulas in mathematics articles, but rather to broaden their use to allow formulas in other technical article leads. So your edit seems to be based on mistaken premises to me. —David Eppstein (talk) 05:19, 2 March 2012 (UTC)
 * Thank you taking the time to discuss this here. The edit made several improvements to the article, including improvements to the layout, and several others plus the moving of the equations. I was concerned that all of the changes were reverted (not just the equation-moving part). If the equations are the only concern, then please put back the other improvements and then we can discuss the equation issue in the following section.  Sparkie82  ( t • c )  05:41, 2 March 2012 (UTC)
 * I'd rather you broke down your changes into smaller chunks and tried them again separately. The removal of all the mathematics from the lead was what I primarily objected to, but in part that was because you made a lot of changes and it was difficult to tell what the effect of them was all at once. —David Eppstein (talk) 05:55, 2 March 2012 (UTC)
 * Okay, I did the edits separately, except for moving the equations which I'll hold off on until we work it out.  Sparkie82 ( t • c )  06:58, 2 March 2012 (UTC)
 * I don't believe the changes were improvements. -- 203.171.197.72 (talk) 11:52, 2 March 2012 (UTC)
 * I think I would agree that there are too many illustrations in the lead, and I'd move the "construction" to a golden rectangle section below. But leave the basic rectangle division, which is such an important part of the concept.  Dicklyon (talk) 16:24, 2 March 2012 (UTC)

Equations in intro
I feel the article would be improved by moving the equations from the intro. If this were only a mathematics article, then the equations would be appropriate in the introduction, however, this article covers a broad number of disciplines, including the arts, music, nature and many others. Readers will be coming to this article from many differing areas and with a variety of levels of understanding of mathematics. If there was no other way to introduce the subject and explain what the ratio is, then the equations would be needed, however, the prose, along with the graphical representation to the right of the intro adequately explain the ratio. Plus, the equations are revealed in the very next section of the article.  Sparkie82 ( t • c )  05:41, 2 March 2012 (UTC)
 * Sparkie82, be aware that this article has a long history of attention and compromise by lots of good editors. If you have an "improvement" you want to make, make your case here.   We have no problem assuming your edit was in good faith, but perhaps more of a problem believing that removing the symbol, value, and defining relationship from the lede is an "improvement".  As for the rest of your edit that was reverted, you can try less controversial parts again; it will be best to make changes in smaller chunks that can be digested by others, and discussed as needed.  If you look at your diff, you can see it's got a lot going on, making it hard to review.  And don't take out the blank lines after headings, or I'll revert you just for that.  As for the field of this article, it's basically mathematics; the "applications" in all those other areas are interesting, too, but not the real topic.  Dicklyon (talk) 05:48, 2 March 2012 (UTC)
 * I looked at the talk page before making the edit and didn't see anything pertaining to the changes I was making, but yeah, I see what you mean about bunching them up in one edit. I did some of changes again -- a bit at a time -- so it's clearer. Regarding the stuff removed from the intro, I was more concerned about the two equations themselves. The value and the symbol, as part of the explanation text needs to be in the intro, I think. I stumbled upon this article by looking up something I saw on TV -- a news program -- so the concept is definitely part of the popular culture. And the goal of the style guide is to make article introductions accessible to those who read them.  Sparkie82 ( t • c )  07:20, 2 March 2012 (UTC)
 * I disagree that the prose adequately explains the ratio. The formulas should be retained.  They are accessible to anyone with a minimal background in algebra.  Our readers might not always have a college degree but they are not idiots.  Tkuvho (talk) 09:09, 2 March 2012 (UTC)
 * If the text is rewritten to include the value and the symbol and explains that the value is derived, then the text, along with the graphic to the right, would explain the concept adequately for purposes of an introduction. Remember, this is not a mathematics-only article. Even though most people (maybe) would be able to understand the equations, there is likely a significant fraction who would not and would avoid the article if the equations were in the intro, which is why WP:MOSINTRO advises against including them in introductions. I know in the US, most people would not understand the equations, unfortunately. If you doubt that some readers of WP are this ignorant, just look at some of the feedback comments at Special:FeedbackDashboard.  Sparkie82 ( t • c )  23:46, 2 March 2012 (UTC)


 * The concept is not adequately explainable without the formulae. -- 203.171.197.72 (talk) 11:50, 2 March 2012 (UTC)
 * I agree. But we're not talking about removing them from the article completely, just moving them out of the lead.  Sparkie82 ( t • c )  00:06, 3 March 2012 (UTC)
 * There is no need to remove them from the lead, the lead is fine as it is. Various style guides are merely a rule of thumb and have to understood in the context of the given article. The formulas given in the lead are as easy as to understand as the text description, people really struggling with them are unlikely to properly understand the plain text description either. Furthermore the concrete value belongs definitely in the lead and is actually the easiest thing to understand. Even if you don't understand the concept then you still get an idea of what the actual number is.--Kmhkmh (talk) 01:04, 3 March 2012 (UTC)
 * The lead is fine as it is. In the spirit of the inverted pyramid, a compact algebraic definition and a numeric formula are central to the subject, and are appropriately placed where they can be quickly seen. Readers will not be helped by pushing those items further down into the article. __ Just plain Bill (talk) 03:15, 3 March 2012 (UTC)

I find it very difficult to imagine anyone who would find Sparkie82's proposed replacement lede easier to understand than the one that was there before. The phrase "the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one" does not communicate anything that is not communicated by "(a+b)/a = a/b", and it does so in a way that is much harder to understand. I am doubtful that there is anyone who will understand phrases of the form "the ratio of the quantity… to …" who will not also understand a simple division sign, and I cannot believe that there is anyone who will understand the phrase "is equal to" but not the = sign.

In fact, I think Sparkie82's change, and the rationale for it, is is completely misconceived. The phrase "the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one" is in fact an equation—that is, it is an assertion of the equality of two quantities. Sparkie82 has not removed the equations from the lede; instead, this user has removed one of the equations, and the one that was most clearly expressed. —Mark Dominus (talk) 15:42, 3 March 2012 (UTC)
 * Thank you for your comments, Mark. I think a key point you made above is:
 * "I find it very difficult to imagine anyone who would..."
 * It is very hard for those of us with a talent for understanding technical subjects to place ourselves in the minds of those who have difficulty with math and science. The reason for making a change to the intro is to make it more accessible for those who don't have a talent for math. Most people experience math anxiety. And a significant portion of those people also suffer from dyscalculia, a condition which interferes with the brain's ability to process numbers. The condition effects people across the entire IQ spectrum. Many of those with the condition are able to understand advanced mathematical concepts and relationships. Dyscalculia is just one example; there are many other forms of learning disabilities and a full spectrum of talents in various areas. For example, many people who may be talented in science and math have trouble in social situations because they have a diminished ability for empathy. Everyone is different. This is why WP has an accessibility policy. It's like installing ramps instead of stairs in public places so those with physical disabilities can have access. It costs a little more and maybe even slightly inconveniences those who are able-bodied, put it's part of living in a civil society.
 * A quick glance at the backgrounds of those commenting here shows that this discussion has been dominated by those with exceptional talent in science or math. With your permission, I would like to solicit input from others who may have math anxiety or otherwise have difficulty with math in hopes of gathering more diverse input and perhaps improving this article. This is a very good article with a lot to offer and it would be a shame to drive off a significant portion of potential readers because the intro makes it look like math talent is required to read it.  Sparkie82 ( t • c )  18:00, 3 March 2012 (UTC)
 * The point is not "could a total mathematical ignoramus understand the lead". Because, a total mathematical ignoramus isn't going to get anything out of the article no matter what we do. The question is, rather, does the lead summarize the rest of the article accurately and in a way that's accessible to as many readers as possible. As many as possible is very different from all of them. The mathematics in the lead as it stands is really rather basic, at a level I'd expect my 7th-grade son to be able to read. But more to the point, the mathematics is central to the article; a lead which didn't include it would seriously misrepresent the subject and would do a disservice to the many readers for whom this is accessible. —David Eppstein (talk) 19:24, 3 March 2012 (UTC)
 * Your comments are offensive and inappropriate. Please reread my previous post and do some research of the issue of dyscalculia and math anxiety in general and then come back here and apologize for you comments.  Sparkie82 ( t • c )  20:31, 3 March 2012 (UTC)
 * Frankly, I find your overreaction and your demand for an apology offensive and inappropriate. —David Eppstein (talk) 20:36, 3 March 2012 (UTC)


 * Imho you better let this go. From where I stand I find rather your tinkering at the article than David's comment as somewhat inappropriate and your arguments regarding the lead have a touch of WP:Wikilawyering. There are enough articles that need real help, so your energy is better spend there rather than picking a fight over rather marginal aspect in a well established article.--Kmhkmh (talk) 20:44, 3 March 2012 (UTC)
 * The issue about discalculia (hope I spelled it correctly) is an interesting one. Perhaps a way of solving it is by creating a separate article on the golden ratio in the "simple english" wiki?  Arguably formulas should be left out of the lede there.  Tkuvho (talk) 22:06, 3 March 2012 (UTC)
 * Golden ratio in simple English still uses algebraic notation, as it should. Simple English uses limited vocabulary and simple syntax because it is aimed at an audience whose first language is not English. (How well it succeeds with that aim is another question.) Arguably, mathematical notation is more universally understood than any register or dialect of English. __ Just plain Bill (talk) 22:45, 3 March 2012 (UTC)


 * Is it being alleged that people with discalculia have troulbe with equations? That seems like a misinterpretation.  Also not very relevant to how best to write this article.  Dicklyon (talk) 00:55, 4 March 2012 (UTC)
 * I will be very interested to see a cite for your claim that persons suffering from discalculia will understand an equation in the form "the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one" but not in the form "(a+b)/a = a/b". Until then, I will continue to believe that your changes are ill-conceived. —Mark Dominus (talk) 01:17, 4 March 2012 (UTC)
 * I agree with the comments above to the effect that the established lead is fine, and it would not be assisted by removing formulas. While it would be great to have an article that appealed to everyone, that is simply not possible. There is always Golden ratio. Johnuniq (talk) 02:16, 4 March 2012 (UTC)


 * The phrase cited above, "the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one", does not seem very effective. However, one might be able to devise a more effective phrase, not necessarily for inclusion in the lede, but perhaps elsewhere in the article.  The trick would be to use the concept of the aspect ratio.  This already incorporates the idea of choosing the bigger side and dividing by the smaller.  Thus, one could define the golden ratio as the aspect ratio of a rectangle with the property that, when it is cut into two smaller equal rectangles, the smaller rectangle has the same aspect ratio as the bigger one.  Any takers?  Tkuvho (talk) 16:57, 4 March 2012 (UTC)
 * You've just defined the silver rectangle, not the golden rectangle. —David Eppstein (talk) 18:17, 4 March 2012 (UTC)
 * Just now I learned about the silver rectangle, but actually Tkuvho defined the related Lichtenberg ratio. __ Just plain Bill (talk) 18:28, 4 March 2012 (UTC)
 * Sorry, just daydreaming. Tkuvho (talk) 18:40, 4 March 2012 (UTC)
 * A variation on a theme: cut a big rectangle into a square and a small rectangle so that the big and small rectangles have the same aspect ratios. Hope I got it right this time.  Tkuvho (talk) 18:42, 4 March 2012 (UTC)
 * That's more like it, and is shown in this diagram near the top of this article. Looking further into it, it appears the "Lichtenberg ratio" is just a fancy term, newly coined, for a ratio of 1:√2. __ Just plain Bill (talk) 18:53, 4 March 2012 (UTC)

I'm testing a proposed new introduction for the article and requested those who are unfamiliar with the topic to comment on it. Those of you who are already familiar with the Golden ratio can continue to comment here.  Sparkie82 ( t • c )  05:24, 5 March 2012 (UTC)
 * Re Dicklyon inquiry about the usability test, because this is a first test, it is open structured so that comments will be open-ended. Users will likely (hopefully) compare the proposed version with the existing version when making comments, but that's up to them.  Sparkie82 ( t • c )  05:32, 5 March 2012 (UTC)

Introduction - Usability test
This is a proposed replacement for the introduction of the Golden ratio article. If you are unfamiliar with the golden ratio, please add a comment at the bottom of this section. Your comments will be used to help improve this article.

In mathematics and the arts, two quantities are said to have the golden ratio when the ratio between the larger and the smaller quantity is equal to the ratio between their sum and the larger quantity.

Expressed graphically,



When it is calculated, the ratio is 1.61803398...

The symbol for the golden ratio is the Greek letter phi($$\varphi$$). The golden ratio is often called the golden section (Latin: sectio aurea) or golden mean. Other names include extreme and mean ratio, medial section, divine proportion,divine section (Latin: sectio divina), golden proportion,golden cut, golden number, and mean of Phidias.

At least since the Renaissance, many artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to beaesthetically pleasing (see Applications and observations below). Mathematicians have studied the golden ratio because of its unique and interesting properties. The golden ratio is also used in the analysis of financial markets, in strategies such as Fibonacci retracement.

Please add your comments below. (If you are already familiar with the golden ratio, or want to comment on the usability test itself, please use another section.) Thank you.  Sparkie82 ( t • c )  05:15, 5 March 2012 (UTC)

Discussion
How are you going to find people unfamiliar with the golden ratio to come here and take the test? And how are you going to compare the usability with the usability of what we have already? And why not express the ratio by using the aspect ratio of rectangles, as is pretty typical? Dicklyon (talk) 05:23, 5 March 2012 (UTC)
 * I strongly prefer the existing lead. The wide horizontal separation of the two graphical representations of ratios makes it hard to tell that the pieces within them are supposed to be the same height as each other, I dislike mixing pictures and text as if the pictures are parts of speech (and doing so has severe usability issues for blind readers of Wikipedia), and the new version loses important information (the golden ratio has an exact value involving the square root of five, not just an approximate decimal value). And the "when it is calculated" phrasing makes no sense — it has that value whether or not some person happens to be calculating it. —David Eppstein (talk) 05:36, 5 March 2012 (UTC)
 * A "usability test" should be conducted somewhere else as there are eight editors who have disagreed with the premise behind the proposal (David Eppstein, Dicklyon, Mark Dominus, Johnuniq, Just plain Bill, Kmhkmh, Tkuvho, 203.171.197.72). There is no reason to spend further time discussing this non-issue. And the proposed diagrams do not help. Why are two adjacent lines a "ratio"? Johnuniq (talk) 06:31, 5 March 2012 (UTC)
 * That's fine. Examining the user pages of this small cadre, I see: a computer science professor, a research engineer, a computer programmer and student of mathematics, a programmer with an interest in math, a BSEE (I think),  a mathematician, an editor with "Lists of mathematics topics" on his page, and an IP address. An exceptional list of people with exceptional talents for math. I get that you disagree with me and don't understand how the article could be improved and that some folks are scared by formulas. I understand that you don't understand. That's not wrong. Adults don't understand children, men don't understand women. That's why corporations spend billions of dollars each year in market research. And that's why I'm doing this simple little user test, because I don't completely understand either. But I'm willing to try in hopes of improving Wikipedia.
 * So yes, it's probably best that we step aside for a few weeks and let the general readership of this article provide input. Thank you for your comments.  Sparkie82 ( t • c )  18:20, 5 March 2012 (UTC)
 * But you won't find the general readership on this talk page. This page is for editors to discuss how to improve the article.  Your survey needs a different venue if you expect it to do anything.  Dicklyon (talk) 19:47, 5 March 2012 (UTC)


 * Sparkie, I'd encourage you to take a look at some of the topics linked in the navbox Template:Visualization for a sense of the amount of study that has gone into the presentation of quantitative subject matter so people can grasp it easily. If the bulk of that seems daunting, I highly recommend finding a paper copy of Edward Tufte's The Visual Display of Quantitative Information to start with. Suggesting that others "don't understand how the article could be improved" seems premature at this point. __ Just plain Bill (talk) 19:30, 5 March 2012 (UTC)

"At least since the Renaissance"
"At least since the Renaissance" is in dispute. In fact, there is no concurrent evidence of Renaissance artists using this ratio; everything is line-drawing and measuring after the fact, which is notably vulnerable to selection bias. Matthew Miller (talk) 23:02, 13 March 2012 (UTC)
 * You don't think Pacioli counts as concurrent evidence? —David Eppstein (talk) 23:19, 13 March 2012 (UTC)
 * It doesn't appear to. He describes the geometric properties, and delves into its relationship to the Platonic solids, not its use in art. The part about the divinity of numbers is more mystical than aesthetic. And there's no evidence of anyone — even Da Vinci, who illustrated the book! — having followed up with actual art or architecture devised around the golden ratio, until at least the 19th century. Matthew Miller (talk) 19:54, 16 March 2012 (UTC)
 * From http://www.emis.de/journals/NNJ/Frings.html#anchor656497: "Neither in the text nor in the illustrations is the Golden Ratio recommended for practical use." Matthew Miller (talk) 20:53, 16 March 2012 (UTC)

The German WP article has some sourced information on that. According to that there's a number of renaissance artwork in which the golden section "appears numerically" (da Vinci among others). The notion that this was designed and influenced by Pacioli and there there was a cooperation on that between Pacioli and da Vinci was promoted by the philosopher and golden section guru Zeising the 19th century. However Zeising's arguments are merely speculative and have not substantiated by direct/hard evidence ever since. There has been actually some systematic x-ray analysis of those renaissance paintings by some art expert to verify actual construction sign of the golden section among the paint, but they haven't turned up anything. The explicit, verified use of the golden section doesn't seem to take off before the 19th century.--Kmhkmh (talk) 01:56, 18 March 2012 (UTC)

Removal of Pacioli woodcut
The image http://en.wikipedia.org/wiki/File:Divina_proportione.png does not illustrate the golden ration, despite its caption. None of the lines or rectangles appear to illustrate the golden ratio! It appears to illustrate a system of integer division — 1, 1, 2, 2 for the horizontal divisions, and then a ratio of 6:7 for the box as a whole. 6:7 is not a very good approximation of phi. The horizontal division is clearly by half. So even if this image is well-sourced, it does not appear to be an appropriate illustration. http://www.emis.de/journals/NNJ/Frings.html#anchor656497 confirms that this image illustrates the Vitruvian section, not phi. Matthew Miller (talk) 20:55, 16 March 2012 (UTC)


 * I agree. I had looked for sources connecting it to phi, and found none; but I hadn't found that source with "Vitruvian section".  Good find.  Dicklyon (talk) 15:24, 17 March 2012 (UTC)

Two Platonic solids
There is no image about regular polyhedra in the current article. In my opinion, we have to talk about the two dual  Platonic solids.  For example, two opposite edges of a Platonic icosahedron are two smaller sides of a golden rectangle. — Aughost (talk) 11:59, 17 March 2012 (UTC)


 * Good idea; though this one is awful busy, and the "yellow" is not really recognizable as such. Dicklyon (talk) 15:25, 17 March 2012 (UTC)


 * About the good idea,  thank you.  About colours, how might we name the golden tint associated to the fourth and last length of the increasing sequence?  Weak ocher?  This is depending on our screens and our eyes and our terminology.  Anyway, stripes have to draw our attention all the more when they take up less space in the image.  Actually, we find the weakest colour because it is the one of the largest length, equal to the sum of some lengths very well marked, and because of this equality written within the image:  a/φ + a  =  φ&thinsp;a.


 * In the current section that is entitled Geometry,  the first image shows two spirals.  The text deals with pentagon and icosahedron… — Aughost (talk) 09:16, 19 March 2012 (UTC)

The two following images show the same twelve points built through a stellation  of a Platonic dodecahedron. More informations in several images, of course. — Aughost (talk) 16:01, 20 March 2012 (UTC)

Those images look extremely busy and confusing to me. —David Eppstein (talk) 17:11, 20 March 2012 (UTC)

These are extraordinary images, but they are too complex for use in an article. The Platonic solids are wonderful and have many interesting properties, but this level of detail only makes sense after intense study. Johnuniq (talk) 01:46, 21 March 2012 (UTC)

An article is not a course page. In the current article, for example, what does everybody understand in the first image of section "Geometry"?  Actually, this current first image does not correspond to the first paragraph. And we cannot explain everything about an interesting 3D image. — Aughost (talk) 11:00, 21 March 2012 (UTC)


 * The idea of illustrating the presence of the golden ratio in a platonic solid seems a good one, but how about starting with the simplest illustration of a single such relation for a single solid, rather than the superposition as in these figures? The icosahedron in the first figure seems to play almost no role in the relations.  Tkuvho (talk) 16:16, 21 March 2012 (UTC)


 * Through a stellation  of a Platonic dodecahedron, we build a great dodecahedron,  a Platonic icosahedron, and twelve stellated regular pentagons. Each face of the great dodecahedron is a duplicate of a face of the initial dodecahedron, to scale  φ2  or  φ + 1. Two opposite edges of a great dodecahedron are the smaller sides of a golden rectangle. — Aughost (talk) 18:47, 21 March 2012 (UTC)


 * Whew. Let's start with something simple.  Let a denote the distance between two opposite edges of a dodecahedron.  The first figure suggests that the edgelength is then $$(2-\phi)a$$.  Is this correct?  Something that can be stated in English rather than Coxeterish may be appropriate for this page.  Tkuvho (talk) 18:54, 21 March 2012 (UTC)


 * $$2\,-\,\varphi$$   is  the  multiplicative  inverse  of  $$\varphi^{\,2}.$$ — Aughost (talk) 19:14, 21 March 2012 (UTC)


 * Very good then, we see that phi^2 appears as the ratio of the edge to the distance between opposite edges of a dodecahedron. That seems like an English sentence that could be added here.  Any comment, David?  Tkuvho (talk) 15:14, 22 March 2012 (UTC)


 * How to yield a geometric sequence with common ratio φ from two consecutive terms?  From (1, φ),  for example, we can yield (2 φ – 3,  2 – φ,  φ – 1,  1,  φ,  1 + φ,  2 φ + 1), through a few additions and subtractions. More generally, given two positive values  a  and  b  that fulfill  $$\tfrac{\,a\,}{\,b\,}\,=\,\varphi,$$  we can yield a geometric sequence from  (b, a ),  either through successive additions or through successive subtractions, depending on the sense of the extension, right or left. Is it an article or a book that we are trying to write? — Aughost (talk) 17:26, 22 March 2012 (UTC)

If two opposite faces of a Platonic dodecahedron are not distorted under an orthographic projection,  the outline of the regular polyhedron is a convex  regular decagon.  Through a stellation of a Platonic dodecahedron and such a projection, we obtain eleven points,  that are the common center of regular decagons and their ten common vertices. In the top view,  five black crosses are the images of five of the twelve vertices of the icosahedron, which are in the upper horizontal face plane of the dodecahedron.

The current rubric "Architecture"  presents the only occurrence of "decagon" in the article. Someone that plays with this puzzle  can discover some properties of regular pentagons and decagons, notably that r/a = φ   and   s/a = φ + 1, by denoting  a,  r  and  s three lengths in a convex regular decagon:  sides, radius of circumcircle, and some diagonals. — Aughost (talk) 09:29, 23 March 2012 (UTC)


 * The last picture looks less busy than the others and may actually be accessible to the uninitiated. It looks like there may be aspects of the dodecahedron related to the golden ratio that are not already present in the regular pentagon.  If so, these could be included in the article in addition to the discussion of the pentagon (perhaps in the same section).  Tkuvho (talk) 11:09, 27 March 2012 (UTC)


 * John, I think you are overreacting (see previous message). Tkuvho (talk) 11:11, 27 March 2012 (UTC)
 * Sorry, but I did check the history and at the time of my edit the last comment made by someone other than the user posting the images which are not useful for this page was on March 22. Do you think something useful for this article may come from these deliberations? If so, please undo my change and feel free to remove my comments here. Johnuniq (talk) 11:16, 27 March 2012 (UTC)


 * As I mentioned above, the last figure may be usable. What do you think?  Tkuvho (talk) 11:26, 27 March 2012 (UTC)
 * I was hoping to not be forced to say anything more because there is obviously an enormous effort behind creating the images. However, I saw the new image and, no, I do not think it is useful in an article. This talk page usually attracts fast attention from several editors, if they feel a comment is needed. I think that given the time that has elapsed, the lack of discussion regarding how an image like these might be used indicates that it is unlikely there is much support for their use. I will stop commenting for a while, and wait for others to offer an opinion. Johnuniq (talk) 11:45, 27 March 2012 (UTC)

See Also Roses?
OK, I'll bite. What is the relevance of Roses of Heliogabalus? Aldenrw (talk) 16:30, 21 April 2012 (UTC)


 * It used to have a whole section devoted to it in a different article, Mathematics and art, claiming without adequate sources that its canvas is an almost perfect golden rectangle. That was removed in January 2011, and the same information in the article on the painting itself was removed June 2011, but I guess traces of it persist elsewhere. At this point I think it shouldn't be in the see-also section here any more either since nothing in the remaining article about the painting mentions the golden ratio and in any case the fact that some obscure painting used that aspect ratio is not especially interesting or surprising. —David Eppstein (talk) 17:12, 21 April 2012 (UTC)


 * It was I who removed it from at least one of those places. I had long ago searched for its dimension, or for any source tying it to the golden ratio.  I found several different dimensions of the painting, and of reproductions of it for sale, but not particularly close to the golden ratio.  I had added an image from a seller that was sort of close, but later realized that was a bad idea. Dicklyon (talk) 05:42, 4 June 2012 (UTC)

Golden Ratio in atomic nuclei
The chemist Jan Boeyens has noted what appears to be a limit for neutrons versus protons in atomic nuclei with a value of Phi, as atomic number increases (see his Number Theory and the Periodicity of Matter, coauthored with Levendis, Demetrius C.).

In fact, the N/P ratio starts out at 0 (for H), is 1 (for D), and 2 (for T), but after, for stable nuclei, hovers around 1 until Ca (20N,20P). But Ca also has a very stable isotope with 28 neutrons (20 and 28 are 'magic' numbers)- this gives an N/P of 1.4 This seems to be approximately the start of the part of the N/P nuclide curve that hovers around 1.6. It continues out past 82, Pb, the last stable element.

However, it may be that what is really going on here is a shift between Metallic Means- with 1.000 for the first stable part of the nuclear periodic system, 1.6 as Golden Mean for the second stable part, and then finally the Silver Mean for the last- never seen because even supernova neutron fluxes are too low to produced such nuclei. Thus we would have, it this were true, a multitrack system, with stability shifting between the three tracks. — Preceding unsigned comment added by 69.121.117.192 (talk) 05:38, 4 June 2012 (UTC)

over-aggressively deletions by User:Kmhkmh
I want to ask what can be done to avoid such kind of revertions see History between 20:00 & 22:20. Three times he simply deleted my added content -- should I/he start a revision war? :-(
 * First time he deleted the word instead of correcting it to the preciser/informative adjective.
 * Second time, I gave no reference, so one may discuss the issue (or move it to the later in the article) -- but not totally delete the information. Else we (and even I) may delete much if all articles.
 * Third time he deletes a remark which I want to have in a footnote. This remark also includes a high-quality reference, which now is gone!

This user, Kmhkmh, is also involved in an article fight in wikipedia-de in "goldener-Schnitt" where I withdraw (like others) to continue to help because of the too chaotic discussion. Now it looks like he must also look after the english article "golden ratio", which is a way better designed article (IMHO) because in the german article about the same topic the "arts" aspect is degraded to a minor aspect -- it seems effectively to be reworked to become a mathematical article with some applied facts. Achim1999 (talk) 20:36, 13 June 2012 (UTC)


 * Also over-aggressive insertions and comments by Achim1999 are a problem. Let's talk here about what improvements are proposed, instead of warring in the article.  This article attracts an awful lot of well-intentioned changes, but lots of editors watch and care, so don't expect to just put in whatever you want without some pushback.  And maintain politeness even if someone is objecting, please, per WP:AGF and WP:BRD.  Dicklyon (talk) 21:01, 13 June 2012 (UTC)


 * I have rolled back all of your contributions to the article of today, which started with a large expansion of a section on a property, and came with a new section heading with improper capitalization. This is not German; please respect that the article is in good shape by carefully adhere to both style and content guidelines.  And it's already pretty large, so major additions need to be carefully considered.  Dicklyon (talk) 21:08, 13 June 2012 (UTC)
 * What you did I noticed. But I miss an objectively content reasoning for this! :-( If you are much better in English feel free to correct this like others already did. Achim1999 (talk) 21:18, 13 June 2012 (UTC)
 * BTW: On a pretty large article, a major addition may be small -- as in the section "Rational approximability"! Don't use so subjective comparisons. Achim1999 (talk) 21:21, 13 June 2012 (UTC)
 * Lots of editor watch and care, but none since my first change today asked me or made a bigger revert! YOU must suddenly revert anything. Think twice of this behavior compared to all these other editors you called for witnesses, please. Achim1999 (talk) 21:24, 13 June 2012 (UTC)


 * your first reversion, claimed an edit war! But exactly this I tried to avoid!! I did not reinsert the unreferenced part, 2nd deletion of Kmhkmh, and moved the questioned addition of the lead totally into the footnote section! Sorry, but you are badly mistaken in judgment in this case. It would be nice if you place your 2nd reversion, which I still did not undo to the appropriate place, showing CONSTRUCTIVELY working on an improvement. Achim1999 (talk) 21:30, 13 June 2012 (UTC)
 * It gets late, and I will soon go asleep. What will the other editors/writers/fellows of this article think of your stupid (my very sorry) behavior so that others have much work sorting out my inserted (very good IMHO)references, typos/corrections etc. – or it get lost – in your emotionally sudden reversion attitude? :-/
 * I hope you can consider this formulation still as polite (and this is not ironically meant). Achim1999 (talk) 22:09, 13 June 2012 (UTC)
 * Frankly at first glance I'd even doubt that you actually read all the references you've cited. At least some of them seem to be simply copied over from the German article (including the errors in the citations).--Kmhkmh (talk) 22:17, 13 June 2012 (UTC)

Achim: Actually I left most of your edits untouched aside from fixing citations (despite considering all of them bit problematic) and just deleted one completely unsourced paragraph regarding the golden section only appearing "in popular and didactic math". Also I already outlined in de.wp why this opinion of yours is at least questionable. So if you can't source it, it stays out. Another thing is that you cannot mess up the display of featured article and asking others to fix it. If you have a problem with the wiki format make a text suggestion here and ask somebody to incorporate it into the article in proper format.--Kmhkmh (talk) 22:14, 13 June 2012 (UTC)
 * Totally Right, Kmhkmh. And this was/is no problem. I already stated that this was NO EDIT WAR because I tried to avoid it. If one can't source something, then this is NO REASON to have a automatically judification for deletion generally!! Else we must deleted the majority of all content here on wikipedia! And I respected this (as long as I have no reference at hand) I also wondered about the old content of my pushed up section 'approximability' about the subject, unsourced statments. Noone had challanged this (because they assume they may be correct I think -- this is the point!).

Sorry, I did asking for formating-help immediately, but see Help_desk and look at the time-stamps. You was too eager to delete, IMHO, and provocate this developemnt, IMHO. :-( Achim1999 (talk) 22:35, 13 June 2012 (UTC)
 * A tiny correction: Firstly I wrote only "Popular mathematics" and you didn't correct the false adjective but delete it (in my opiniona a bad attitude, but okay). Then I changed it to the correct form of "Recreational and didactic mathematics" -- a minor point, but you remember my saying about usage in the german article, I assume. And this small issue seems/seemed to be solved for you and me.
 * English language corrections are easy, geting useful inforamtion is way harder! But I totaly agree, I surely did not want to force or only expect that someone anonymous else should/must correct my typos/grammar/expression/style -- which is the same principle in german (thus I actively searched for help). Achim1999 (talk) 22:41, 13 June 2012 (UTC)
 * Popular mathematics is not incorrect term afaik. But I generally disagree with your notion of the golden section existing popular, rcreational or didactic math only. That seems to be your personal opinion only and imho is even false. Since it was unsourced as well, I deleted it and will delete it again unless you can produce a reputable source making that claim. In that case I'd probably still disagree with that reputable source personally, but I wouldn't delete it from the article.--Kmhkmh (talk) 22:56, 13 June 2012 (UTC)
 * In featured articles you can expect unsourced to be routinely deleted. Maybe you are not aware of various quality management problems of WP, but plenty of people constantly add nonsense to articles, so the easiest (amd most efficent) way to avoid a possible deterioration of an already featured article is to simply delete all unsourced stuff (even though occasionally it might lead to to temporary deletion of a correct content addition).
 * Nobody is or will block your suggestions as long as you source them properly and use in doubt the discussion page first. In particular in featured articles it is always best to make content suggestions on the talk first (or only) as long as you do not have the according sources at hand or struggle with the wiki format. Another editor will pick it up from there then. This way we avoid that a featured article has temporarily unsourced content or a messed up format.--Kmhkmh (talk) 22:50, 13 June 2012 (UTC)
 * As I told you: there is even in this article unsourced text (the section about approximability I build up had a part older text) which I wondered, that it was accepted without question! So this is very subjectively behaviour (the statements about phyllotaxis and this "simplest number" was no source at all given! And I added them!) Achim1999 (talk) 22:58, 13 June 2012 (UTC)
 * You may have noticed that this part was not deleted by me despite having some reservations, I just fixed the citations there.--Kmhkmh (talk) 23:01, 13 June 2012 (UTC)
 * Indeed, and as it looks now you even would not be against a reversion to the last state before my minor correction 23:37, 13 June 2012 of a typo. And if you have now a look on User_talk:Dicklyon, you may assume the same for him. Achim1999 (talk) 23:18, 13 June 2012 (UTC)
 * That I didn't delete that section (yet) doesn't mean I condone it, it just means that I didn't aggressively revert as you claimed at the top of this thread.--Kmhkmh (talk) 10:04, 14 June 2012 (UTC)

I don't really see much in the added material that is worth keeping. The article already appears to state the rational approximation properties concisely, and I don't think there is much that we should add to that, aside from pointing the reader to the relevant articles. Sławomir Biały (talk) 00:33, 14 June 2012 (UTC)


 * And that's why I suggested "Let's talk here about what improvements are proposed." It's very hard to review properly a string of 20 edits made in a day, without a framework for thinking about what their intent is.  There might be something in there that he thinks would benefit the article, and he could articulate that here, we could look and see if it's duplicative, and see how to include it without so much bloat.  Dicklyon (talk) 01:13, 14 June 2012 (UTC)
 * I'd also propose to reset the article to the state before Achim's edits and instead list the edits here discussion, this way it is also easier for other editors to understand what's going and compare the different options.--Kmhkmh (talk) 09:03, 14 June 2012 (UTC)

Achim's edits/suggestions
Note:

Since additional editors have reverted most of the edits as well (and addition removed an additional edit by Giufra9396 (newly introduced cinema section) the current version essentially matches the state before Achim's edits.The exact state version in the version history is:

to the lead
additional paragraph:

An often occuring misunderstanding is, that this golden ratio must be a number, but effectively it should and shall "only" be a ratio. This explains why also many people call the value $$0.61803\,39887\ldots = \tfrac{1}{\varphi}$$, its reciprocal, the golden ratio. Moreover, popular science need not to be unique or consistent.
 * This was my point 2) and I already wrote, I respected Kmhkmh revert and withdarw this addition as long as I have no source ad hand! :-( Achim1999 (talk) 11:02, 14 June 2012 (UTC)

additional footnote(?):

There is a remarkable, high quality mathematical monograph by a leading authority in computer-science and mathematics which uses the wording golden-ratio, but (almost?) only in the book-index. The notable exception in his well-known book is the paragraph on pages 80-81, where a short historic overview about $$\varphi$$ is given. The author also says why he uses this notation $$\phi$$ and where it is used mainly! See D. E. Knuth, The Art of Computer Programming, Vol 1, Fundamental Algorithms, 3rd Edition, Addison-Wesley 1997, chapter 1.2.8


 * Did you liked to ignore my 3rd(?) point? It was about "popular" (wrong wording) which I later changed to "Recreational and didactic" in this lead! And therefore I set the "paragraph" in small lettering, which I want to have as a footnote, to not disturb the reader, but inside I needed a reference, thus my first problems! And this I finally succeeded in. And therefore I give the reference!! Without this, the plain stated "In mathematics and arts" the reader is mislead about the usage of the wording "golden ratio" in (total!) mathematics (and I believe that this might be also in arts)! If one is more specific one discovers easier this "try of opinion-coinage in wikipedia" :-( Achim1999 (talk) 11:02, 14 June 2012 (UTC)
 * I don't like any variation of that sort, since they are questionable not to say false as I repeatedly try to explain you (to no avail apparently). I'm not sure what you want with Knuth here, the term "golden ratio" is completely undisputed and not the issue. The issue are your attempts to associate the appearance of the golden ratio with "popular math" or ""Recreational and didactic [math]" only as it is false. It appears in math - plain and simple!--Kmhkmh (talk) 11:33, 14 June 2012 (UTC)
 * You cite your imagination / wishes!,Kmhkmh. :-(
 * I wrote "Mainly in recreational and didactic mathematics and the arts, two quantities are considered to be ..." Thus Mainly, not only. For reference I use the version of 22:51, 13 June 2012‎ the last before Dicklyon started his reversion-attack! Achim1999 (talk) 16:23, 14 June 2012 (UTC)
 * BTW: I will stop now defending my contribution/work because it is apparently a waste of my time! I have set you an ultimatum and will see say at 14 July what had happened on the article page of this topic! Achim1999 (talk) 16:23, 14 June 2012 (UTC)
 * "Mainly" is not cutting it either from my perspective, at best it moves it from actually false to just questionable. There is absolutely no need to add questionable qualifiers or adjectives to math here. As far as the rest of your comment is concerned (ultimatum - really?) for me the lead was fine as it is/was and it is not misleading anybody except you maybe, as you seem to have a rather odd reading of that sentence. "Appearing in math and arts" does in no way implicate appearing in every area of mathematics or art ("in its totality"). So to me it seems your misreading a phrase and hence you perceive it is as problematic and consequently try to fix. However from my perspective you are simply attempting to correct a non existing problem and in the process you were actually making it worse.--Kmhkmh (talk) 17:10, 14 June 2012 (UTC)

separate section for rational approximation replacing the current text under other properties
The golden ratio (considered as ratio, but see below) has the simplest expression (and slowest convergence) as a continued fraction expansion of any irrational number (see Alternate forms above). It is, for that reason, one of the (infinite many) worst cases of Lagrange's approximation theorem. For all integers $$k$$, the numbers $$\varphi + k$$ form the set of the worst possible approximable real numbers by rational numbers.

In reality if one considers a ratio a:b of two lengths or general two physical sizes of the same type, you are free also to consider the reciprocal value of b:a. But if a certain phenomen is identified or discovered to be caused by a special numeric ratio a:b then the explanation must also provide exactly the same phenomen for the numeric value of b:a. E.g. either one considers the typical angle by which handles are rotated around a certain pole, or look at the average number of handles needed for having a full rotation around this pole. Each explanation which reasons a value a:b will also lead to the value b:a from the "exchanged point" of view of the same phenomen.

Two important examples (in nature) are: the angles close to the golden ratio often show up in phyllotaxis (the growth of plants) and the discovery in 1964, that sufficient irrational ratios for orbits are prefered in survive-duration and maximal stabilizing if they have the value 1:&phi;. Such orbits are called KAM-orbits (siehe see Kolmogorov–Arnold–Moser theorem). According to the just said, as well the ratio a:b as the ratio b:a should be maximal bad for approximation by rational numbers in these natural occuring cases. Because practical measured sizes must be positive, their values can only be $$\Phi$$ or $$\varphi$$ to be a value of worst possible approximability. In this sense, this is an important unique distinction of the golden ratio among all (positive) real numbers. Therefore this number is sometimes denoted in mathematical literature as the most irrational number.

Comments/Discussion

 * I agree with Dicklyon, Kmhkmh etc.; Achim's proposed additions are difficult to follow and do not improve the article. Gandalf61 (talk) 09:52, 14 June 2012 (UTC)
 * Well, if some "advisors" here are unable to follow my contributions and unwilling to see the depth of new important, information, but use superfically reasons (spelling, grammar, style) to delete this contribution, then I will sure not help to write better articles here. To say it shortly: A fine, nice looking article is very well, but a chaotic difficult to follow article which has more important information well be used/read eagerly, because in the first case you get only the trivialities you already knew. These are the two Extrema. And I will see what you are able to present of my contributions to give back to the article/reader WITHOUT my help. You have it still in the history. Moreover you make massive subjective judgments, mainly supported by grammar/style/typo, not by information of content!

I like to cite the last reason for revision (Revert again to pre-today version. Ungrammatical and misspelled ("recursivly expansion"), unsourced (failure to converge for the other expansion), badly organized (phyllotaxis in rational approximation), etc.)

The phyllotaxic was in rational approximation integrated by purpose! Why did noone delete this unsourced statements prior to my given two sources there? :-/

Did you say anything about the convergence of these two given expansions? No, but I did! And the sqrt-expansion was not unique, you can also make a quadratic expansion from the given formula with doesn't convergent. I pointed this out, you not, but deleted my valuable hint -- (a good lecturer who knows the facts, would maybe formulated this differently, but not delete it).

As I just pointed very precisely out, you measure really subjective and to your personal likelyness (restricted knowledge), this is by far not scientific, as I like to work. But we will see what will have happened with my valuable contributions in say 1 month. There is a proverb: "It gets dangerous, if silly people get busy!" Sorry, but interpretation is still up to you. Achim1999 (talk) 11:26, 14 June 2012 (UTC)

Diagram
Diagram shows "a" x "a" as a rectangle with about 35% greater width than height. The adjacient text says it is a square which is what "a x a" signifies. Tiddy (talk) —Preceding undated comment added 13:38, 24 July 2012 (UTC)
 * I don't see a diagram that meets that description. Perhaps your screen is distorted?  Dicklyon (talk) 15:20, 24 July 2012 (UTC)
 * It is in the second box of the first diagram in introductory paragraph. And no, my screen is not distorted. That 35% distortion also shows up on other computers. Tiddy (talk) 02:54, 9 September 2012 (UTC)
 * Looks square here, using Chrome, FireFox, and IE. -- Scray (talk) 04:16, 9 September 2012 (UTC)

Monitor set at 1024x768 but looks like aspect ratio must be wrong for screens we are using. Thanks. Tiddy (talk) —Preceding undated comment added 04:22, 10 September 2012 (UTC)

Skeptical NY Times article
"Proportion Control" by Steven Strogatz, September 24, 2012... AnonMoos (talk) 13:19, 26 September 2012 (UTC)
 * Nice. I copyedited a paragraph in the lead section of our article as an excuse to add a reference to it. —David Eppstein (talk) 00:41, 27 September 2012 (UTC)

At least since 20th Century
The text of the article stated that artists and architects used the golden ratio "at least since the Renaissance" for several years starting in 2006, if not before. This was changed, apparently without discussion, to "at least since the 20th Century" in March 2012. The comment on the edit was that there is "no evidence" for Renaissance use. However, the article itself gives examples. Even if the editor is correct, "at least since the 20th Century" is silly, and it would have been better simply to have removed claims as to the length of time the golden ratio has been used, rather than have it say that it is only since the 20th Century. I am reverting this change back to what the article stated before March 2012, namely "Renaissance". 98.229.134.2 (talk) 16:28, 11 November 2012 (UTC)
 * The article itself does not give any examples of conscious use by artists earlier than Dali. —David Eppstein (talk) 17:19, 11 November 2012 (UTC)
 * Some of the 2006 attempts to improve that timing, like mine here, were based on the idea that Pacioli promoted the golden ratio as aesthetic proportions. As the article now describes, this idea has been traced to an error; Pacioli didn't do that.  The only thing that goes back around there is the Agrippa man illustration, but to say that a pentagram illustrates an aesthetic preference for GR proportions in not supportable; same with da Vinci's illustrations of the solids.  So, 20th century may be right.  Or maybe 19th, after Ohm's "golden" term got applied, though I don't have an example.  Still, this "At east since the 20th century" seems like a poor way to put it.  Dicklyon (talk) 17:54, 11 November 2012 (UTC)

The March 2012 discussion is at Talk:Golden_ratio/Archive_5. Dicklyon (talk) 19:11, 11 November 2012 (UTC)
 * If that is so, then the "at least", etc. should simply be removed. The only reason it is there is that the article originally said "at least since the Renaissance".   "At least since the 20th Century" sounds like some kind of joke. like "at least since last week".  — Preceding unsigned comment added by 98.229.134.2 (talk) 01:32, 12 November 2012 (UTC)
 * It's awkward, but it does allow for the possibility that there were earlier cases. Probably it's best just to ditch the whole sentence, and say something more supportable.  Dicklyon (talk) 02:08, 12 November 2012 (UTC)