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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)

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 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 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 08:00, 20 December 2011 (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 (diff) 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)

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 simple: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(${\displaystyle \varphi }$). 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)

Comments: (click the first edit link to the right) ---->-Introduction_-_Usability_test">

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 Misplaced Pages), 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 Misplaced Pages.

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/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:  / _φ + a  =  φ 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  φ  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 ${\displaystyle (2-\phi )a}$. 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)

${\displaystyle 2\,-\,\varphi }$   is  the  multiplicative  inverse  of  ${\displaystyle \varphi ^{\,2}.}$
— 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 values  a  and  b  that fulfill  ${\displaystyle {\tfrac {\,a\,}{\,b\,}}\,=\,\varphi }$,  we can yield a geometric sequence from  (b, a ),  either through successive additions or through successive subtractions, depending on the sense of the extending, 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:  ten images of ten vertices of a Platonic icosahedron. Five of these ten vertices are in the upper horizontal face plane, represented by five thick black crosses.

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   / _a = φ   and   / _a = φ + 1,   by denoting a,  d  and  r  three lengths in a convex regular decagon:  sides, some diagonals, and radius of circumcircle.
— Aughost (talk) 09:29, 23 March 2012 (UTC)

1. Livio, Mario (2002). The Golden Ratio: The Story of Phi, The World's Most Astonishing Number. New York: Broadway Books. ISBN 0-7679-0815-5.
2. Piotr Sadowski, The Knight on His Quest: Symbolic Patterns of Transition in Sir Gawain and the Green Knight, Cranbury NJ: Associated University Presses, 1996
3. Richard A Dunlap, The Golden Ratio and Fibonacci Numbers, World Scientific Publishing, 1997
4. Euclid,Elements, Book 6, Definition 3.
5. Summerson John, Heavenly Mansions: And Other Essays on Architecture (New York: W.W. Norton, 1963) p. 37. "And the same applies in architecture, to the rectangles representing these and other ratios (e.g. the 'golden cut'). The sole value of these ratios is that they are intellectually fruitful and suggest the rhythms of modular design."
6. Jay Hambidge,Dynamic Symmetry: The Greek Vase, New Haven CT: Yale University Press, 1920
7. William Lidwell, Kritina Holden, Jill Butler, Universal Principles of Design: A Cross-Disciplinary Reference, Gloucester MA: Rockport Publishers, 2003
8. Pacioli, Luca. De divina proportione, Luca Paganinem de Paganinus de Brescia (Antonio Capella) 1509, Venice.

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