Talk:Golden ratio/Archive 1

message: can anybody please suggest what should be the correct name for a quadratic equation since quad means four and is not approriately used in this context
[Quadratic in this case refers to 'square' (ie, foursided) rather than 4th power, and so is used correctly for an equation where x^2 is the dominant term.]
And if you wondered, the term for an equation with four roots is "quartic".  Quadratic, cubic, quartic, etc. Japhy 14:38, 16 October 2005 (UTC)
thread_title: why quadratic equation?

message: The following is in the article:
I am not good at edits so could someone find a place to put in this the simplest equasion for "Phi is 5^.5 x .5 + .5" it is as universal as the fingers on your hands and the toes on your feet and uses only positive symbols thanks greg
----
But more interestingly, it is usually found in natural shapes:
 Leaves length / width
 On faces, it's everywhere! Ratio mouth width / nose width, etc.
 More examples welcome!
----
The first is obviously wrong - leaves come in all sorts of proportions.
The second doesn't make much sense - mouth width divided by nose width may be close to the golden ratio for most people, but it's also close to π/2, 1.6, √e, etc. --Zundark, 2001 Nov 6
: I put a discussion of the relationship of φ to phyllotaxis at Talk:Fibonacci number/Phyllotaxis.  It might be appropriate to incorporate some of that discussion here. -- Dominus 15:42, 11 Mar 2004 (UTC)
thread_title: Errors in article

message: Work remains in this article to describe the golden mean better to the everyday person. Kingturtle 21:56 Apr 19, 2003 (UTC)
:I have attempted to better describe the golden ratio to laypeople (since I basically consider myself one) by adding a blue sidebar with an illustration of the golden ratio represented as a line divided into two segments (along with a description). When I first read about the golden ratio, what helped me understand it was an example of a line that had been divided into segments according to the golden ratio. So I attempted to capture that with the illustration I put on the page (Image:Golden ratio line.png). I'd be interested to know if people find that helpful. Please give a shout out if it's too big or factually incorrect (don't try measuring it, it's not exact). - Eisnel 08:28, 22 Jun 2004 (UTC)
thread_title: "Everyday people" explanation

message: Should add its uses in statistics or optimization. Wshun
I agree fully with this, however I am nowhere near qualified to write it.  Anybody care to try? Joblio 10:38, 21 Feb 2005 (UTC)
thread_title: Statistics?

message: Maybe something should be added about the multitude of seemingly unrelated places that the golden ratio appears (Stock market, pyramids of egypt, etc.).  Also maybe a mention of fractals? --Starx 00:05, 8 May 2004 (UTC)
thread_title: All over and fractals

message: I do not like this edit at all.  First, it moved the nice, friendly introduction into multiple sections, which are unnecessary.  The history and other names sections are pretty pointless.  Second, that edit starts off the article with some math, which I don't think is a good idea.  Next, the nice, flowing derivation of the math equations is interrupted, and part of it is just diverted to a "Mathematical Properties" section. --Chan-Ho Suh 22:22, Dec 14, 2004 (UTC)
:I thought the introduction was a bit vague and unfocused and some math would be better at the beginning. But no problem. Jacquerie27 22:36, 14 Dec 2004 (UTC)
thread_title:  Edit by [[User:Jacquerie27]] 

message: The introduction to the article has been rewritten by user:Bill Cannon. Among other changes is this addition: The golden ratio seems to have been understood and used by the Egyptians. Can this claim be substantiated by primary sources? Otherwise, it should be moved down from the introduction, perhaps to a section dedicated to unsubstantiated historical claims.--Niels Ø 18:00, Apr 8, 2005 (UTC)
I have added a disambiguation message to the top of the page because "golden mean" redirects to this page. This seemed like the simplist and clearest manner to go about clarifying where Aristotle's theory is to be found. If anyone feels that this is inappropiate, or that there should be a seperate disambiguation page, feel free to discuss or create. ~CS 05:09, 15 Apr 2005 (UTC)
thread_title: Re recent revision of introduction

message: Is the ratio mentioned in the article The Roses of Heliogabalus correct? The 'golden mean' page would suggest so, or am I missing something? I figured I check here first instead of changing the article.
:*Yup, it looks fine -- MacAddct1984 01:52, July 14, 2005 (UTC)
I looked at this article, and was confused because no mention was made of the Golden Ratio.  It turns out that someone deleted it.  He mentions the reason on the discussion page, and I don't know enough about it to agree or disagree with that move Bunthorne 04:13, 5 August 2005 (UTC)
thread_title:  The Roses of Heliogabalus 

message: Perhaps the Golden Mean article should be merged with this article? Note that this is improperly named, with large M, not "Golden mean" with small m which redirects to this article. PAR 02:57, 14 July 2005 (UTC)
replies: text: Perhaps a good idea.  I dare to suggest, however, that whomever decides to attempt has their work cut out for them.  I estimate it will take a long time and I hope the daring individual has some experience in such a task. GeneMosher 03:44, 15 July 2005 (UTC)
replies: text: Merge 'em!  They describe the same notion; retain as much information as possible and, where there are significant differences, treat them appropriately in a single article – Golden ratio – under different sections and with notes. E Pluribus Anthony 16:07, 22 September 2005 (UTC)
replies: text: On the other hand, this article is pretty good, while the article on Golden Mean is not as well written. Also, Golden Mean mostly concentrates on the philosophical meaning of the term (not too much, not too little), although it also, confusingly, touches on the mathematics of the golden ratio and other "harmonious proportions".  Perhaps the solution is a disambiguation page for golden mean, distinguishing its meaning as a synonym for golden ratio (pointing to this page), and its philosophical meaning (pointing to a version of Golden Mean that is limited to that meaning and substantially edited to improve it [unless it gets deleted first!]). Finell 10:12, 4 October 2005 (UTC)
thread_title:  Duplicate article 

message: Why is it that the number .618 is not acceptable as representing the golden ration while 1.618 is acceptable.
In other words, why it is not acceptable to represent the golden ratio this way
:\frac{x}{1} = \frac{1}{x+1},
or, equivalently, the quadratic equation
:x^2+x-1=0.\,
while it is acceptable to represent it this way 
:\frac{x}{1} = \frac{1}{x-1},
or, equivalently, the quadratic equation
:x^2-x-1=0.\,
:I think both are equivalent. To avoid confusion, 1.618... is chosen for historical reasons. PAR 14:54, 24 July 2005 (UTC)
replies: text: When I entered the former expression it was removed and replaced by the latter expression.  If both expressions are not wrong, they should both be there.  I don't see the point of removing an expression that is correct.  I think if they're both correct then they both should be shown. GeneMosher 18:11, 24 July 2005 (UTC)

text: 1.618... is the golden ratio. Mathematically, theres no reason to prefer 1.618... over 0.618... but the golden ratio has been chosen to be 1.618... rather than 0.618. By chosen, I mean its the majority view of humanity, not just a few editors on Wikipedia. At least this is my present understanding. PAR 18:02, 1 August 2005 (UTC)
replies: text:  It's my opinion that this number's very special fascination to us derives precisely from the fact that it satisfies BOTH equations.  The idea that removing an expression of a number is justified because it 'reduces confusion' makes no sense.  There's no logic in such an idea.  How can censoring a mathematical fact do anything but obscure the truth?  It's a shame that, in yet another area, Wikipedia is a showcase of the triumph of editorial swagger over truth. GeneMosher 14:07, 6 August 2005 (UTC)

text: I regret that I'm not a mathematician.  I do understand, thanks to M. Hardy, that this number, the Golden Ratio, is not a rational number!  It cannot be expressed as a simple fraction, using only whole numbers, but although some prefer to express it as an indeterminate decimal, I'm uncomfortable with that.  I prefer to express it as above because it makes sense to me that way.  It's not a rational number but it is famously recognized as The Golden Ratio.  It's an intellectual rush for me because I discovered this number for myself expressed as  \frac{x}{1} = \frac{1}{x+1},  So, perhaps someone who is comfortable with the language of mathematics can do what you suggest.  What is, by the way, the term for a number that can be expressed as a ratio which uses not just whole numbers but also simple expressions?GeneMosher
Well, "simple" is hard to define mathematically, but there is such a thing as computable numbers. These are numbers which can be calculated to any precision you wish. They include
every number which is "known", like any integer, any fraction, any square root, π, the golden ratio, etc. Any number for which there is a "recipe" which allows you to write it down to as many digits as you wish, is a computable number. Strangely enough there are infinitely more non-computable numbers than there are computable numbers. PAR 03:30, 8 August 2005 (UTC)
thread_title:  I'd like to understand this 

message: Maybe someone more numerate than me can evaluate the possibility of including a mention of the use of the ratio in design of loudspeaker enclosures? This seems like a very widespread use of phi (almost everyone reading this article either has loudspeakers or at least is familiar with them).--demonburrito 19:50, 5 August 2005 (UTC)
thread_title:  Acoustics 

message: I'm sorry for perceivably messing up the article; I didn't mean to. Initially I was trying to make some simple clerical errors, then I began to eliminate redundant or extraneous information, and finally I got flustered by the seemingly random equation (which has now been asterisked) that seemed to imply manipulating two equations to equal one another was a valid proof or equivalency.
I'm glad that things have been sorted out, although I think there should be some note included to address the conjugate golden number.
--24.126.30.46 01:07, 16 October 2005 (UTC)
replies: text: That's OK.  Thanks for contributing! -- Dominus 02:07, 16 October 2005 (UTC)
thread_title:  My Apologies 

message: I believe that the disambiguation legend at the top of this article should be deleted, but I wanted to solicit others' views before doing this myself. No one who is specifically looking for information about golden ratio is trying to learn about the philosophical concept of the golden mean (i.e., the middle course between the extremes excess and insufficiency), so the dab legend is unnecessary. On the other hand, the dab legend at the top of Golden mean (philosophy) is appropriate because some people use golden mean as a synonym for golden ratio—but not vice versa! By the way, I am familiar with the history of the proposal to merge this article with the article that is now called Golden mean (philosophy), which was defeated in favor of editing both articles to eliminate overlap.
Does any one disagree or agree? Finell  (Talk) 11:13, 9 November 2005 (UTC)
replies: text: Agree. --R.Koot 17:13, 9 November 2005 (UTC)
replies: text: In the absense of disagreement, I did it. Finell  (Talk) 02:44, 17 November 2005 (UTC)
thread_title:  Remove dab legend? 

message: A new entry was created  at Phi (Golden Ratio). It seems an obvious merge, unless someone explains why. Agree? -- ( drini's vandalproof page ☎ ) 04:22, 16 November 2005 (UTC)
replies: text: I agree, but suggest that we keep all discussion at Talk:Phi (Golden Ratio), to avoid having duplicate discussions of that duplicate article. Finell (Talk) 02:31, 17 November 2005 (UTC)
thread_title:  [[Phi (Golden Ratio)]] 

message: It is historical fact that shapes according to the G.R. have long been considered pleasing.  If you have a different personal aesthetic that may consider them non-pleasing, it doesn't alter the historical fact.  Writers since the time of the ancient Greeks have written about how the shapes have been pleasing.  To call it a myth that it has been considered pleasing is to introduce your non-neutral point of view.  I suspect that what you are trying to say is that the pleasingness is a myth.  That is closer to the truth, but because the pleasingness of the aesthetic is debatable does not make it a myth, it just makes it debatable.  All the same, it is important to distinguish between "considered pleasing" and "pleasing". Hu 01:09, 1 March 2006 (UTC)
thread_title:  So-called Myth 

message: This sentence has been removed due to bad wording and debatable truth:  "It crops up frequently as a simple consequence of the law of small numbers and therefore mathematical investigations involving this number often arise even when the golden ratio is the farthest thing from the investigator's mind."
I think the writer is trying to say that in their opinion, the coincidence of the golden ratio with natural phenomena is just chance.  That means the sentence is in the wrong section, i.e. "History" is not the place to discuss the significance.  And the sentence has nothing to with Egyptians, astronomers or ancient Greeks.  Further, the law of small numbers has nothing to do with this.  The appearance of the golden ratio is not a numerical bias, nor is it a consequence of the pigeonhole principle referenced by the LoSN article.  Then the sentence talks about mathematical investigations arising and links that to the investigator being lead to the GR unexpectedly, which contradicts the unspoken thesis of bias behind the first part of the sentence.
If an editor wants to clarify the point attempted by the sentence, I invite them to do so here, and then if it can be written in a sensible neutral PoV way, we can find an appropriate section to put it in. Hu 01:26, 1 March 2006 (UTC)
thread_title:  Law of Small Numbers 

message: Does any country or province use the golden ratio for its official flag? Finland seems to come close, but maybe there's closer?--Sonjaaa 06:42, 19 March 2006 (UTC)
thread_title: World Flags

message: The lead claims that the Pyhthagorians appraised the Golden Ratio. This is unlikely to be correct as the golden ratio is an irrational number not expressible in terms of whole numbers, and the pythagorians refused even to admit the existence of irrational numbers. It is well known that they murdered to keep the irrationality of the square-root of two unknown. Loom91 12:32, 28 March 2006 (UTC)
replies: text: If they didn't know this was irrational, why would its irrationality prevent them from studying it, just as they did √2?  And if they did know that √2 is irrational, why could they not have known the same thing about this number?  Michael Hardy 22:22, 28 March 2006 (UTC)
replies: text: I was just asking someone to verify this doubtful factoid. They were unlikely to be fascinated by an irrational number. Only possible scenario is that they thought it to be a rational number, but this needs to be verified. Loom91 10:35, 29 March 2006 (UTC)
thread_title:  Wrong lead? 

message: From the article
"The early digits can be found fairly easily on a calculator, using the formula"
What formula??  --Dumarest 22:31, 10 May 2006 (UTC)
replies: text: Between the word formula and the period is a math-mode formula using the text {1+\sqrt{5} \over 2}.  Is it not showing up in your browser?  You may need to change your math preferences.  Or if your calculator doesn't have a square root, use a ratio of successive fibonacci numbers to get pretty close. Dicklyon 22:58, 10 May 2006 (UTC)
thread_title: Something missing?

message: In the section of "Mathematical Uses" , in a third paragraph "..Furthermore, the successive powers of φ obey the Fibonacci recurrence:..." I believe there is an error in the column section starting at
"φ3 = 2φ + 1, > should read φ3 = 3φ + 3?
φ4 = 3φ + 2,  > should read φ4 = 4φ + 4?
φ5 = 5φ + 3," > should read φ5 = 5φ + 5?
Can someone who understands golden ratio professionally, make sure the successive powers formula is correct?
Sorry, if i'm wrong... 
Thanks  —Preceding unsigned comment added by MaestroMuzon (talk • contribs) 10:29, 13 June 2006
:I'm afraid you are wrong! The formulas are correct as given, and you can check them with a calculator: for example, if you evaluate [(1+sqrt(5))/2]^5 and 5(1+sqrt(5))/2 + 3. you should get the same answer. Madmath789 18:39, 13 June 2006 (UTC)
replies: text: Muzon, consider the ratio between successive terms of the sequence.  Your version,  {{\phi^{n+1}} \over {\phi^n}} = {{(n+1)(\phi+1)} \over {n(\phi+1)}} = {{n+1} \over {n}}  which is not equal to φ!  —Tamfang 21:22, 13 June 2006 (UTC)
replies: text:  How did you get that ratio?  The general term is \varphi^n = F(n)\varphi +  F(n - 1). Dicklyon 01:17, 14 June 2006 (UTC)
replies: text:  I gave the ratio between successive powers if MaestroMuzon's correction were accurate.  —Tamfang 02:24, 14 June 2006 (UTC)
replies: text:  Oops, my misunderstanding. Dicklyon 00:07, 18 June 2006 (UTC)
thread_title:  ERROR in "the successive powers of φ obey the Fibonacci recurrence" ? 

message: Wouldn't it be advisable to merge "History" and "asthetic uses", as they both deal with uses of the Golden ratio?  Also, it seems that it would be best to put the article either in the order of all sections made up of text, then mathematical sections, or vice versa, rather than having the two mixed helter-skelter throughout the article. Phi*n!x 23:06, 20 June 2006 (UTC)
replies: text: Done, except I kept the (shortened) calculation right after the header. −Woodstone 08:51, 4 July 2006 (UTC)
thread_title: Organization

message: Did anyone else notice that the golden ratio is very close to wide-screen computer monitors? (16:10) or (1.6:1)--God Ω  War 04:30, 9 July 2006 (UTC)
replies: text: No, wow, that's an awesome discovery!  I'm sitting in front of one right now, and damned if I didn't miss that!  Dicklyon 04:42, 9 July 2006 (UTC)

text: put another way, 8:5 is a Fibonacci ratio, a member of the sequence of rational approximations to φ  —Tamfang 05:03, 9 July 2006 (UTC)
replies: text:  exactly, just like 5:3, 3:2, 2:1, and 1:1 are. Dicklyon 06:08, 9 July 2006 (UTC)
replies: text:  though, is there such a thing as a 2:1 or 5:3 monitor?  (PLATO IV was 512×512, and the early Mac was 512×342.)  —Tamfang 06:35, 9 July 2006 (UTC)

text:  All of those numbers are approximations. The closer you get to 0 the farther off the approximation is. However at 8:5 you are only 1% away from the true golden ratio. Numbers like 5:3 and 3:2 are way off.--God Ω  War 06:53, 9 July 2006 (UTC)
replies: text: Indeed, due to the continued fraction with all 1s, each step cuts the error just more than in half.  5:3 = 1.6667 is a little over 2% off, and 13:8 = 1.625 is less than a half percent off.  The 5:3 is an excellent rational approximation to some wide-screen formats.  Invoking the golden ratio to explain that is, however, just another false sighting. Dicklyon 15:54, 9 July 2006 (UTC)
replies: text: ...or not. ≈ jossi ≈ t • @ 00:17, 23 August 2006 (UTC)
thread_title:  Wide-Screen 

message: Did anyone else notice that the football has 20 hexagons and 12 pentagons?  Beside the golden ratios inherent in the pentagons, there's also that ratio of 20:12, or 5:3, one of the fibonacci approximants to the golden ratio.  Besides that, the flags of both Italy and France, the world cup finalists, are composed of three rectangles of ratio 2:1 arranged into one rectangle of 3:2.  So we have today a spotting of ALL successive ratios from the sequence 1, 1, 2, 3, 5, 8 if you watch it on a 8:5 TV.  And I'll give 13:8 odds that France wins.  Dicklyon 18:06, 9 July 2006 (UTC)
replies: text: Richard K. Guy points out: "There are not enough small integers available for the many tasks assigned to them."  —Tamfang 21:16, 12 July 2006 (UTC)
thread_title: Futbol (soccer)

message: I think the opening of what it's called needs to be well documented, so I found a set of three books that cover the alternate names, and added the other names that I encountered along the way.  I had to throw out some comments that were hard to find a reliable source for.  For example, there seems to be considerable difference of opinion about what da Vinci first called it; a sentence with a reliable source for that would be useful.  Whatever we add up front about terms, let's make sure it has a reliable reference (I prefer older ones, since there seems to be an unneeded explosion of terms in very recent books, but I haven't found old books for all the terms). Dicklyon 17:47, 13 August 2006 (UTC)
replies: text: Luca Pacioli used divine proportione and sectio divina in his Divine Proportione (1509). We can use that as a source for these two terms. As for Da Vinci use of sectio aurea, The source I have is the same as the one I used for the "Timeline" subsection: Hemenway's Divinie Proportion. ≈ jossi ≈  t • @ 19:22, 13 August 2006 (UTC)
thread_title: Golden names again

message: Doesn't the timeline need dates?  It looks sort of uninformative, or hard to relate to anything I know, without dates.  Dicklyon 00:29, 14 August 2006 (UTC)
replies: text: I will add the dates. ≈ jossi ≈  t • @ 02:20, 14 August 2006 (UTC)
thread_title: Timeline

message: I think that a grey rectangle on its own does not make this article better. The rectangle construction diagram, shows both the rectangle itself, and a way to construct it. ≈ jossi ≈ t • @ 19:09, 15 August 2006 (UTC)
replies: text: The point of the rectangle image was to make the so-called most pleasing shape as apparent as possible, without distractors, and as accurate as a square-pixel screen could do in a limited space.  It also introduces the notion of "golden rectangle". Does it make the article better?  Certainly better than it was when its caption was transferred to the construction image.  Opinions? Dicklyon 19:55, 15 August 2006 (UTC)

text: What about moving these two images to Golden rectangle? I have many nore images in the works for this article. ≈ jossi ≈ t • @ 20:01, 15 August 2006 (UTC)
replies: text: If there are no objections I will move these two images to Golden rectangle in a couple of days. ≈ jossi ≈ t • @ 20:53, 16 August 2006 (UTC)
replies: text: You can go ahead and add them to the other article, but we should still illustrate a golden rectangle on this page, since it has a lot of words about how pleasing the same is due to its ratio.  The simple gray rectangle illustrates the point well, and only uses space that would be blank otherwise. Dicklyon 01:17, 17 August 2006 (UTC)

text: How do you make a true golden rectangle with discrete pixels?  —Tamfang 06:36, 25 August 2006 (UTC)
replies: text: Easy: start with non-square pixels of aspect ratio phi or something rationally related to it.  Dicklyon 06:47, 25 August 2006 (UTC)
replies: text: So you are going to manufacture your own special displays with Golden Ratio pixels? −Woodstone 22:29, 25 August 2006 (UTC)
replies: text: Not me.  Just telling Finell and Tamfang what would be required to beat the Fibonacci rectangles that we can use as approximations when we're stuck with square pixels. One could also use a gray-scale anti-aliased fuzzy edge to make a sort of better approximation, but it will tend to look more fuzzy rather than more precise, which is why I elected to make the Fib rect.  I used the next size up initially, which has a ratio that at least agrees with the digits 1.618, but someone complained it was too big.  The image is still there, I think, and you should be able to infer its name from the present one and see how it looks. Dicklyon 22:54, 25 August 2006 (UTC)
thread_title:  Rectangle image 

message: Jossi, your rework of the article really sounds like it's designed to push the agenda of ancient mysticism or something.  Have you even read Livio or any of the other things you're writing about? Dicklyon 04:41, 22 August 2006 (UTC)
replies: text: My rewrite of the History section's lead simply removed the editorializing and the reaching of conclusions that breached WP:NOR, and attributing the POVs. This article is not Mario Livio and the golden ratio, is it? Livio is already used to as references for four passages. That is quite enough, given that super-abundant literature on the subject. I would appreciate if you can WP:AGF. I am not into mysticism  or trying to push an agenda, neither I am accusing you of pushing a skeptic agenda. I simply find the subject fascinating, to which I arrived due to my interest in typography, and the geometry involved in book design. Let's make the article better, by using good research and the editorial tools at our disposition, and the parameters defined by WP:NPOV, WP:V, and WP:NOR. ≈ jossi ≈ t • @ 14:19, 22 August 2006 (UTC)

text: I have not read the specific book by Livio, but I have read various of his articles. I intend to read the book as soon as I get hold of a copy. As for the use of the golde section in book design, I have modified the wikilink to the appropriate page Golden section (page proportion). ≈ jossi ≈ t • @ 17:28, 22 August 2006 (UTC)

text: What I know about Livio, is that he does not accept that there is a link between aesthetics and the golden ratio, and believes that "we should abandon its application as some sort of universal standard for "beauty," either in the human face or in the arts." That statement can be used in the article, as he is an authorative source on the subject, but we can only mention it as Livio's opinion, and not as a fact. ≈ jossi ≈ t • @ 17:39, 22 August 2006 (UTC)
replies: text: Yes, that's fine.  But have you read his book?  It will be useful to inform your writing on these topics.  From my point of view, this is a mathematics and history article, and I agree with Livio that people who want to assign aesthetic concepts to this irrational number are without any solid basis for doing so. Dicklyon 18:00, 22 August 2006 (UTC)
replies: text: I disagree that this article's focus is mathematics and history. There is a massive body of work going back 500 years that applies the golden ratio to many human endeavors, including architecture, art, book design, psychology, aesthetics in general, cosmology, philosophy, natural sciences, etc. Livio's viewpoint is significant but certainly not the prevalent or most significant. This article needs to be informative for our readers, and present all significant viewpoints, including these that assert that there is an aesthetic component to this ratio (or mystic, esoteric, etc.) and those that do not, as per our policy of WP:NPOV. Eventually, and if we do our work well, this article can spin out multiple articles and become a summary article as per Wikipedia:Content_forking#Article spinouts - "Summary style" articles, in which the different aspects of the golden ratio, including the dispute about its application can be fully explored.  ≈ jossi ≈ t • @ 18:09, 22 August 2006 (UTC)
thread_title: History

message: Especially since several Wikipedians are doing a lot of work to bring this article up to Featured Article quality, I believe that all of the citations should be in the same form. I suggest that we standardize on the Wikipedia citation templates—they are tedious, but they ensure consistency and full bibliographic info. Yes, it will be a lot of work. Yes, I know that I am a pedant, but I can't help that. What do others think (about my proposal, not my personality)? Finell (Talk) 06:36, 24 August 2006 (UTC)
replies: text: Go for it. Dicklyon 06:39, 24 August 2006 (UTC)

text: Sure. ≈ jossi ≈ t • @ 00:52, 25 August 2006 (UTC)
thread_title:  Consistent citation form 

message: I think that;
 \frac{1}{\varphi} = \varphi -1  is a property of \varphi . Is there another real number that has this property out there? This was discussed (briefly) furthur up the talk page but was not in the article. --Zven 22:13, 24 August 2006 (UTC)
replies: text: yes, because it leads to the defining quadratic equation, which has two real roots. Dicklyon 22:55, 24 August 2006 (UTC)
replies: text: And isn't it wonderful that the other root is -\Phi. Woodstone 08:20, 25 August 2006 (UTC)
replies: text: Wonderful.  I prefer to avoid the case confusion and call it 1-\varphi. Dicklyon 14:53, 25 August 2006 (UTC)
thread_title: Properties of <math>\varphi</math>

message: There is substantial information about the application of the Golden mean by the Bauhaus and well as its by Carl Jung in his works. Are others willing to help and research the subject? ≈ jossi ≈ t • @ 16:53, 27 August 2006 (UTC)
replies: text: Maybe you better help us get started.  My quick search in books.google.com didn't turn up any connections. Dicklyon 17:13, 27 August 2006 (UTC)
replies: text: Oh... Google books have but a very small sample of all books printed. Hopefully one day, publisher's permitting... ≈ jossi ≈ t • @ 17:17, 27 August 2006 (UTC)

text: Indeed, it's a modest sample, but on topics with "substatial information" it can be very helpful already.  So, as I said, we need your help since I know you have books that aren't on it. Dicklyon 18:15, 27 August 2006 (UTC)
thread_title:  Bauhaus, Jung and the golden mean 

message: I have decided to remove this article from my watch list for a month or two. My reasons are explained here: Talk:Canons_of_page_construction#Merge_proposal ≈ jossi ≈ t • @ 05:24, 28 August 2006 (UTC)
replies: text: That is a real shame. Over a long period of time, you have done a lot of excellent work on this article. Please reconsider. Finell (Talk) 08:24, 29 August 2006 (UTC)
thread_title:  Wasting my time 

message: Jossi, it's OK to mention my name as the editor you have this problem with.  Here's how I propose we move on.  I will (unilaterally) totally refrain from editing any of your contributions; however, I also suggest that you not directly edit mine nor revert recent things that have settled out.  Instead, I will only comment on talk pages, and I invite you to do the same, so that changes will be made by others who support one approach or another.  I urge you to agree, but I will adopt this approach unilaterally in any case.
Our issues stem from this very issue of how to attribute controversial statements, starting with your initial additons of the Rice stuff to this very article.  I really only have one important issue with you, and I'm sorry that I or we allowed it to escalate; I apologize especially to the other editors here who may have been annoyed and inconvenienced by it.  To summarize for others, the issue is this: statements of the form "X discovered (or describes) the use of the golden rectangle in Y", when controversial, unproven, or at odds with other material or widespread belief, should be rephrased as "X asserts that..." or "X hypothesized..." or something that indicates what X said without implying that it is accepted.  I know you hate the word hypothesized for some reason, which is why we end up with asserts.  Perhaps others will find a better way to avoid introducing the POV that such statements are accepted on their face. 
I don't think we have any other substative issues, and I will try to avoid allowing myself to engage in any more bickering on non-substative issues.
Everyone else, feel free (as I've said many times) to undo any of my recent changes, additions, figures, etc., if you think it will help the article. Dicklyon 16:55, 29 August 2006 (UTC)
replies: text: It can all be resolved if we focus on creating a great article that we can all feel proud of. I appreciate your comments and offer above, but for know I would remain unengaged for a while. It helps cool things off, and bring the common sense back. It is OK. We are all learning, an that is a good thing. Note that I have this page off my watchlist, so if you need my attention, please add a comment in my talk page. ≈ jossi ≈ t • @ 17:45, 29 August 2006 (UTC)
replies: text: OK, we're good.  By the way, I ordered a copy of Tshichold off ABE, but my order got cancelled because two other people ordered it, too.  I guess somebody is noticing things... Dicklyon 17:50, 29 August 2006 (UTC)
thread_title: Truce proposal

message: To me, one of the most interesting things about the golden ratio is the controversy over it.  Like religion and politics, you find people with strongly held but opposing views on its place in art, history, and nature.  We've danced around these issues by just saying who says what here and there, but I think it would be easier, and more productive to collaboration, if we could address it head on.  It's pointless to argue over which view is correct; much better to address the differences, and discuss the analyses and viewpoints in the literature, than to just point at a few authors' opinions while ignoring the elephant in the room.  We should be able to assemble and compare sources in an NPOV way (it would be WP:OR to use such assembly to support one point of view, so that must be avoided).
I think this would work better than sprinkling the controversy into history, aesthetic, and "disputed sightings" sections.  Not that it won't be a challenge to get it right and broadly acceptable, but it's an approach that might help.
So, how about a section on "Controversies around the golden ratio" or something like that?   We could juxtapose contrary viewpoints quite explicitly, so that the article could stay neutral instead of having POV items sprinkled here and there couched in quotes and weasle words. 
For example, juxtapose the words of H. E. Huntley in his recent book The Divine Proportion, 
*There seems to be no doubt that Greek architects and sculptors incorporated this ratio in their artifacts.  Phidias, a famous Greek sculptor, made use of it.
with the words of Mario Livio, who, after noting that the mathematical theorems about the extreme and mean ratio were all developed some time AFTER the Pathenon was built, says, 
*This is another example of the number-juggling opportunity afforded by claims based on measured dimensions alone.  Using the numbers quoted..., I am not convinced that the Parthenon has anything to do with the Golden Ratio. ... Other researchers are also skeptical about phi's role in the Parthenon design."
Probably a better source than Huntley can be found, since he provides little reason to accept his assertion.  This particular example is sort of "meta" in that it's a contrast between two authors' opinions on what is believed by others.  More particular assertions on specific topics will be easy to find, too. 
If this approach works, we can address the controversy without getting caught up in it.
Comments?  Dicklyon 20:11, 30 August 2006 (UTC)
replies: text: I would agree to this approach, if there is another source for opposing views tha nLivio. Otherwise this article will be Livio vs others and that will make the article tedious to read and innapropriate. ≈ jossi ≈ t • @ 00:51, 31 August 2006 (UTC)
replies: text: I guess by "opposing" you mean on the skeptical side, like Livio and me.  I'm sure we can find other sources, like Martin Gardner's 1955/57 book Fads and Fallacies in the Name of Science that has a section on Pyramidology.  And others, though the more speculative works seem to be much more numerous.  I suppose anything on which we don't find two sides is not properly part of this section, although not everything that I might regard as controversial is necessarily specifically addressed by the skeptical guys. Dicklyon 01:10, 31 August 2006 (UTC)

text: Actually, on quick look back at Gardner, he takes Taylor to task for his Pyramidology, but doesn't talk about the golden ratio claim per se, as far as I can see.  Still  might  have some relevant quotes. Dicklyon 01:18, 31 August 2006 (UTC)

text: Here are some useful sources:   Dicklyon 01:37, 31 August 2006 (UTC)

text: Thanks for your feedback.  Personally, I think the current structure has invited more POV pushing.  If we had a section where controversies could be explicitly aired, in terms of pairs of opposing views with citations, but omitting anything that doesn't fit that mold, then we could avoid the "excessive citation" problem when controversial points get embedded in other sections.  Let's see who else has an opinion or counter-proposal. Dicklyon 04:23, 31 August 2006 (UTC)
thread_title: Controversy

message: The complicated Rice statements on both sides of the Eqyptian question leave one wondering what Rice's conclusion was.  As I read him, he thinks the random ocurrence of golden ratio is unlikely, but he concludes with a balanced observation: "There are no examples from the surviving Egyptian literature which can be accepted as demonstrating the conscious or planned use of the Golden Section in any theoretical or abstract sense.  It may be quite simply, that the Eqyptians' extraordinary instinct for form and balance produced the effect of the Golden Section without the need actually to define it."  That sounds to me like the thing most worth quoting in the article. Dicklyon 04:47, 31 August 2006 (UTC)
thread_title: What Rice said 

message: Here's another "definition" of sorts from Euclid (one of the early books; p. 81 in 1828 edition of the Rev. Dionysius Lardner's London edition):
*Proposition XI. Problem. 
:(279) To divide a given finite right line (AB) so that the rectangle under the whole line and one segment shall be equal to the square of the other segment.
:A line divided, as in the proposition, is said (vide Book VI) to be cut 'in extreme and mean ratio.'
Corresponding and related definitions are found in other 19th century books. 
Elements of Geometry, Theoretical and Practical: Including Constructions of the Right Line and by...
By Eugenius Nulty,
Philadelphia: J. Whetham
1836
p.94 
*PROBLEM VIII.
:57. To divide a given right line AB in extreme and mean ratio, or so that the square of the greater part may be equal to the product of the whole line and the less part. 
New Plane Geometry
By Webster Wells, Robert Louis Short,
D.C. Heath & Co.
1909
p.132
*272. Def. A Straight line is said to be divided by a given point in extreme and mean ratio when one of the segments is a mean proportional between the whole line and the other segment.
A Treatise on Elementary Geometry: With Appendices Containing a Collection of Exercises for Students and An Introduction to Modern Geometry
By William Chauvenet,
Philadelphia: J.B. Lippincott & Co.
1884
p. 120
*73. Definition. When a straight line is divided into two segments such that one of the segments is a mean proportional between the given line and the other segment, it is said to be divided in extreme and mean ratio.
Enjoy. Dicklyon 05:18, 31 August 2006 (UTC)
replies: text: Excellent. Please consider adding these definitions, maybe in their own section in the article. ≈ jossi ≈ t • @ 01:47, 10 September 2006 (UTC)
thread_title: Variant definitions

message: There's an OK plot of preferences versus aspect ratio of a rectangle in this old book: . It shows a very broad preference centered near 1.6.  This might be worth citing as one of the early psychological studies. Dicklyon 01:32, 4 September 2006 (UTC)
replies: text: Excellent find. It is definitively worth citing. ≈ jossi ≈ t • @ 01:48, 10 September 2006 (UTC)
thread_title: Broad preference

message: The gray rectagle does not provide any value to the article's lead. I propose to delete it. ≈ jossi ≈ t • @ 13:38, 11 September 2006 (UTC)
replies: text: If there's nothing in the article that suggests that a golden rectangle is a particularly pleasing shape, then we have no need to illustrate such a shape.  If there is, we do.  I'll have to review it. Dicklyon 15:23, 11 September 2006 (UTC)

text: In my opinion, this particular (almost) golden rectangle doesn't add much. I think that a golden rectangle with the same labeling and color scheme as the sectioned line segment (which is great) would aid readers' understanding. Further, discussion of the aesthetics of phi and its aesthetic applications usually involve golden rectangles (occasionally golden triangles). Finell (Talk) 17:20, 11 September 2006 (UTC)
thread_title: Gray rectangle

message: Please do not use the edit summaries to express your POV. Describe your edit, and that will be more than enough. Thanks. ≈ jossi ≈ t • @ 03:05, 10 September 2006 (UTC)
replies: text: Why?  What better place is there to express a POV than in an edit summary? Dicklyon 06:22, 10 September 2006 (UTC)
replies: text: The Talk page (i.e., here) is the better place. Finell (Talk) 17:22, 11 September 2006 (UTC)

text: Because edit summaries cannot be refactored. ≈ jossi ≈ t • @ 14:35, 10 September 2006 (UTC)
replies: text: I guess I just don't get your point.  As usual.  Dicklyon 14:42, 10 September 2006 (UTC)
replies: text: Edit summaries stay forever in  page history. So, when you use the edit summaries, just state what you did and then discuss your reasons here. Basic etiquette. ≈ jossi ≈ t • @ 15:14, 10 September 2006 (UTC)
replies: text: Sorry, if that's the etiquette of wikipedia I will try to respect it.  Is it on a policy page some place?  Because it seemed to me that having a POV in an edit summary would be useful to people trying to review and understand the history of edits. Dicklyon 15:55, 10 September 2006 (UTC)
thread_title:  Edit summaries