Talk:Golden ratio/Archive 3

message: Its pretty clear to me that the "Sherrifs" of this page are in VIOLENT OPPOSITION TO THE PRINICPLES OF WIKIPEDIA.  They are going to stick to the idea that the Greeks were the first with Phi, no matter what the evidence.  The deletion of refrences to Egypt and Hebrew use is uttlery without excuse.  The Hebrew Temple deletion refered to the text itself, so assuming the reader can do fractions, then the lack of another citation is not a "reason" for deltion.  It is an EXCUSE TO PROMOTE A POINT OF VIEW. —Preceding unsigned comment added by 71.96.78.217 (talk) 12:05, August 24, 2007 (UTC) 
:You have provided no references for your assertions.  Until you do, they will not be in the article.  — Arthur Rubin |  (talk) 17:58, 24 August 2007 (UTC)
replies: text: I'm with Arthur on this.  We've spent the last year or more getting unsourced bull out of this article.  If there are facts we missed, please bring them in and share your sources.  And read up on the principles of wikipedia yourself, esp. WP:V and WP:RS. Dicklyon 04:23, 25 September 2007 (UTC)
thread_title:  Non-Greek Origins 

message: Regarding this reversion. If Phi is definded recursively (1 + 1/(1+1/(etc...))) the subscript means nothing, but if defined iteratively (1 + 1/1 = 2, 1 + 1/2 = 1.5, 1 + 1/1.5= 1.66, etc..), the subscripts are absolutely necessary (as none of the subscripted Phis are actally Phi but approximations of Phi). This should be explicitly stated in the applicable section as it is a little confusing. Adam McCormick 05:08, 27 August 2007 (UTC)
replies: text: I've made an edit which should alleviate any possible confusion. Please discuss before reverting. Adam McCormick 05:27, 27 August 2007 (UTC)
replies: text: I don't think it helped.  The old way was more clear and correct, so I restored it.  There's no need to introduce the subscripted phi notation for the convergents.  Dicklyon 06:57, 28 August 2007 (UTC)
replies: text: But when calculating Phi iteratively, none of the calculations actually produces Phi, it may need to be put somewhere else but it does need to exist, I'm reverting back to my version, please reorganize if you don't think this applies to convergents  Adam McCormick 16:38, 28 August 2007 (UTC)

text: I understand that, my problem is that a non-math person trying to approximate Phi wouldn't have any idea how to implement the continued fraction, and even with some exposure to the subject I still find the convergents statement very confusing. I think the iterative form needs to exist somewhere, that's all. Adam McCormick 19:20, 28 August 2007 (UTC)
replies: text: But it is somewhere: it's in the decimal expansion / calculation methods section, which is I think a more likely place to look for this as a calculation method. Specifically, the continued fraction section that you've been trying to edit says that the convergents are ratios of Fibonacci numbers, and the last sentence of the calculation methods section says to take the ratio of consecutive Fibonacci numbers. However as a method for approximately calculating the golden ratio this iteration is significantly slower than the Newton iteration described earlier in the calculation methods section. —David Eppstein 19:35, 28 August 2007 (UTC)

text: The alternative typographical convention of not putting end punctuation after displayed equations is also quite commonly used by reputable publishers.  Does wikipedia have a policy on this?  Or a style guideline? Dicklyon 23:27, 24 September 2007 (UTC)
replies: text: Examples, please? I just checked some journals by AMS, SIAM, ACM, Elsevier, Wiley, Springer, and World Scientific, and they all had punctuated displayed equations. I did find a Kluwer journal in which some sentences that ended in displayed equations had a period, others didn't, often within the same article, but that seems more like a lack of copyediting than a consistent house style. —David Eppstein 00:49, 25 September 2007 (UTC)
replies: text: The first book I picked up off the top of my stack consistently omits end punct on displayed equations (6th ed. of Hunt's The Reproduction of Colour in case you want to check).  I'm not saying it's the most popular convention these days, but in fact it's what I was taught, maybe 15 years ago or so, when I had been doing endpunct.  The argument is that it's less likely to introduce confusion into equations if you don't add dots and things in the display. Dicklyon 04:20, 25 September 2007 (UTC)
thread_title:  Recursive/continuous fractions notation 

message: "The height of this pyramid is Phi times the semi-base...The slope of the face is also Phi." This is kind of redundantly redundant. Since the height of a right triangle is always the base times the slope of the hypotenuse, the statement says the same the twice. You think that we should change that, or leave it anyway? ROBO_HEN5000 ROBO 01:43, 27 September 2007 (UTC)
replies: text: See if you like the way I fixed it.  The link that was hanging on there was also irrelvant, so I took it out. Dicklyon 02:59, 27 September 2007 (UTC)
thread_title:  Mathematical pyramid redundancy 

message: :copied here from my talk page: Dicklyon 22:33, 14 October 2007 (UTC)
replies: text: Your edit also added some stuff not supported by the reference.  I added a link to the ref so you can check what it says; so try again, but if what you add is not supported by, or contradicts, the reference, than you'll need to find a new reference to support it.  We have to be rather strict on this particular article as it tends to accumulate a lot of junk otherwise. Dicklyon 22:30, 14 October 2007 (UTC)
replies: text: Sorry for posting on wrong page, I'm new here. I definately believe that this page would accumulate a lot of junk - so many misconceptions - so I understand your vigilance. You should definately consider changing the part about Bartok's use of Fibonacci numbers...how about a musical score as a reference? For us musicians, that is much better than any book. It is, in fact, not even known for a fact that Bartok used the Fibonacci numbers. Even the passage discussed, although definately suggestive of their use, is marked rubato. Bartoks musical language conceals his use of the Fibonacci numbers and the golden ratio if he in fact used them - and that should be noted here. If someone can provide a writing in which Bartok states that he used it, only then is it proven beyond any doubt. I checked out the reference; if you want to take such writing as a reference you are welcome to, but you are doing a disfavor to wikipedia. Check the score and you will see that my addition was more complete; ask educated musicians and you will see that terminology was incorrectly used.  —Preceding unsigned comment added by 89.49.56.56 (talk) 21:00, 15 October 2007 (UTC)
replies: text: If you have sources with more info, please do fix it; however, also keep in mind that this article is supposed to be about the golden ratio, so if you have expansions on the fib.no. stuff, that might be better in a different article.  Or if there's reason to believe the source cited is not to be regarded as a reliable source, tell us the reason and take that info out. Also, wikipedia prefers to report what is in secondary sources, not new interpretations of primary sources; the latter are called WP:OR and are discouraged. Dicklyon 05:52, 16 October 2007 (UTC)
replies: text: I guess I can understand that policy. Just goes to show it is impossible to have a perfect policy. Thanks for the info anyway.  —Preceding unsigned comment added by 89.49.32.214 (talk) 15:04, 20 October 2007 (UTC)
thread_title:  Bartok 

message: http://www.pennyarcademerch.com/pat070421.html  —Preceding unsigned comment added by 71.116.131.170 (talk) 14:17, 9 November 2007 (UTC)
thread_title:  penny arcade reference? 

message: The term explicit expression is used in its mathematical sense in about 20 Wikipedia articles, but I did not see a definition in any of them. I redlinked its use in Golden ratio. It would be helpful for Wikipedia to have a definition of this term to which usages can be linked, either as a short article devoted to the term or as a section in an appropriate article on mathematical expressions. Finell (Talk) 06:00, 14 December 2007 (UTC)
replies: text: It's implicitly defined in implicit function; I recommend you redirect to there. Dicklyon (talk) 06:22, 14 December 2007 (UTC)
thread_title:  ''Explicit expression'' 

message: Just wanted to comment that the Golden Mean isn't "the felicitous meeting of two extremes." According to the article it seems to be more about moderation and temperance, not a random meeting of two unlike things. [{Special:Contributions/71.82.122.91|71.82.122.91]] (talk) 01:13, 19 December 2007 (UTC)
replies: text: It says "middle", not "meeting", and is accurate and sufficient for the purpose of disambiguation. Finell (Talk) 09:02, 19 December 2007 (UTC)
thread_title:  Disambiguation 

message: I read a journal article on this topic that shows that most of these interpretations of art matching golden ratios are rather unlikely. There is nothing but correlation, and the connection between the golden ratio and these masterpieces may be a simple effect of biased selection: In other words, there are many measurements in a building or a face, and to dismiss the measurements that do not conform, or the aesthetically pleasing art that doesn't conform to the golden ratio would certainly introduce bias.
Here is a link to the article: http://laptops.maine.edu/GoldenRatio.pdf by George Markowsky. Deepstratagem (talk) 17:07, 20 December 2007 (UTC)
replies: text: We decided about 18 months ago to not have a controversy section, but just to focus on verifiable points.  We've already done a pretty good job of reducing the frivolous claims, so it's not clear to me where you feel there's a problem.  The Markowsky paper is already linked in further reading; if you figure out what journal it's from, you might want to use it as a source and add a bit of what it says where needed. Dicklyon (talk) 17:27, 20 December 2007 (UTC)
thread_title:  Controversy section needed 

message: In the "Music" section, I have added "Phi and the semitone". However, I have used non-Wiki terms for mathematical expressions. Perhaps someone more familiar with Wiki math would be kind enough to revise my mathematical expressions.  Thanks!  Prof.rick (talk) 19:49, 22 December 2007 (UTC)
replies: text: Since it's just unsourced numerology, I just took it out.  Let us know if you have a reliable source connecting phi to the semitone, and maybe we can put it back. Dicklyon (talk) 21:25, 22 December 2007 (UTC)
replies: text: We could use a third opinion about this now in Mathematical coincidences. Dicklyon (talk) 09:31, 28 December 2007 (UTC)
thread_title:  Phi and the semitone 

message: Life is too short to debate this edit; so I provide the deleted information here, for anyone who is interested:
:The oldest known applications of the golden ratio are likely in vedic mathematics (more than 3.000 BC) and likely also in some Egyptian pyramids (2000 BC).
— Xiutwel ♫☺♥♪ (talk) 23:34, 22 December 2007 (UTC)
replies: text: It's not about debate.  See WP:V and WP:RS.  Dicklyon (talk) 00:25, 23 December 2007 (UTC)
thread_title:  timeline 

message: In April 2007, a well-meaning Wikipedian, who had not participated in the article and appears not to have expertise in its subject matter, nominated Golden ratio to be a featured article. This drive-by nomination was short lived: all who commented on the nomination opposed it. Since this nomination was essentially an accident, and the embarrassment of failure was not self-inflicted, I propose deleting the box concerning its failed FA candidacy from the top of this Talk page. Comments? Finell (Talk) 06:29, 14 December 2007 (UTC)
replies: text: I would agree. I wonder somewhat what difference it makes, but I don't think its presence really matters. Adam McCormick (talk) 05:49, 18 December 2007 (UTC)
replies: text: Done. Finell (Talk) 23:01, 2 January 2008 (UTC)
thread_title:  Former FA candidate 

message: "Some suggest that he.."
in the bit about Mona Lisa.  —Preceding unsigned comment added by Lukechumley (talk • contribs) 04:02, 27 January 2008 (UTC)
thread_title:  Weasel Words 

message: Is there established consensus of \Phi versus \varphi. I ask because they've all been changed (the intermediate edit by Jossi looks good though) and should be reverted or not based on that consensus. Adam McCormick (talk) 22:49, 12 March 2008 (UTC)
replies: text: Yes there is. Most modern professional works on the golden ratio use lower case phi for the golden ratio. See, for example, the Mathworld link. That has been the accepted usage on Wikipedia for over a year, at least; feel free to check the edit history for yourself. Although I have great respect for Jossi and his many contributions to this article and throughout Wikipedia, there is long-standing consensus here that the lead would be incomplete without the defining equation. If Jossi wants to reopen discussion of whether the equation should be in the lead, he is welcome to do that on this Talk page. I reverted the anon edits and Jossi's to restore the consensus. Finell (Talk) 23:24, 12 March 2008 (UTC)
replies: text:  No problem. So long as Jossi's edit was considered separately, I've got no complaints. Adam McCormick (talk) 06:21, 13 March 2008 (UTC)

text:  I think that the lead could do without the formula, per WP:LEAD. ≈ jossi ≈ (talk) 23:29, 13 March 2008 (UTC)
replies: text: Dear Jossi: Welcome back! What specifically in WP:LEAD makes the formula inappropriate? Finell (Talk) 02:01, 14 March 2008 (UTC)
thread_title:  Capitalization of Phi 

message: Dear Dicklyon: Thanks for clearing up the misinformation about the sculpture. I assumed (but should not have) that it was entitled "Golden Ratio" because that is what the text and image caption said; likewise, I should not have uncritically qualified my {Fact} tag with the hidden comment. Since you're on a roll, how about cleaning up the bee ancestry entry. For starters, integer:integer can't be irrational, so it can't be the golden ratio (although it can approach it). Finell (Talk) 19:18, 16 March 2008 (UTC)
replies: text: I've tried, and can't find anything on the bees, or where that idea came from, or what the actual ratios might be.  I'd just get rid of it.  But I did some work on the Roses of H., and concluded that it's probably just a wikipedian's original research, since there's absolutely nothing on it in books or papers that I can find. Dicklyon (talk) 20:33, 16 March 2008 (UTC)

text: I cannot find anything either. ≈ jossi ≈ (talk) 20:48, 16 March 2008 (UTC)
thread_title:  Disputed sightings 

message: Why do they call it golden ratio? the ratio goes from the middle pont (that's 0.5) of a side of a perfect square, to the opposing vertex. After you extent the circle to 0° or 180°, you se that the extra section is 0.618, that's 0.5 + 0.618 = 1.118, thus the golden ratio is 1.118 of a square of 1 per side. The golden section might be 1.618, but the ratio is not. 
Can someone explain what's happening to me?--20-dude (talk) 03:35, 17 March 2008 (UTC)
replies: text: It's the ratio a:b or (a+b):a as shown; or the ratio of the dimensions of a golden rectangle; or (1+sqrt(5)):2; etc.  In the rectangle picture, the sum of the distances sqrt(5)/2 and 1/2 is it: 1.118 + 0.5, not as you describe.  "They" can call it whatever they want; we just report on it.  Sorry, I can't explain what's happening to you. Dicklyon (talk) 03:41, 17 March 2008 (UTC)

text: Dude: The OED traces the etymology of golden ratio and golden section. I believe that the first use of golden was in German by Ohm (mentioned in the article), which led to translations such as golden section. I hadn't heard of auric (Latin for golden?) section. Where did you find that one? Finell (Talk) 22:34, 17 March 2008 (UTC)
thread_title:  Title 

message: The material reverted is about the golden ratio's relationship to inflection points of a fourth degree polynomial. \phi is the root of a quadratic; the quadratic is the second derivative of quartics; and inflection points are roots of second derivatives. In other words, the OR appears to be tautological. Find a reference in a peer-reviewed math paper, otherwise it just doesn't seem worth reading much less proving. Pete St.John (talk) 18:34, 25 March 2008 (UTC)
replies: text: While it's not the deepest result ever, I don't think it is entirely trivial either. The result says that the line segment between the points of inflection intersects the quartic in the two points that divide it in the ratio φ:Φ. And that ratio is the same for any quartic with real points of inflection. That's not completely obvious. Alexander Bogomolny discusses it in some detail at Cut-the-knot, and he doesn't typically write up trivia. And a peer-reviewed paper in On Math was cited above. Gandalf61 (talk) 19:51, 25 March 2008 (UTC)
replies: text:  Well yeah that sounds nontrivial, but now I don't see my own revert in the article history. Sometimes I'm flumoxxed; I could have sworn that I had undone to Paul's version, but he doesn't have one for days back. Anyway, Gandalf, feel free to put in maybe something more brief? Pete St.John (talk) 20:39, 25 March 2008 (UTC)

text: Has anyone actually seen this paper from On Math?  Dicklyon (talk) 21:34, 25 March 2008 (UTC)
replies: text: Well, there is certainly a paper with the cited title in the index of the relevant journal issue here. I think you need a subscription to see the paper itself. But why be so suspicious ? Do you have any evidence that suggests the paper may not be legitimate ? If not, I think we should follow WP:AGF and asume that the paper is a valid reference. Gandalf61 (talk) 09:16, 26 March 2008 (UTC)

text: Is it possibly this?  -- Dominus (talk) 13:37, 26 March 2008 (UTC)
replies: text: That's a different paper, different title, apparently self-published.  That one I have, but I'm wondering if there's a published peer-reviewed one that anyone has seen.  I'm not suspicious of its existence, but how can we cite it as a source if nobody has seen it?  Do we even have reason to believe that it's peer-reviewed at this point?  Someone who has it or knows of its content should just speak up and fix this; the rest of us should wait, or go try to get a copy. Dicklyon (talk) 15:34, 26 March 2008 (UTC)
replies: text: I've requested a copy from the author. -- Dominus (talk) 15:59, 26 March 2008 (UTC)
thread_title:  regarding the recent "OR" reverts 

message: It was just a slip that I removed this image along with the Rose of H., but now that I look at it, I see that the commentary on it is completely weasel-worded and unsourced.  And it's not at all clear from the figure what distances are supposed to be in the golden ratio.  Could somebody who knows about this please fix it? Dicklyon (talk) 04:57, 17 March 2008 (UTC)
replies: text: I believe the source of the idealized face with golden ratio reference lines is Divina, which Leonardo illustrated. In my research I found a sketch by Leonardo of a real face with the same grid of lines superimposed. I wanted to track down more information before adding it to Wikipedia. Finell (Talk) 22:25, 17 March 2008 (UTC)
replies: text: At this point, I can accept that it's from that book since the page headers appear to say so.  But how does it relate to golden ratio?  No way that I can see. Dicklyon (talk) 15:37, 26 March 2008 (UTC)
replies: text: Here is a link to an image of that page, from a copy of the book in the LoC's collection . Perhaps you or someone who speaks Italian (Jossi?) can explain in more detail, from the surrounding text, what this image represents in a book that is about or largely devoted to the golden ratio. Or, if we wait a few months, an English translation of the book is scheduled for publication in June 2008. Finell (Talk) 01:37, 27 March 2008 (UTC)
replies: text: Thanks for that pointer.  I hadn't realized the LoC had that sort of online collection.  Looks like there's no text near the picture, however, and lots of the figures appear to be about things other than the divine proportion.  So maybe we just shouldn't make any claims about it being an application of the golden ratio unless someone finds evidence that it is.  I look forward to that translation. Dicklyon (talk) 02:50, 27 March 2008 (UTC)
replies: text:  It reads, Divina Proportio, and it refers to mapping the human face to the golden ratio. Check the ratio of the six rectangles (the leftmost two are split in the middle). ≈ jossi ≈ (talk) 22:24, 27 March 2008 (UTC)

text:  The full title is Divina proportione: opera a tutti glingegni perspicaci e curiosi necessaria oue ciascun studioso di philosophia, prospectiua pictura sculpura, architectura, musica, e altre mathematice, suauissima, sottile, e admirabile doctrina consequira, e delectarassi, cõ varie questione de secretissima scientia. M. Antonio Capella eruditiss. recensente. it is in ancient Italian. ≈ jossi ≈ (talk) 22:31, 27 March 2008 (UTC)
replies: text: Yes, and the title page would be a nice image; doesn't make much sense to me, but nice.  Jossi, since you uploaded the face image in the first place, what do you know about it?  I was looking for reason to suspect that the rectangles with diagonals across them were meant to be golden rectangles, but I couldn't find one. There's another face (page seventy something iirc) with various and sundry unexplained proportions marked as well.  Any clue? Dicklyon (talk) 23:01, 27 March 2008 (UTC)
replies: text: What page number, Dick? ≈ jossi ≈ (talk) 20:38, 28 March 2008 (UTC)

text:  You probably mean this . My knowledge of Italian is basic, and the olde Italian used by Pacioli does not help.... ≈ jossi ≈ (talk) 20:40, 28 March 2008 (UTC)
replies: text: Right, that one.  It's got the same top and bottom rectangles with diagonals across them, but they're divided up different ways.  I wonder still if those, or some other proportions, are said by Pacioli or Da Vinci to be approximately divine. Dicklyon (talk) 22:49, 28 March 2008 (UTC)
replies: text:  Dunno... All we have is Divina Proportio stamped above the head. We can just simply describe that without additional commentary. ≈ jossi ≈ (talk) 01:37, 29 March 2008 (UTC)
replies: text:  There's some stuff here  ≈ jossi ≈ (talk) 01:40, 29 March 2008 (UTC)
thread_title:  The da Vinci face 

message: I went through the page a couple of times but couldn't find a "general form" that involves deriving the golden ratio for all positive n.  That is, if you take any positive n and add 1, then add the original number.  Then add the previous number.  Take many iterations and when you divide the new number by the one before it, it is close to the golden ratio.  For example:
{7,8,15,23,38,61,99,160,259}  259/160 = 1.61875
Do this with any n.  Here is another:
{5.2,6.2,11.4,17.6,29,46.6,75.6,122.2}  122.2/75.6 = 1.616402
Has anyone seen this before? InfoNation101 | talk | 19:06, 22 April 2008 (UTC)
replies: text: This property of number sequences similar to the Fibonacci sequence is described in generalizations of Fibonacci numbers#Fibonacci integer sequences. Gandalf61 (talk) 19:32, 22 April 2008 (UTC)
replies: text: Hm.  Interesting page.  Thanks for the heads up.  InfoNation101 | talk | 19:39, 22 April 2008 (UTC)
thread_title:  General Form 

message: That doesn't seem approximate (thesaurus: about, almost, nearly, roughly) to me, that's 11 significant figures.  I've done plenty of science, and "approximate" tends to me values such as Avogadro's number being 6.022X10^23, or the specific heat capacity of water being 4.18j/kgC. On the page for pi, pi is "approximately equal to 3.14159". That seems more like an approximation to me.
Either we should:
*Cut down on the number of significant figures (possibly to 1.618, the commonly stated value of the golden ratio), or
*Switch "approximate" with something like "the golden ratio, to the tenth decimal place, is valued at 1.6180339887."
What are everyone else's thoughts? (Bonzai273 (talk) 04:09, 24 May 2008 (UTC)
thread_title:  "Approximately 1.6180339887" 

message: That doesn't seem approximate (thesaurus: about, almost, nearly, roughly) to me, that's 11 significant figures.  I've done plenty of science, and "approximate" tends to me values such as Avogadro's number being 6.022X10^23, or the specific heat capacity of water being 4.18j/kgC. On the page for pi, pi is "approximately equal to 3.14159". That seems more like an approximation to me.
Either we should:
*Cut down on the number of significant figures (possibly to 1.618, the commonly stated value of the golden ratio), or
*Switch "approximate" with something like "the golden ratio, to the tenth decimal place, is valued at 1.6180339887."
What are everyone else's thoughts? (Bonzai273 (talk) 04:09, 24 May 2008 (UTC)
replies: text: I don't see the problem. "Approximate" doesn't mean "inaccurate", it just means that it's not perfect. —David Eppstein (talk) 04:25, 24 May 2008 (UTC)

text: Sure, it's unnecessary.  So what?  We've fought the creeping digit syndrome for years, and we've held the line stable here for a long time.  Why mess with it?  Dicklyon (talk) 04:55, 24 May 2008 (UTC)

text: If you want "better" you need to justify that and get consensus.  This article has a long history of compromise, so if you just jump in and make random-looking "improvements" that will typically not be accepted. Dicklyon (talk) 05:18, 24 May 2008 (UTC)
replies: text: The expression of the number with 11 digits is approximate, as must be any expression in decimals of this irrational number. It is also verifiable. I do not think it Wikipedia's mission to dumb down facts or to be so patronising as to segregate readers according to whether they are allegedly non-mathematical or crave warm, fuzzy feelings. It is a straw man argument by Bonzai273 to confuse contentment with the expression with a wish to lock down the whole article.  —Preceding unsigned comment added by Cuddlyable3 (talk • contribs) 14:50, 24 May 2008 (UTC)

text: I strongly support approximately 1.618 in the lead. Even building a monument - if you want a 10 m tall golden rectangle, this would give the width to plus/minus 2 mm. Just a few paragraphs further down, 10 decimals are given.--Noe (talk) 15:01, 24 May 2008 (UTC)
replies: text: I would support starting off with the same precision as we do pi:  3.14159, 1.61803.  But not less than that.  Dicklyon (talk) 15:36, 24 May 2008 (UTC)
thread_title:  "Approximately 1.6180339887" 

message: I moved a number of this items to refs, since they usefully support some points in the article.  It's not clear what the remaining 6 are good for, or why we'd want a further reading section in addition to all the cited reading.  Some are not very accessible.  I bought a copy of Doczi, and it doesn't have much useful (lots of fanciful stuff about spirals that someone might find interesting, but most of it not very connected to the golden ratio).  The Walser book looks pretty (), but I haven't spotted a great place to cite it.  
So should we remove these, if they're not sources that support the article?  Or if someone has a copy of some that arent' online, can we add something that they support? Dicklyon (talk) 05:13, 24 August 2008 (UTC)
replies: text: Per WP:MOS, the Further Reading section is intended for additional books on a topic that are not cited in the article as sources. I think we would need a rationale to remove an entry that fits this definition. Also, I see no need to make an extra effort to cite something that is now in Further Reading. The only one that I have read is Huntley, which is a pretty good overall treatment by a mathematician (I don't have it; I got it from a local library). Finell (Talk) 03:06, 26 August 2008 (UTC)
thread_title:  on Further Reading 

message: Just an observation, the major and the minor grooves of DNA are in the golden ratio. Also, when a string on a guitar is separated in the golden ratio you get the tonic resolving tone.  —Preceding unsigned comment added by Niubrad (talk • contribs) 11:23, 26 October 2008 (UTC)
thread_title:  Nature 

message: I've seen stuff that tells me 1.618 is the golden ratio, but I've seen people call the Golden ratio 0.618 as well. What is the difference? and can anyone tell me anymore natural stuff that is based on the goloden ratio? Thanks a lot.Ericrules2363 (talk) 03:04, 2 October 2008 (UTC)
replies: text: The difference? 1.618 − 0.618 = 1. Fredrik Johansson 05:54, 2 October 2008 (UTC)
replies: text: Phi, phi, pho, fum, I smell a troll...  Dicklyon (talk) 05:58, 2 October 2008 (UTC)
thread_title:  Difference? 

message: I found this out using a calculator.
Maybe it could be added to the article.  —Preceding unsigned comment added by 74.58.215.201 (talk) 20:47, 28 June 2008 (UTC)
replies: text: It already says that \varphi = {1\over2}\csc 18^\circ, which is exactly the same, since \sin 30^\circ = {1\over2}. -- Dominus (talk) 21:02, 28 June 2008 (UTC)
replies: text: More generally, things you find out using a calculator are not encyclopedic, per WP:RS and WP:NOR. Dicklyon (talk) 21:04, 28 June 2008 (UTC)
replies: text: A calculator isn't a reliable source? KenFehling (talk) 07:13, 21 July 2008 (UTC)
replies: text: That's like putting your own chemistry researches on here and claiming a test tube is a reliable source. Reyk YO! 07:44, 29 July 2008 (UTC)
replies: text: That's not really the same at all.  The results of a calculator are verifiable by anyone.  In fact, this very article and many math related articles have computations that someone did with a calculator. KenFehling (talk) 19:19, 29 July 2008 (UTC)
replies: text: If the calculations and examples are used to illustrate a known fact, then that's fine. For instance look at the example section in Engel expansion. I picked the number 1.175 because it would illustrate the algorithm concisely, and I did those calculations with the aid of a calculator. But that's not original research because I didn't invent the algorithm and I'm concerned only with explaining an already known fact. If I'd just been fiddling around with my calculator one day, found something interesting and decided to put it up on Wikipedia going, "Look what I've found out!", then that would be OR. The fact that anyone with a calculator could check to see if I'm right is immaterial. Reyk YO! 22:16, 29 July 2008 (UTC)

text: PS: See also exact trigonometric constants. Michael Hardy (talk) 22:58, 29 July 2008 (UTC)
replies: text: Not all calculators always approximate their results.  The TI-89 Titanium, for example, performs symbolic computation.  Given the expression \frac{\sin{30^\circ}}{\sin{18^\circ}}, it can display either an exact result of \frac{\sqrt{5}+1}{2} or an approximate result of 1.6180339887499. –Wdfarmer (talk) 03:52, 29 October 2008 (UTC)
thread_title:  (sin 30) / (sin 18) = Golden number 

message: I recently saw a Nova program on the current Greek reconstruction of the Parthenon.  The program implied that the Parthenon did not use the Golden ratio anywhere, and that the theory that it did was a creation of renaissance thought, not careful measurement.  —Preceding unsigned comment added by 71.104.240.132 (talk) 03:56, 4 September 2008 (UTC)
replies: text: There is no evidence the Greeks used golden ratio in art or architecture (they favoured rational proportions). I don't know who first cooked up the theory that they did, but I doubt it goes as far back as the rennaisance - I think it is after Fechner's psychophysics (which was about 1890, as far as I recall). The golden ratio myth is based on speculation and secondary popular modern sources. (Please prove me wrong, if you can!)--Noe (talk) 06:37, 4 September 2008 (UTC)
replies: text: The earliest such claim I've seen is this guy in 1912.  And he clearly doesn't know what he's talking about (see this note 2 on p.22). Dicklyon (talk) 07:18, 4 September 2008 (UTC)

text: I just noticed that he attributes some of the Parthenon proportioning to Jay Hambidge, though not necessarily the divine section aspects; here is more on that guy and the Parthenon. Dicklyon (talk) 07:31, 4 September 2008 (UTC)
thread_title:  That the Parthenon uses Golden Ratio is now contested? 

message: The first proof of its irrationality, using the Euclidean Algorithm, seems to me to need work.  I may try something later (say, by March of 2009). Rick lightburn (talk) 21:28, 15 November 2008 (UTC)
thread_title:  Short Proofs of Irrationality 

message: Now look up at the table of contents. Don't do this. — CharlotteWebb 14:36, 23 November 2008 (UTC)
replies: text: On a related subject, please avoid using the superscript-2 character — I see you have just replaced many 2 with this, and in general it's a bad idea. The reason is that it produces very different spacing of the characters than is obtained for other superscripts. See WP:MOSMATH#Superscripts and subscripts. —David Eppstein (talk) 16:20, 23 November 2008 (UTC)

text: No doubt the issue of scaling is important, but I have to say that the fix introduced by CharlotteWebb has a downside: there is now a mixture of fonts used to represent phi, and the result is displeasing to my eye. For example, just under the "Golden ratio conjugate" heading, we see a bold phi in one font (why bold?), then we see an attractive varphi in an expression. The capital phi at the end of the sentence is particularly disappointing (BTW, shouldn't "capital Phi" just be "capital phi"?). --Johnuniq (talk) 07:55, 24 November 2008 (UTC)
thread_title: The <math>\sqrt{}</math> of <math>5</math> is <math>\sqrt{5}</math>

message: Over at Fibonacci number, a couple of us have recently changed the math expression used to display varphi because we found that the png image was not being delivered, so the browser was displaying "varphi". While I did lookup the docs to confirm that there was a rational basis for the change I made, I have almost no knowledge of <math> and no idea why it had failed.
I see that the same problem is now apparent here (I think the problem was not there yesterday, becaused I scanned the article to see if it suffered the problems I was seeing at "Fibonacci"). Just above the Geometry heading, there are two equations where the png is not delivered. They appear as:
:-\frac{\varphi}{2}=\sin666^\circ=\cos(6\cdot 6 \cdot 6^\circ).
:-\varphi=\sin666^\circ+\cos(6\cdot 6 \cdot 6^\circ).
The two images are each downloaded as an empty file. What's going on? --Johnuniq (talk) 07:55, 24 November 2008 (UTC)
thread_title: Images disappearing

message: The only positive solution to this
:x^2 - x - 1 = 0.
is this
:x = \frac{1 + \sqrt{5}}{2} \approx 1.61803\,39887\dots\,
but the negative solution is this
:x = \frac{1 - \sqrt{5}}{2} \approx -0.61803\,39887\dots\,
This negative number seems to have all of the same properties as phi ie. the number squared is itself + 1 (0.381), and 1 / the number is itself - 1 (-1.618).
I don't know how significant this is, but I hear people say all the time that phi is the only number that does this. (Though I'm glad to see this article makes no such claim.)  Aykantspel (talk) 18:26, 29 June 2009 (UTC)
thread_title:  Phi's evil twin? 

message: : \sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\ldots}}}}}} = \varphi = \frac{1+\sqrt{5}}{2}\approx 1.61803\,39887\ldots  —Preceding unsigned comment added by 98.165.243.53 (talk) 21:21, 27 November 2008 (UTC)
thread_title:  Infinite Surds 

message: Recently, the Golden Ratio was linked to cardiac and hand development, in relation to optimal form and function. The full article can be found at http://www.facebook.com/ext/share.php?sid=46890696782&h=VLLLZ&u=9dzAQ
Enjoy, and comment!
Jasoncys (talk) 11:35, 3 January 2009 (UTC)
replies: text: That's a facebook link that leads to a warning page. Dicklyon (talk) 18:41, 3 January 2009 (UTC)

text: Ah, I see that you can get past facebook to the link you probably intended: at journals.tums.ac.ir. Dicklyon (talk) 18:44, 3 January 2009 (UTC)

text: Interesting conjecture.  Too bad there's so little support for it; just speculation.  Is this journal thought to be a reliable source? Dicklyon (talk) 18:54, 3 January 2009 (UTC)
thread_title:  The Golden Ratio Optimizes Cardiomelic Form and Function