Talk:Golden ratio

Diagram

Diagram shows "a" x "a" as a rectangle with about 35% greater width than height. The adjacient text says it is a square which is what "a x a" signifies. Tiddy (talk) —Preceding undated comment added 13:38, 24 July 2012 (UTC)

I don't see a diagram that meets that description. Perhaps your screen is distorted? Dicklyon (talk) 15:20, 24 July 2012 (UTC)

It is in the second box of the first diagram in introductory paragraph. And no, my screen is not distorted. That 35% distortion also shows up on other computers. Tiddy (talk) 02:54, 9 September 2012 (UTC)

Looks square here, using Chrome, FireFox, and IE. -- Scray (talk) 04:16, 9 September 2012 (UTC)

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

Skeptical NY Times article

"Proportion Control" by Steven Strogatz, September 24, 2012... AnonMoos (talk) 13:19, 26 September 2012 (UTC)

Nice. I copyedited a paragraph in the lead section of our article as an excuse to add a reference to it. —David Eppstein (talk) 00:41, 27 September 2012 (UTC)

At least since 20th Century

The text of the article stated that artists and architects used the golden ratio "at least since the Renaissance" for several years starting in 2006, if not before. This was changed, apparently without discussion, to "at least since the 20th Century" in March 2012. The comment on the edit was that there is "no evidence" for Renaissance use. However, the article itself gives examples. Even if the editor is correct, "at least since the 20th Century" is silly, and it would have been better simply to have removed claims as to the length of time the golden ratio has been used, rather than have it say that it is only since the 20th Century. I am reverting this change back to what the article stated before March 2012, namely "Renaissance". 98.229.134.2 (talk) 16:28, 11 November 2012 (UTC)

The article itself does not give any examples of conscious use by artists earlier than Dali. —David Eppstein (talk) 17:19, 11 November 2012 (UTC)

Some of the 2006 attempts to improve that timing, like mine here, were based on the idea that Pacioli promoted the golden ratio as aesthetic proportions. As the article now describes, this idea has been traced to an error; Pacioli didn't do that. The only thing that goes back around there is the Agrippa man illustration, but to say that a pentagram illustrates an aesthetic preference for GR proportions in not supportable; same with da Vinci's illustrations of the solids. So, 20th century may be right. Or maybe 19th, after Ohm's "golden" term got applied, though I don't have an example. Still, this "At east since the 20th century" seems like a poor way to put it. Dicklyon (talk) 17:54, 11 November 2012 (UTC)

The March 2012 discussion is at Talk:Golden_ratio/Archive_5#.22At_least_since_the_Renaissance.22. Dicklyon (talk) 19:11, 11 November 2012 (UTC)

If that is so, then the "at least", etc. should simply be removed. The only reason it is there is that the article originally said "at least since the Renaissance". "At least since the 20th Century" sounds like some kind of joke. like "at least since last week". — Preceding unsigned comment added by 98.229.134.2 (talk) 01:32, 12 November 2012 (UTC)

It's awkward, but it does allow for the possibility that there were earlier cases. Probably it's best just to ditch the whole sentence, and say something more supportable. Dicklyon (talk) 02:08, 12 November 2012 (UTC)

Aughost's christmas present

Today we got to Golden ratio#Geometry looking quite garish, and a bunch of large-scale rearrangement that's hard to review. I think we've rejected that big complicated image before (or something much like it) as being not very informative and way too busy and complicated looking. Aughost should say here what he's up to, and why such big changes need to be made so fast. I think we should revert and consider more incremental changes. Dicklyon (talk) 17:20, 26 December 2012 (UTC)

Binksternet has reverted only the last step in Aughost's changes, leaving most of what I'm referring to. Dicklyon (talk) 17:54, 26 December 2012 (UTC)

Aha, because of holiday festivities I did not see the big changes made by Aughost. I don't think the reader is served by complicated images or convoluted text. We are here to break it down and make it comprehensible as much as possible. Binksternet (talk) 18:17, 26 December 2012 (UTC)

See also Pythagorean tiling and its talk page for past problems of a similar nature with the same user. —David Eppstein (talk) 19:24, 26 December 2012 (UTC)

Structural dynamics

I took out the section "Structural Dynamics", which seemed too odd. Nobody had bothered even to convert it to WP style (heading case, refs, etc.), and it seemed to give too much prominence to one minor occurrence of phi in obscure mechanicals systems, not well described or illustrated or relevant to any reason to think it interesting. Does anyone else think it should go back in? Dicklyon (talk) 22:42, 28 December 2012 (UTC)

I don't care for the section. It seems to be written in a singularly unilluminating manner. If no one can be persuaded to rewrite it, then it should be removed altogether. Sławomir Biały (talk)|

Well, Tibbits has put it back with summary "This is not obscure to anyone with a smattering of engineering or scientific education. Suggestions for improving clarity are welcome." He ignored my suggestions implicit in my statement above, but I agree it probably can't be rescued by anything simple. And yes I do have "a smattering of engineering or scientific education." Dicklyon (talk) 18:02, 3 January 2013 (UTC)

If it's not obscure then it would be covered in a text book somewhere, which should be given as a ref. instead of the journal article that is cited. There are certainly lots of quadratic equations that appear in science and certainly some have solution φ just by coincidence, so it seems to be that including every occurrence is not encyclopedic. There was a similar paragraph I tried to delete recently from the Right triangle article; when you worked out the solution to the quadratic equation you got φ³, but otherwise the connection to the golden ratio was tenuous at best. The golden ratio appears in many popular math books and most of the material is total crap, long since debunked but reappearing over and over to appeal to the kind of folks who want to believe aliens built the pyramids and Mayans knew when the end of the world will happen. The golden ratio is a very interesting number, but material consisting of coincidental connections to other scientific phenomena just make the article appear less reliable. It's like adding to the article on the Philippines that the population is the same as the number of miles from the Earth to the Sun; true enough but ultimately nonsensical trivia.RDBury (talk) 20:07, 3 January 2013 (UTC)

The "obscure physical system" is the harmonic oscillator. It's significance is phi's appearance in time as well as in space. No more coincidental than it's appearance in the line segment division problem. — Preceding unsigned comment added by Tibbits (talk • contribs)

A system of two masses and two springs and a support is a two-mode system, not a harmonic oscillator. The description, without specifying the one-dimension constraint that you have in mind, is obscure. The particular system is itself "obscure" if you don't say why or where it comes up in an important way. An illustration would help, if it's an important system, but probably it's not worth bothering. Dicklyon (talk) 22:27, 3 January 2013 (UTC)

The two masses, two springs and one support are not important here unless they are shown to model an important practical system. We don't need trivial solutions in an encyclopedia. Binksternet (talk) 22:34, 3 January 2013 (UTC)

Well it would certainly help if the section would elaborate exactly how φ appears in the problem, rather than fetishically dwelling on things like page and figure numbers in books that a reader is not very likely to have access to. It isn't much good to tell the reader that the golden ratio appears on such and so page of such and so book. This conveys no useful information. Sławomir Biały (talk) 23:25, 3 January 2013 (UTC)

It's the 31st of 35 problems at the end of a chapter in this book. The Moorman and Goff paper mentions a previous solution in which the golden ratio went unmentioned. So why are they mentioning it now? Hard to see. And it has nothing to do with structural, just simple dynamics. It's not obvious that it can be made into something useful for the article; perhaps a brief observation when a small illustration. Dicklyon (talk) 00:18, 4 January 2013 (UTC)

I think an illustration and brief comment is worthwhile, at least if it's done properly. Sławomir Biały (talk) 01:21, 4 January 2013 (UTC)

I will be happy to rework the description, provide an illustration, and an equation or two. The references can be footnoted. Couple two identical harmonic oscillators. The two degree of freedom system then divides time with two frequencies whose ratio is the golden ratio. — Preceding unsigned comment added by Tibbits (talk • contribs) 03:09, 4 January 2013 (UTC)

That's not even correct. What does it mean to divide time here? And the two frequencies are in the ratio of the square of the golden ratio. Dicklyon (talk) 04:18, 4 January 2013 (UTC)

Yes, the ratio is the square of phi. To understand the division of time, consider the pendulum of a clock. The pendulum is a harmonic oscillator, which divides intervals of time into equal segments. If one pendulum were hung from the end of another, identical pendulum, would they divide time with frequencies in the ratio of phi squared? An example of an engineering problem in which this relationship of two modal frequencies appears is a three-story building, where the second and third floors have the same mass, and where they are supported on columns of equal stiffness. — Preceding unsigned comment added by Tibbits (talk • contribs) 14:36, 4 January 2013 (UTC)

But the two-mode system is not generally going to oscillate periodically like the pendulum. Only very special cases excite one periodic mode and not the other, and you don't get both time divisions at once in any case. Do to the irrational frequency ratio, the motion is in general not periodic. Dicklyon (talk) 18:31, 5 January 2013 (UTC)

The book by Morin cited above by dicklyon contains ten references to the golden ratio. The author lectures (lectured?) on physics at Harvard. Perhaps that addresses the concern about the system not appearing in a text. It also opens the possibility of a more general description of the occurrence of phi in the time domain of dynamic systems. Suggestions are not being ignored. It will take time to learn the syntax of including equations, references, and illustrations, as well as signatures.Tibbits (talk) 15:32, 4 January 2013 (UTC)

Solid matter can be approximated as an assembly (lattice) of point masses (atoms) coupled by springs (bonds), i.e., a multi-degree of freedom system of coupled harmonic oscillators. Texts such as Kittell or Ashcroft and Mermin use the phrase "harmonic potential" for the interatomic energy vs distance relation. It happens that quasi-particles in electronic enviroment of the solid state lattice can exhibit modal phenomena in which the golden ratio appears as the ratio of the first and second energy peaks. The ratio is not simply a numerical coincidence, but is predicted by theory. SCIENCE VOL 327 8 JANUARY 2010.Tibbits (talk) 17:55, 4 January 2013 (UTC)

Trimmed earlier speculation. Included text suggested by dicklyon. Included examples of significant systems. Relegated references to footnotes. Ilustration and equations still to come. Tibbits (talk) 18:16, 5 January 2013 (UTC)

Please fix heading case, put references after end punctuation, including URL in refs via templates such as cite book, and tell us what "mode shape" means (I'm pretty sure it's inappropriate, since the "mode shape" is not different from the modes of any other LTI system). The comments on "division of time" still seem appropriate, as well as separately commenting on period as if it was not obvious from frequency. Dicklyon (talk) 18:22, 5 January 2013 (UTC)

Reviewing the book and paper, I'd say the book is worthless; it's just a bunch of problems cooked up that happen to involve golden ratio in the solution. The paper is more interesting. It would make some sense to show the equation being solved, maybe plot the x1 and x2 for the two modes and for a mixed solution. But not go through the derivation, which anyone interested could easily do. As for the building as an example of this equation, it's not a good one. Dicklyon (talk) 18:43, 5 January 2013 (UTC)

I've taken it out until such time as someone is willing to make a decent section of it. Dicklyon (talk) 22:10, 10 January 2013 (UTC)

A one-word value judgement does not constitute a rational argument. — Preceding unsigned comment added by Tibbits (talk • contribs) 15:03, 14 January 2013 (UTC) The author of one of the references has committed to contributing his version of the discussion. Tibbits (talk) 17:58, 14 January 2013 (UTC)

This has been submitted to dispute resolution. Tibbits (talk) 20:05, 19 January 2013 (UTC)

Could Some One Sort Out the Reference to Plato's Timeaus

As it stands it is vague, and probably irreverent as Plato's Timaeus (as the article states) predates the invention of the concept. The description of the dodecahedron and icosahedron in terms of the golden number is probably fairly recent. What might be better would be a reference to the golden section as the ratio of a side and diagonal of a regular pentagon if any one knows when that was discovered. — Preceding unsigned comment added by 86.27.193.180 (talk) 22:10, 6 January 2013 (UTC)

Not irreverent, but possibly irrelevant. The timeline item is probably intentional vague, to make it correct. Probably you're right that it doesn't belong, since there's no mention of extreme and mean ratio in it (as far as I can tell). Dicklyon (talk) 23:29, 6 January 2013 (UTC)