Talk:Golden ratio/Archive 2

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)
replies: text: I don't see the reason why they made computer monitors 16:10 whereas televisions remain 16:9. Is it to do with the taskbar top and bottom, so one can watch full HD movies and still have the taskbar on screen? Stoney3K 22:38, 24 September 2007 (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)

text: Is that an exact conversion ratio, or an approximation?
For some further trivia, current 35mm Panavision movie prints have an aspect ratio of approximately 2,6:1 (being 35mm Academy with sound with a 2:1 anamorphic lens). That's the golden ratio squared ;-)... Regarding photography though, the classic 3:2 print format for 35mm still photo may be derived from the golden ratio, as it corresponds with the book pages, and would have been easier in print purposes. Stoney3K 22:38, 24 September 2007 (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)

text: I don't think German uses the Greek letter β. In fact.. I don't even think Fuβbol is a word in any language. Did you mean Fußball? oops, forgot to sign RedAugust 06:31, 28 July 2007 (UTC)
replies: text: Yes, I believe so. I have seen the Greek β often used in place of ß for spelling German words. Back in the days of IBM Selectric typewriters, you had to do this. I recall in later years, computers would render the ISO-Latin-1 character xDF ambiguously so you could use it as either β or ß. I doubt many non-Germans can tell the difference unless they see the two characters side by side. =Axlq 16:44, 28 July 2007 (UTC)
thread_title: Fuβbol (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)

text: Another unique and interesting property of \varphi, not mentioned (that I can see) on the main page, is that \varphi^2=\varphi+1.  Perhaps this could be worked into the article somewhere? And perhaps mention the irony of the fact that "the golden ratio" isn't a ratio as such, but an algebraic irrational. 193.122.47.170 20:43, 22 April 2007 (UTC)
replies: text: It is not a unique property and only a slight variant of the defining equation and it is mentioned several times in the article, e.g. under "Alternate forms", "Other interesting properties", in "Relationship to Fibonacci sequence" in a more general form. It is a ratio, but not between whole numbers. −Woodstone 21:05, 22 April 2007 (UTC)
replies: text: According to my calculator's quadratic-solving program, the only solutions to x^2=x+1 are (as already mentioned in this section) \varphi and -\Phi. As the one is the negation of the reciprocal of the other, this clearly indicates that this property is unique to \varphi. 193.122.47.170 14:03, 23 April 2007 (UTC)
replies: text: You're not making sense.  If it's true to two numbers, it's not unique to one.  And it's already in the article that there are two solutions of that quadratic equation.  What more can be said about it? Dicklyon 17:38, 23 April 2007 (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)
replies: text: It's unclear why you say "(almost)" here while at the same time suggesting that a real golden rectangle is possible.  As has been discussed above, this is the most accurate possible golden rectangle that can be clearly delineated in square pixels. It's 144/89 = 1.61797753, off by only 0.000056. For the new one, Inkscape shows me a ratio of 1.61754492, off by 0.00049, almost 10X as much. And by the time the SVG scaling and line thickness and fuzziness are incorporated, there's no telling what it is.  So we've gone from an exact-as-possible golden rectangle to an "almost" one.  Dicklyon 01:23, 12 September 2006 (UTC)

text: That greay rectangle is in the lanscape orientation, and does not show the rectangle as it is depicted in most sources. Usually it is depicted in "portrait" mode (Narrow side on top), and not filled-in. A simple outline on a pleasant color or uncolored would be best. ≈ jossi ≈ t • @ 23:35, 11 September 2006 (UTC)
replies: text: The sources I looked at always had it in landscape orientation, your book-page sources being the exception. Dicklyon 01:23, 12 September 2006 (UTC)

text: Replaced the rectangle as per above, for editors consideration. Ratio 1.618:1 ≈ jossi ≈ t • @ 00:05, 12 September 2006 (UTC)
replies: text: I editted the caption to be consistent with it.  Suggestion, Jossi: can you put more border around it, and equal border all around, so that the shape is not so much confounded by the thumbnail frame?  And should we worry that the golden color will confuse the meaning in the minds of some readers? Dicklyon 01:03, 12 September 2006 (UTC)
replies: text: Border fixed. ≈ jossi ≈ t • @ 02:38, 12 September 2006 (UTC)
thread_title: Gray rectangle

message: Some book refs on landscape orientation:  .  What you got showing portrait orientation? Dicklyon 01:32, 12 September 2006 (UTC)
replies: text: Yes, there are books that show it in landscape orientation. But most contruction diagrams I have show it in portrait mode. Feel free to replace with this landscpe version :Image:Golden Rectangle landscape.svg. IMO, the proportion is better appreciated in portrait mode, but maybe that is just my artist's eye. ≈ jossi ≈ t • @ 02:47, 12 September 2006 (UTC)
replies: text: Well, if you're not going to give us a reference, I guess I have to.  Here's more in landscape format:    Dicklyon 03:07, 12 September 2006 (UTC)

text: OK, changed it, and it's less ugly than the big tall one, imnsho.  At this point, if anyone wants to remove it altogether, I won't object.  I think that the figure has totally lost its point, since it no longer illustrates the shape very exactly, nor in sufficient isolation to allow the shape to appreciated as distinct from the frame around it.  And the color and border also distract from the basic shape. It could be improved by giving it more border still, and if you gave it enough border then a portrait-mode one would even be an improvement. Whatever. Dicklyon 03:15, 12 September 2006 (UTC)

text: Here's another possibility to illustrate the idea of the golden rectangle.  A rectangular painting that actually was designed to be a golden rectangle (or at least is unbelievably close, if I can believe the article The Roses of Heliogabalus), and doesn't have an extra frame line.  But it's still not portrait orientation. And unfortunately the JPEG is not anywhere near the quoted shape; but we could stretch it up to fix that. Dicklyon 03:42, 12 September 2006 (UTC)
thread_title: rectangle orientation

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)
replies: text: No answer?  I can't find any such etiquette quideline.  In fact, Help:Edit summary says "An edit summary should strive to answer the question, "Why did you make this edit?". Providing an edit summary, even if the edit is minor, makes Wikipedia work better by quickly explaining to other users what your change was about."  So if I put a bit of my POV into the summary to help explain why I'm making it, isn't that a good thing?  Of course, if it's too big or complicated to fit, I do bring it up on the talk page.  So am I missing something, or are you guys just making up new rules for some reason? Dicklyon 01:12, 12 September 2006 (UTC)
thread_title:  Edit summaries 

message: These cornerstone ideals of the WP community are being flouted here, both in the editing of this article and on this talk page. The editing of this article has become a nightmare, and the article is suffering as a result. It is time for the combatants to direct their considerable knowledge and competence toward cooperation, with the objective of improving this article to the point where it can be a featured artilce candidate. It is nowhere close to that quality now, in my opinion, and the substantial work since July of adding content and sources is not bringing it closer.
Many of the primary combatants' edits are aimed alternately at pushing his own POV (often subtly, sometimes not) and cutting back the other's POV. Adding so-called factual statements selectively (even with citation) can be a form of POV pushing, as can weakening statements with unnecessary qualifiers, as can promoting or deprecating sources (e.g., "James's analysis demonstrates" versus "Jones asserts that"). I can understand, although not condone, POV disputes over controverial subjects like the War on Terrorism, for example, but what is so controversial about the golden ratio or the explicit references to it in several areas of aesthetics (e.g., architecture, painting, page design)? Although most of the the golden ratio's history is undisputed, why does our History section devote disproportionate space to the fringe areas of dispute? Why is this article the place for a dig at pyramidology; most readers who see that word would interpret it literally as the study of pyramids, not realizing that this prarticular -ology has a derogatory connotation.
This is a primarily a math topic: a ratio is a mathematical relationship. But that does not mean that the history, applications, and cultural significance of this particular ratio should be ignored or downplayed in an encyclopedic treatment.
I hope that other non-combatants who have contributed to this article will express their views on how we can move forward productively. While the combatants are of course free to comment as well, in my opinion they have already expressed themselves sufficiently. Finell (Talk) 08:33, 12 September 2006 (UTC)
replies: text: Well said, Finell. It has become a real nigthmare indeed. I will make efforts not to get upset and not to bring that feeling into play. ≈ jossi ≈ t • @ 09:21, 12 September 2006 (UTC)

text: Same here. Dicklyon 14:26, 12 September 2006 (UTC)

text: My view is that as per NPOV, we need to describe widely held viewpoints, even if these are mistaken, subjective, non-scientific, etc. This specific subject has a huge variety of reliable sources that describe the viewpoints. The article needs to describe these, and that is what we are doing. I personally do not care one way or another, Dick believes that I have a "POV" in respect of this fascinating ratio. I do not. ≈ jossi ≈ t • @ 22:25, 12 September 2006 (UTC)
replies: text: And this is the kind of statement that makes it hard for me to WP:AGF when I see your edits.  I at least admit my POV. Dicklyon 23:59, 12 September 2006 (UTC)

text: My POV is that we need to apply NPOV to this and other articles, as expressed above. I really do not have a "pseudoscientific" POV about this subject as you seem to think. As an artist, typographer and book designer, I look at this subject from an artistic perspective rather than a scientific one... Maybe that is my POV... but it should not be an opposing POV to yours, just different. ≈ jossi ≈ t • @ 00:20, 13 September 2006 (UTC)
replies: text: OK, then we're in total agreement.  We need to apply NPOV even though we approach it with different "perspectives". Dicklyon 00:25, 13 September 2006 (UTC)

text: Sure. That is the spirit. We need to report signficant viewpoints, and attribute them to those that hold them. ≈ jossi ≈ t • @ 00:27, 13 September 2006 (UTC)

text: No, no, no, no, no.... You cannot delete material because you think it is "distracting". If it is a controversy, let's describe it. You could just have done what you asked others to do: move the material to a different section. 04:10, 13 September 2006 (UTC)
replies: text: That's a good way to test and see if anyone cares.  If anyone but you had put it back, we would have learned something.  To paraphrase you anyway, "My action "against obvious consensus" resulted in a much better section that we had before." Dicklyon 04:26, 13 September 2006 (UTC)

text: Just a quck check on the databases I have access to, I found more than 200 sources that describes the pyramids and golden section, and possible explanations. It will take time to research these, but I will start slowly with the most prominent ones. ≈ jossi ≈ t • @ 04:17, 13 September 2006 (UTC)
replies: text: That's consistent with what I've been saying.  The question is what to do about it, since there's no evidence that anyone's been able to find to support any of that pyramidology. Dicklyon 04:26, 13 September 2006 (UTC)

text: I look forward to your improvements on this section.  Dicklyon 15:10, 13 September 2006 (UTC)
thread_title:  Cooperation and civility 

message: It would be extremely helpful if others would jump in with edits or opinions, especially when Jossi and I find ourselves on opposite ends of a 1-to-1 deadlock.  Opinions before we get frustrated with each other would go a long way to preventing our "sarcasm" and such.  Finell, your questions above are very good ones; please do weigh in with suggested changes, or just do it. Dicklyon 14:50, 12 September 2006 (UTC)
thread_title: Plea for help

message: Finell, you ask "what is so controversial about the golden ratio or the explicit references to it in several areas of aesthetics?" and "why does our History section devote disproportionate space to the fringe areas of dispute?"  I think both Jossi and I have provided partial answers to these questions.  We even agreed on a possible resolution, to which you strongly disagreed.  The problem is that history of the golden ratio, starting from Pacioli, is the history of overloading a mathematical concept with divine, mystical, pseudoscientific, and aesthetic properties and wild theories; and the frequent uncritical repetition of wild theories by numerous authors.  Jossi likes to quote them in a way that to me makes it look like what they are saying is implicitly accepted; I've pushed back, and said that if we include such things we need to make it clear that they are just the statements of particular individuals, and try to not imply any connection to objective reality when no such support exists.  For example, historian John Man has written a great book about Gutenberg, but in the section where he claims that Gutenberg's page is proportioned according to the golden rectangle, at the same time that he states dimensions that are in the ratio 1:1.45, and with a footnote that makes it clear just how innumerate he is, he must just be repeating something he heard somewhere.  Jossi has added Man's statements in articles Johannes Gutenberg, Golden canon of page construction, etc., so I figured it would be a good one to add here an example of false sightings.  I would welcome your rewrite of the history section, in collaboration with Woodstone and others here who have less extreme POV than Jossi and I have; and I'll keep my hands off unless Jossi puts something in that I need to react to again. Dicklyon 17:35, 12 September 2006 (UTC)
replies: text: My view is that as per NPOV, we need to describe widely held viewpoints, even if these are mistaken, subjective, non-scientific, etc. This specific subject has a huge variety of reliable sources that describe the viewpoints. The article needs to describe these, and that is what we are doing. I personally do not care one way or another, Dick believes that I have a "POV" in respect of this fascinating ratio. I do not. ≈ jossi ≈ t • @ 22:25, 12 September 2006 (UTC)
replies: text: And this is the kind of statement that makes it hard for me to WP:AGF when I see your edits.  I at least admit my POV. Dicklyon 23:59, 12 September 2006 (UTC)

text: My POV is that we need to apply NPOV to this and other articles, as expressed above. I really do not have a "pseudoscientific" POV about this subject as you seem to think. As an artist, typographer and book designer, I look at this subject from an artistic perspective rather than a scientific one... Maybe that is my POV... but it should not be an opposing POV to yours, just different. ≈ jossi ≈ t • @ 00:20, 13 September 2006 (UTC)
replies: text: OK, then we're in total agreement.  We need to apply NPOV even though we approach it with different "perspectives". Dicklyon 00:25, 13 September 2006 (UTC)

text: Sure. That is the spirit. We need to report signficant viewpoints, and attribute them to those that hold them. ≈ jossi ≈ t • @ 00:27, 13 September 2006 (UTC)
thread_title: History issues

message: OK, I took the messy controversial distracting pyramid stuff out of the history section.  If someone wants to talk about it, put it in a section on pyramids, disputed histories, controversies, or something.  Dicklyon 03:15, 13 September 2006 (UTC)
replies: text: No, no, no, no, no.... You cannot delete material because you think it is "distracting". If it is a controversy, let's describe it. You could just have done what you asked others to do: move the material to a different section. 04:10, 13 September 2006 (UTC)
replies: text: That's a good way to test and see if anyone cares.  If anyone but you had put it back, we would have learned something.  To paraphrase you anyway, "My action "against obvious consensus" resulted in a much better section that we had before." Dicklyon 04:26, 13 September 2006 (UTC)

text: Just a quck check on the databases I have access to, I found more than 200 sources that describes the pyramids and golden section, and possible explanations. It will take time to research these, but I will start slowly with the most prominent ones. ≈ jossi ≈ t • @ 04:17, 13 September 2006 (UTC)
replies: text: That's consistent with what I've been saying.  The question is what to do about it, since there's no evidence that anyone's been able to find to support any of that pyramidology. Dicklyon 04:26, 13 September 2006 (UTC)

text: I look forward to your improvements on this section.  Dicklyon 15:10, 13 September 2006 (UTC)
thread_title:  Pyramids 

message: Finell, your changes to the lead  have good and bad parts.  The Livio quote is much better that what we had.  But starting with the value instead of the definition is not so good.  Definition, then value, then explanations and properties, like we had before, would be my preference. As it stands, the concept of cutting a line segment into extreme and mean ratio looks like an incidental property of the value; it is actually the definition. Dicklyon 15:10, 13 September 2006 (UTC)
replies: text: That would be OK, too, if the summary is generally acceptable to us all.  That's pretty much what we had before, though perhaps too brief.  Would you propose to put that one back, or do you have a new one to propose? Dicklyon
I'm giving it another try now. I'll do it in 2 or 3 edits, so please be patient. Finell (Talk) 16:46, 13 September 2006 (UTC)

text: I pretty much like it, except for the fatty math equation in the opening paragraph, in which the equal sign is used as a verb; this is never a good idea, and looks particularly bad here.  We need to "display" the equation or remove it, in my opinion; it's not really crucial to the definition, which works fine in words, so it can be put later or left for the calculation section. The definition and value are the top items to lead with, not the derivation or explication.  The new paragraph on uses is good; not too waffly, not so specific that citations are needed.  Dicklyon 18:31, 13 September 2006 (UTC)
replies: text: I don't like the look of my inline equation either. Perhaps it can be formatted better. However, in my opinion, equation is the essential definition; that is, the golden ratio is the irrational number, and the rest of it is descriptive, although important. If the article were entitled golden section, I would say that the sectioning of the line is the definition and the ratio is a calculated result. I have to go back to work and can't do anymore for 8-10 hours. Please play nice, everyone! Finell (Talk) 18:52, 13 September 2006 (UTC)
replies: text: You could just as well take the definition to be one plus the square root of five over two.  But historically, the definition is geometric, not algebraic.  See some of the old definitions that I described above in talk.  See if you like the way I rewrote it.   Dicklyon 18:56, 13 September 2006 (UTC)
replies: text: Looking good! ≈ jossi ≈ t • @ 19:17, 13 September 2006 (UTC)

text: I like it too. I tweaked the golden section paragraph and figure caption to coordinate better and was able to eliminate some duplicate text that way. Please see what you think. Finell (Talk) 20:55, 13 September 2006 (UTC)

text: I agree with the statement above tat the sequence should be: definition (geometric, then algebraic), value, explanations (in the sense of usage) and properties. But we discussed about explicitly attributed quotes before and they should be minimised. This is not an article about books about the golden ratio. Surely a lengthy quote does not belong in the intro. −Woodstone 20:37, 13 September 2006 (UTC)

text: Let's see if others express an opinion about the long quote. I don't disagree with Woodstone's principle, but in this case I think Livio's quote says what we want to say as well as it could be said. Finell (Talk) 21:01, 13 September 2006 (UTC)
replies: text: It could be summarized, don't you think? ≈ jossi ≈ t • @ 21:49, 13 September 2006 (UTC)
replies: text: We won't know until someone tries.  I don't think I could express it as eloquently, but if we summarize it we can put it in a bigger font! Dicklyon 02:15, 14 September 2006 (UTC)

text: I did not put that text. I just reverted an anon edit without explanation. ≈ jossi ≈ t • @ 02:27, 14 September 2006 (UTC)
replies: text: Oops, I guess I misread the diffs; I see it was Finell who originally put that in.  The question remains open: what is the situation on golden ratio in nature? Refs? Dicklyon 03:50, 14 September 2006 (UTC)

text: I put in that whole paragraph, including the nature sentence. And I thought Dicklyon approved of that paragraph. My source was Livio, which I am reading (2 chapters to go). That is one area of golden ratio appearances that Livio does not debunk, although most do involbe Fib sequences. As I recall, though, he mentions an eagle's golden spiral flight path (so it can keep a steady eye on dinner) with φ-based angles, and also φ-based angles in the spacing of leaves around the stem (to maximize leaves' exposure to sun, air, and rain), and a few others. Also, Livio stresses the close relationship between Fib sequence and φ. (NOTE: I wrote this reply before I saw Dicklyon's preceding comment, which I discovered when the edit conflict blocked my save.) Finell (Talk) 03:59, 14 September 2006 (UTC)
replies: text: Well, it's true that I did not disapprove of it.  Only after I saw that sentence coming and going was my attention drawn to it, and hence my question as to whether anyone knows a basis for it.  And I did look in Livio already and didn't find any specific support for golden ratio in nature, just the fib stuff and the plant leaf angle stuff, which I see repeated many places but never with any data or reference that would lead to a credible primary source for it.  I've found a few more books and papers that discuss golden ratio truths and fictions, and they usually put the nature stuff as true, but when you read it, it's usually just the fib numbers and the leaf angles again; other sources say the leaf angles are quite variable.  I'd feel better with it if we could find a credible source, not necessarily to reference in the lead, but to follow up with later. Dicklyon 05:12, 14 September 2006 (UTC)
replies: text: Perhaps you would like to take a look at the references that Livio cites for his nature chapter. And there is also the eagle. Finell (Talk) 06:37, 14 September 2006 (UTC)
replies: text: The eagle constant-angle thing is again a characteristic of ANY logarithmic spiral; this defect in Livio of confusing logarithmic spirals in general with the golden spiral in particular has been discussed at length before (see [archives]). I'll take another look at what else Livio says and cites. Dicklyon 06:53, 14 September 2006 (UTC)

text: Do crystals of alluminum manganese alloy count as nature? I realize that the alloy is human made, but their cryatal structure is formed by laws of nature without human guidance. Finell (Talk) 20:30, 15 September 2006 (UTC)
replies: text: I think they're natural enough.  Do you have a reliable source that says they embody the golden ratio?  Most that I've looked at jump from golden ratio in 2D Penrose tilings to 3D quasicrystals without saying whether such ratios are in them or not. Dicklyon 23:12, 15 September 2006 (UTC)
replies: text: I got it from Livio. Finell (Talk) 17:42, 16 September 2006 (UTC)
replies: text: OK, I looked some more and found it this time in the sizes of the steps in the aluminum-copper-iron and aluminum-palladium-manganese alloys.  The earlier bit about Golden Rhombohedra was a construction, not something identified in nature. Dicklyon 17:54, 16 September 2006 (UTC)
thread_title: The lead again

message: Jossi put in "The golden ratio also makes surprising appearances throughout nature." and someone took it out.  I'm a bit skeptical myself, because most of what I see is about Fibonacci numbers, not so much golden ratio.  Can someone recommend a good book on golden ratio in nature so I can see what the thinking is on this? Dicklyon 02:22, 14 September 2006 (UTC)
replies: text: I did not put that text. I just reverted an anon edit without explanation. ≈ jossi ≈ t • @ 02:27, 14 September 2006 (UTC)
replies: text: Oops, I guess I misread the diffs; I see it was Finell who originally put that in.  The question remains open: what is the situation on golden ratio in nature? Refs? Dicklyon 03:50, 14 September 2006 (UTC)

text: I put in that whole paragraph, including the nature sentence. And I thought Dicklyon approved of that paragraph. My source was Livio, which I am reading (2 chapters to go). That is one area of golden ratio appearances that Livio does not debunk, although most do involbe Fib sequences. As I recall, though, he mentions an eagle's golden spiral flight path (so it can keep a steady eye on dinner) with φ-based angles, and also φ-based angles in the spacing of leaves around the stem (to maximize leaves' exposure to sun, air, and rain), and a few others. Also, Livio stresses the close relationship between Fib sequence and φ. (NOTE: I wrote this reply before I saw Dicklyon's preceding comment, which I discovered when the edit conflict blocked my save.) Finell (Talk) 03:59, 14 September 2006 (UTC)
replies: text: Well, it's true that I did not disapprove of it.  Only after I saw that sentence coming and going was my attention drawn to it, and hence my question as to whether anyone knows a basis for it.  And I did look in Livio already and didn't find any specific support for golden ratio in nature, just the fib stuff and the plant leaf angle stuff, which I see repeated many places but never with any data or reference that would lead to a credible primary source for it.  I've found a few more books and papers that discuss golden ratio truths and fictions, and they usually put the nature stuff as true, but when you read it, it's usually just the fib numbers and the leaf angles again; other sources say the leaf angles are quite variable.  I'd feel better with it if we could find a credible source, not necessarily to reference in the lead, but to follow up with later. Dicklyon 05:12, 14 September 2006 (UTC)
replies: text: Perhaps you would like to take a look at the references that Livio cites for his nature chapter. And there is also the eagle. Finell (Talk) 06:37, 14 September 2006 (UTC)
replies: text: The eagle constant-angle thing is again a characteristic of ANY logarithmic spiral; this defect in Livio of confusing logarithmic spirals in general with the golden spiral in particular has been discussed at length before (see [archives]). I'll take another look at what else Livio says and cites. Dicklyon 06:53, 14 September 2006 (UTC)

text: Do crystals of alluminum manganese alloy count as nature? I realize that the alloy is human made, but their cryatal structure is formed by laws of nature without human guidance. Finell (Talk) 20:30, 15 September 2006 (UTC)
replies: text: I think they're natural enough.  Do you have a reliable source that says they embody the golden ratio?  Most that I've looked at jump from golden ratio in 2D Penrose tilings to 3D quasicrystals without saying whether such ratios are in them or not. Dicklyon 23:12, 15 September 2006 (UTC)
replies: text: I got it from Livio. Finell (Talk) 17:42, 16 September 2006 (UTC)
replies: text: OK, I looked some more and found it this time in the sizes of the steps in the aluminum-copper-iron and aluminum-palladium-manganese alloys.  The earlier bit about Golden Rhombohedra was a construction, not something identified in nature. Dicklyon 17:54, 16 September 2006 (UTC)
thread_title: in nature?

message: Dicklyon wrote above, about a paragraph on Timaeus that has since been deleted: 
The cited page does not mention golden, divine, or ratio, but has the mean-and-extreme-ratio concept in this line: "For whenever in any three numbers, whether cube or square, there is a mean, which is to the last term what the first term is to it; and again, when the mean is to the first term as the last term is to the mean-then the mean becoming first and last, and the first and last both becoming means, they will all of them of necessity come to be the same, and having become the same with one another will be all one."  This is a line worth quoting....
If this sentence is referring to the idea of extreme and mean ratio, it would belong in the History section as the first known published reference to what we now call the golden ratio. But I don't think that it is. Plato's conditions are satisfied by any 3 numbers where a/b = b/c. The numbers 27, 9, and 3, for example, satisfy the ratio requirement and the ratio is not φ. In fact, "whether cube or square," which puzzeled me for awhile, may refer to just this sort of sequence, i.e., x3, x2, x. Then again, the condition is also satisfied by any numbers a, b, c where a=kb and b=kc, k being a constant. So I go back to being puzzled by "whether cube or square."  Am I missing something here about Plato's statement referring to extreme and mean ratio after all? Can anyone say what Plato meant by "whether cube or square"?  Finell (Talk) 06:34, 14 September 2006 (UTC)
replies: text: Yes, I agree that I misinterpreted that one.  There was something else from Timaeus before that made little or no sense to me, but you might want to give it another look. Dicklyon 06:49, 14 September 2006 (UTC)

text: I re-checked it.  The old part was from the same paragraph, referring to this same misinterpretation.  It has since been removed from the article, along with the rest of the rubbish in the philosophical section (Summum stuff and other junk).  Let's just hope that section doesn't come back. Dicklyon 00:46, 16 September 2006 (UTC)
thread_title:  Timaeus? 

message: We could really use some specific examples here (2D artworks like paintings), since there's so much non-specific nonsense in this area (as the quote from Livio that Finell took out said).  The "Roses" is one, though I'd love to see a reliable source for its dimensions; so far it is unverifiable.  
As to the page proportion issue, this one also remains ambiguous.  I've been trying to read Tschichold on this (in Dutch and German, unfortunately, which doesn't work so well for me), and Spanish snippet about Rosarivo, but I can't find any actual examples of books with pages or text areas proportioned by the golden ratio.  These guys are very vague about what they say about it, too, citing medieval manuscripts nonspecifically and things like that.  Does anyone have some specific support for the idea that book pages have sometimes (modern or otherwise) been proportioned to the golden ratio?  I did find an article on "Octavo" with all the modern and classic German, English, and Frence paper sizes, and none of them will lead to golden-ratio page proprtions, though the French has one size that gets closest at 1.607.  If you allow enough extra margin in the gutter, of course, any of them could possibly do golden-ratio-proportioned text areas, but as I said I can't find any specific statements of books that do.
Dicklyon 23:26, 15 September 2006 (UTC)
thread_title: In art?

message: I've started a re-organization of the pyramids section, taking it out of "disputed sightings" and including a mathematical part in it, because it has so much more to it than the other sightings.  The source mentioned above provides most of the needed citations, but a few are drawn from other sources as well, so it will take me a while to rediscover and document all the fact details that I marked.  Feel free to mark more or to rework it if some parts of what I wrote seem like opinions or original research instead of facts. Dicklyon 15:17, 19 September 2006 (UTC)
thread_title: Pyramids re-org

message: A bunch of stuff about Summum, including "Further Reading" was added by User:KamiLian, a Summum advocate whose contributions were all about that.  Since this is a cult-like thing, does it belong?  Certainly not in further reading... Dicklyon 00:33, 16 September 2006 (UTC)
thread_title: Summum?

message: I would like to add a new first section, before History, on Terminology and notation. Also, I intend to expand History substantially, at least doubling its length. I got from the library some good source materials on the history, as well as some more Aesthetics material to work in from scholarly sources.
WP already warns, when you open the edit window, that the article is long by WP standards, and it should get quite a bit longer with all the material being added. I think the best approach is to keep everything in Golden ratio for now, so those involved don't have to run all over WP to see all that is being done. However, we may want to consider, when we believe that the material is substantially complete and in good shape, to spin off some of the content to sister articles. The excellent article on Pi (does anyone to do an animated gif like that article has?) and its spinoffs may serve as model.
What does everyone else think?
Finell (Talk) 09:01, 18 September 2006 (UTC)
replies: text: Sounds good. Let's see how large it gets first, and then we can spin-off sections to articles as and if needed. I can creat animated GIFs if needed. ≈ jossi ≈ t • @ 19:11, 18 September 2006 (UTC)
thread_title:  Plans and proposal 

message: I have reordered some sections. The preceding edits by others moved major pieces around, leading to an unattractive article. After the short intro, a short calculation completes the mathematical definition. Then proceeding into history and aesthetics. Then follows the big math section, only for a limited audience. Concluding by the less interesting "doubtful sightings". If the big math section goes first, many people will never reach the arts section.  They will most likely be able to skip over the small calculation section. (The signalled edit conflict appears to have been a vandal reversal.). −Woodstone 20:53, 18 September 2006 (UTC)
replies: text: Yes. I concurr. Much better now. ≈ jossi ≈ t • @ 21:11, 18 September 2006 (UTC)

text: I like it, too.  Putting all the math in one place is problematic. Dicklyon 21:34, 18 September 2006 (UTC)

text: I like it, three. Great job! Finell (Talk) 06:05, 19 September 2006 (UTC)
thread_title:  Structure 

message: Trying to further my education, I looked at the Wikipedia:Manual of Style (mathematics). The Punctuation section requires a period when a formula ends a sentence. By analogy, this would require other end punctuation appropriate to the formula's role in the sentence of which it is a part. I know that Dicklyon has the opposite opinion of style and eliminated the many instances of end puncuation throughout the article's formulas; for consistency, I did the same for a couple that he missed. What do others think? Would failure to follow WP style guidelines be a negative when seeking FA status? What to do? Finell (Talk) 06:42, 19 September 2006 (UTC)
replies: text: I would certainly expect full and correct punctuation in all formulae, whether inline or displayed (for instance, in a list of cases, I would expect to see commas after all but the last, and a fullstop at the end). In all mathematical journals that I have anything to do with, this is always the case, and mathematics is expected to follow the same rules regarding punctuation as if it were ordinary English. I personally would expect the same to hold for Wikipedia, but it might be argued that Wikipedia is not an academic journal ... :-) Madmath789 07:22, 19 September 2006 (UTC)
replies: text: OK, let's change them back; I apologize.  I wasn't aware of that style page.  When I used to do that, I was corrected by technical book editors who preferred it the other way, and I came to the impression that omitting punctuation after displayed equations was pretty standard (because it sometimes looks confusing out there, like in numbers with two decimal points and funny placed other punctuation).  Dicklyon 13:21, 19 September 2006 (UTC)
thread_title:  End punctuation in formulas? 

message: For what it's worth: the Monoliths in the Stanley Kubrick films 2001: A Space Odyssey and 2010: The Year We Make Contact are Golden Ratio Rectangles.{[ID of unsigned post:  06:33, 28 September 2006 User:Basesurge}
:We could do that if we had a source to cite. I will post the question on the user's talk page. Finell (Talk) 19:06, 28 September 2006 (UTC)
thread_title:  Golden Ratio Trivia 

message: The article's long decimal expansion cites  as the source. However, unless I am missing something, I only see about 104 decimal places in that source. What is the source for the expansion that we have? Also, I consolidated the 2 sections having to do with the decimal expansion into one, subdivided in 2 subsections. The Calculation subsection here, which deals only with calculating the decimal expansion, should not be confused with the more general Calculation section at the beginning of the article. Finell (Talk) 19:55, 28 September 2006 (UTC)
replies: text: It has links to lots more digits, such as these 50,000.  I also had independently verified the digits in the article against my own calculation of 10000 (actually, this was more of a verificatin of my code, but in any case no discrepancies were found). Dicklyon 21:58, 30 September 2006 (UTC)
thread_title:  Decimal expansion 

message: When the unverifiable statement "Many painters used canvases proportioned at or closely approximating the golden ratio" was in there, Jossi was happy.  But when I replaced by one that stated the verifiable truth, with references, that the mean painting proportion is much less than the golden ratio, that is said to be "unrelated" and summarily removed.  Seems to me that putting in the truth to temper the fiction is indeed related. And that statement was in the article for a year or so already without complaint, until someone removed it a few months ago. Anybody? Dicklyon 20:19, 1 October 2006 (UTC)
replies: text: A statistical study on 565 works of art of different great painters was done and it was calculated the ratio of the 2 sides of a paintings. Assuming that all the painters under discussion enter in a statistics with equal weights it is shown that the average value obtained for the ratio of the sides is 1.34. This value, determined experimentally is significantly different from the value of the Golden Section F=1.618, which is a theoretical ratio, obtained from an abstract, mathematical theory, which supposedly ought to impress on a painting a supreme harmony. 
Dicklyon 21:31, 1 October 2006 (UTC)
replies: text: The original statement that you replaced did not have any sources. Find a source that claims that artists used canvases using the golden ratio, and you would be welcome to add the rebuttal. Without such claim, there is no need for a rebuttal. ≈ jossi ≈ t • @ 03:39, 2 October 2006 (UTC)
replies: text: It's not a rebuttal.  It's a report of a study by an academician who sought to determine whether the often expressed idea of golden section proportions being good was reflected in actual dimensions of paintings.  The work stands on its own, in a section on golden ratio relative to paintings. It's the only work I'm aware of that addressed this question, which is certainly relevant to this section on use of golden ratio in the arts, even more so in a section in which various uses of golden section are being cited as examples; it is good to make it clear that these are exceptional, not typical cases. Dicklyon 03:58, 2 October 2006 (UTC)
replies: text: Sorry, but you have this wrong. The use of the golden ratio in paintings is not related to the dimensions of the canvas, but the application of golden rectangles to the composition used by the artists. This "work" is singular, and a minority viewpoint, a rebuttal, without a claim, and thus irrelevant. Reverted yet again. ≈ jossi ≈ t • @ 05:33, 2 October 2006 (UTC)
replies: text: Yes, I see that you did.  And then you put it back, rephrased and expanded.  Good job.  Why the change of mind? Dicklyon 06:20, 2 October 2006 (UTC)

text: Twaddle?  Perhaps so.  I'll be the first to agree that the mean is a very poor statistic for characterizing this distribution.  But did you look at the paper (PDF online)?  It includes a histogram of all the values, and it's clear than the median is around 1.25 and that there's no concentration near phi.  But if I state such an observation, it will probably be removed as WP:OR if history is any guide, so I stuck to more direct quotation of the stated summary results.  I haven't found any ohter relevant studies, but this one certainly is relevant to the question of whether the golden ratio is commonly used to proportion paintings, at least in their overall dimensions. Dicklyon 06:44, 3 October 2006 (UTC)

text: If there is anything to be said about the actual use of golden ratio proportions in art, we should find it and include it.  At present, we just have a couple of examples, nothing at all general.  Yet you do see such broad generalities in lots of golden ratio books and papers.  I didn't find any that said canvasses are often propotioned by the golden ratio, but they say things like that it's common in art.  Is it? Dicklyon 07:03, 3 October 2006 (UTC)
replies: text: No, not really. The use of the golden ration is studied and applied in paintings and graphic arts, mainly to composition. The idea of golden ratio canvases, was news to me. ≈ jossi ≈ t • @ 01:58, 6 October 2006 (UTC)
replies: text: The idea of golden ratio in overall proportions of artworks shows up here and there.  One not so reliable source, is this Reader's Digest publication:  which says "the dimensions of paintings frequently conform to the golden ratio."  It's not clear where they get this stuff, but they person who did the quoted study also seems to have encountered it. Dicklyon 03:26, 7 October 2006 (UTC)
replies: text: Reader's Digest is not a reliable publication, in my humble opinion... I would simply dismiss that without feeling too bad about it... ≈ jossi ≈ t • @ 04:34, 7 October 2006 (UTC)
thread_title: Paintings

message: Finell, sorry about the Huntley ref for the bees.  I was shooting sloppy, going by a google book search hit on a page it wouldn't show me.  Thanks for checking.  The other ones were pages I actually did get to read, by the way, but feel free to check those. Dicklyon 22:19, 5 October 2006 (UTC)
replies: text: Everyone makes mistakes. I happen to have Huntley on loan from the library. I don't have the others you cite, nor would I undertake the chore of checking all of the cited references. Finell (Talk) 22:25, 5 October 2006 (UTC)
thread_title: Bees

message: Finell, does Agrippa actually say something about the proportions of the body in that figure?  It seems very unclear what it's getting at, since the body parts don't line up with the pentagram edges whose lengths we know to be related by the golden ratio.  Do you have a source for this caption, other than the wiki article it came from? Dicklyon 06:55, 13 October 2006 (UTC)
replies: text: Just the WP article from which I copied it. I wouldn't want to stand in that position for very long, either (although I wouldn't mind the physique). Finell (Talk) 10:49, 15 October 2006 (UTC)
replies: text: I suggest we take it out then, unless something thinks he can come up with a verifiable connection between the pentagram and some of those body parts, which pretty much don't even align. Dicklyon 16:57, 15 October 2006 (UTC)
replies: text: Unless the author of the caption was misinformed, which I would not presume, the cited work by Agrippa supports the statement in the caption. The work is not in my library. Perhaps someone else can take a look. If the caption is incorrect, other WP articles where the figure and caption are used should also be corrected. Finell (Talk) 21:52, 15 October 2006 (UTC)
replies: text: I'll ask for sources on those other places.  Dicklyon 21:57, 15 October 2006 (UTC)
replies: text: On what basis do you assume that the cited book does not support the statement, here and in the other article? Adding a {fact} tag is more than "asking" for a source when one is already cited. Finell (Talk) 06:59, 16 October 2006 (UTC)
replies: text: The guy who originally added that caption now retracts it as probably unsupportable User_talk:Nixdorf#Agrippa_caption.  I guess I just had a gut feeling, as it made no sense. Dicklyon 22:18, 16 October 2006 (UTC)

text: And here he says he "made it up": User_talk:Dicklyon#Pentagrams_and_ratios. Dicklyon 22:22, 16 October 2006 (UTC)
replies: text: Your gut was correct, AND you followed through to verify what it told you. Good work! Finell (Talk) 10:30, 17 October 2006 (UTC)
thread_title: Agrippa

message: Why the sudden deletion of material without discussing first? ≈ jossi ≈ t • @ 17:55, 18 October 2006 (UTC)
replies: text: Sorry, perhaps I jumped a bit quick after yesterday's comments (see book above).  Please take a whack at it if you think the way I fixed it is not so good.  Basically, I deleted material for which no verifiable support has been forthcoming, and replaced it by something that is verifiable, making the same point that golden ratio is used in old books. That is, the comments about Rosarivo seem to have been misinterpretations, and nobody has seen the original as far as I can tell; per Tschichold, Rosarivo's canon is about a 2:3 ratio, not golden section; several other articles are in need of similar corrections, so please do examine this issue carefully, as I have been trying to do. Dicklyon 18:14, 18 October 2006 (UTC)
replies: text:  "Verifiability, not truth" as per WP:V. We are reporting what Rosarivo said, and that is verifiable by the provided citation. ≈ jossi ≈ t • @ 18:20, 18 October 2006 (UTC)

text:  If there are reliable sources that challenge Rosarivo's "misinterpretation", or provide a competing viewpoint, we should include it. ≈ jossi ≈ t • @ 18:22, 18 October 2006 (UTC)
replies: text: Rosarivo's interpretation is not what is being challenged; we don't even have access to a copy, so we don't really know what his interpretation is.  What's challenged, based on Tschichold, is YOUR interpretation of Rosarivo, which I find to be unverifiable. Please read my comments again and respond to what I'm actually saying and finding. Dicklyon 18:47, 18 October 2006 (UTC)

text: More specifically, I find nothing to suggest that Rosarivo ever mentioned a "golden canon of page construction"; that concept was developed later by Tschichold. And it has nothing to do with the golden ratio.  Neither do I find evidence that Rosarivo's concept of Divina proporción tipográfica refers to the golden ratio.  So everything you've written about Rosarivo seems to be unverifiable, at least by my attempts.  Please correct me if I'm wrong, with quotes from sources. If there's a sentence in the linked Rosarivo summary that you believe helps to verify what Rosarivo did or said, please quote it there with translation, and also say who wrote it if you know.  If you can find any actual Rosarivo quotes, that would be even more useful. Dicklyon 19:08, 18 October 2006 (UTC)
replies: text: It is all there in Raul Rosarivo. ≈ jossi ≈ t • @ 19:17, 18 October 2006 (UTC)
replies: text: You leave me little choice of action if you won't cooperate by citing the evidence you believe to be "in there". Dicklyon 19:22, 18 October 2006 (UTC)
replies: text: You always have a choice. And your choice is always to shoot first and then ask questions. You deleted the material without an attempt to ask a question, and I take exception with that. ≈ jossi ≈ t • @ 19:26, 18 October 2006 (UTC)
replies: text: You have the sequence wrong.  I posted my long talk item last night, in the book section above; you have not yet acknowledged that you have seen it.  Have you?  Perhaps I didn't wait long enough, but if you won't respond to my inquiries with more than a brush off, I feel safe in assuming that more time is not what you are asking for.  Dicklyon 19:55, 18 October 2006 (UTC)

text: One more thing: the illustration of Van de Graaf's construction is also pretty irrelevant, since there's nothing in that method that is specific to golden ratio.  It's a construction for making a text area the same proportions as the page, with twice as much outer margin as inner margin, twice as much bottom margin as top margin, and text area corners on the diagonal of the spread.  That's all it is, nothing related to golden ratio.  Right? Dicklyon 19:14, 18 October 2006 (UTC)

text: No that is a direct quote from Rosarivo, not an interpretation. I received the quote from a friend of mine in Buenos Aires. The text of the quote is "el número de oro o número clave en que Gutenberg se basó para establecer las relaciones armónicas que guardan las diversas partes de una obra". I will see if I can get the exact page number and edition. ≈ jossi ≈ t • @ 21:14, 18 October 2006 (UTC)
replies: text: Any possibility of borrowing the book or obtaining a copy through a good reserach library? Having the entire context first-hand should resolve the issue difinitively. Finell (Talk) 21:53, 18 October 2006 (UTC)
replies: text: Good idea.  It's impossible to know from this third-hand snippet even whether "el número de oro" refers to the golden ratio, and if so, exactly what he is saying that Gutenberg did with it, since it's been pretty well established in available English-language publications and secondary verifications that Gutenberg's pages and type areas were NOT proportioned in the golden ratio. Also, Jossi's reference to WP:V is well worth paying attention to. Dicklyon 23:50, 18 October 2006 (UTC)
replies: text: I have asked for a copy of Rosarivo's book. It may take a few weeks before I get my hands on it. ≈ jossi ≈ t • @ 23:58, 18 October 2006 (UTC)

text: Just trying to get the article back to verifiable information.  I left your book section until I could amass the references and evidence needed to be sure it was unverifiable and incorrect.  And I laid out the evidence.  And you refused to discuss it.  So, what next? Dicklyon 19:55, 18 October 2006 (UTC)

text: I did not add anything, Finell. I just restored a deletion of text that was there for several weeks. ≈ jossi ≈ t • @ 21:11, 18 October 2006 (UTC)
replies: text: My comment was addressed to Dick, not to you, which I just clarified. Dick had said in the previous item that perhaps one day was not long enough to wait for a response to his lengthy paragraph at the end of #Book [posted 05:56, 17 October 2006 (UTC)
replies: text: Which was pointless, since I had already acknowledged and apologized. Dicklyon 23:45, 18 October 2006 (UTC)
thread_title:  Deletion of material 

message: Why this approach, Dick? Do you really enjoy these squimrishes? I do not. It is a bloody waste of time. ≈ jossi ≈ t • @ 19:31, 18 October 2006 (UTC)
replies: text: Just trying to get the article back to verifiable information.  I left your book section until I could amass the references and evidence needed to be sure it was unverifiable and incorrect.  And I laid out the evidence.  And you refused to discuss it.  So, what next? Dicklyon 19:55, 18 October 2006 (UTC)

text: I did not add anything, Finell. I just restored a deletion of text that was there for several weeks. ≈ jossi ≈ t • @ 21:11, 18 October 2006 (UTC)
replies: text: My comment was addressed to Dick, not to you, which I just clarified. Dick had said in the previous item that perhaps one day was not long enough to wait for a response to his lengthy paragraph at the end of #Book [posted 05:56, 17 October 2006 (UTC)
replies: text: Which was pointless, since I had already acknowledged and apologized. Dicklyon 23:45, 18 October 2006 (UTC)
thread_title: Why?

message: I've been trying to check references and figure out what was behind this line from the article (and other articles):
:Rosarivo's work and assertion that Gutenberg used φ (the "golden number" or "secret number" as he called it) to establish the harmonic relationships between the diverse parts of a work, Rosarivo, Raúl M., Divina proporción tipográfica, La Plata, Argentina, "[...] el número de oro o número clave en que Gutenberg se basó para establecer las relaciones armónicas que guardan las diversas partes de una obra" was analyzed by experts at the Gutenberg Museum and re-published in the Gutenberg Jahrbuch, its official magazine. Ros, Vicente, Infodiversidad. Ral Mario Rosarivo o el amor al libro, Sociedad de Investigaciones Bibilotecológicas, Argentina Vol. 7 (2004) Available online (Spanish)
So I finally got a copy of the 1955 Gutenberg Jahrbuch to see what it says.  I've scanned Rosarivo's article, and put it online temporarily for anyone who wants to help interpret it: here.  
In the process, I also took a closer look at that second reference above.  I figured the statement about Rosarivo's work being "analyzed by experts" was just hype for saying they accepted it for publication.  What I didn't realize was that it was pretty much a direct translation out of the Spanish reference, which I find says this (excuse my poor translation):
:(p.49 Raúl Mario Rosarivo o el amor al libro by Vicente Ros)
:(from German) Raúl M. Rosarivo. Divina Proporción Tipográfica. The book of golden typographic module 1:1.5, the module of Johann Gutenberg and of his contemporaries in the proportion 2:3. Translation from the Spanish by Heinz Nieth. Treatment of the German output by Hermann Zapf. Scherpe publishing house Krefeld, 1961.
:(from Spanish) Study on the aesthetic proportions of the typesetter architecture of the Bibles of 42 and 36 lines, printed in Maguncia in 1455 and Bamberg in 1467-8 respectively. In it he demonstrates that Gutenberg had a module different from the well-known one of Luca Paccioli. This study, according to reference of Rosarivo himself, was analyzed by the scholars of the Museum Gutenberg of Maguncia and published in the Gutenberg Jahrbuch, official organ of the Museum, and in the magazine of the technicians of “The Graphical” book of Madrid, and simultaneously in no. 179 of “Graphical Argentina”, organ of the House of Graphic Industries of Argentina.
So, there it is: it's actually quoting Rosarivo hyping himself.  And it says explicitly that his "module" (the 2:3) is not the one of Luca Paciolli (the golden ratio).  On the other hand, Rosarivo's article that I link my scan of above does mention the "Goldene Schnitt" (golden section) and has a pair of "goldene Linie" (golden line) on one of the illustrations, so there may yet be something in it worth remarking on relative to the golden ratio.  Someone who is more fluent in German please help me find it. 
Dicklyon 04:39, 27 October 2006 (UTC)
replies: text: That is very interesting, Dick, but nontheless you cannot remove the material. You can provide sources that he refers to "golden ratio" to be 2:3 and not Paciolli's phi. The fact that he has been widley cited as one that refers to "goden ratio" as it relates to medieval books, is encyclopedic in itself. I don't speak German so I cannot help with the Gutenberg Jahrbuch. ≈ jossi ≈ t • @ 22:12, 28 October 2006 (UTC)
replies: text: Jossi, I believe that you are in the process of obtaining Rosarivo, so that should decide the matter. However, if Rosarvio is talking only about a 2:3 aspect ratio, no matter what he calls it that has nothing to do with our Golden ratio article. Further, if Rosarivo's terminology misled others into writing that Rosarivo was using the (i.e., our) golden ratio, that doesn't make it so. I do understand the principle of "verifiability, not truth", but that can only be carried so far. Surely it is not encyclopedic to perpetuate demonstrable falsehoods even if uttered by otherwise reliable sources. No other encyclopedia does that, and I cannot imagine that WP intends to make itself a laughingstock by being the first to do so. Am I missing something here? Finell (Talk) 03:42, 29 October 2006 (UTC)
replies: text: I don't think anyone is arguing for including demonstrable falsehoods, but "the material" by and about Rosarivo fits better in other articles, since, as it now clear, it is pretty much unrelated to the subject of this article except via his choice of adjectives equivalent to "golden" and "divine". Dicklyon 04:04, 29 October 2006 (UTC)
replies: text: OK. ≈ jossi ≈ t • @ 15:47, 30 October 2006 (UTC)
thread_title: Books and Rosarivo

message: We still have stuff in the lead like "many artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle" which has already been denied and debunked for the case of paintings; do we have something that it definitely applies to, or something we can cite?  And the unsourced statement about occurrences in nature; that's been long enough looking for a citation that I think I'll take it out now.  Who knows what that first part refers to?  Is Le Corbusier about all? Dicklyon 23:52, 14 November 2006 (UTC)
thread_title: Still speculative stuff in the lead

message: "This illustrates the unique property of the golden ratio among positive numbers, that..."
Given that there are infinitely many positive numbers whose fractional parts are their multiplicative inverses, does anyone else find this misleading? Should it be specified that the golden ratio's unique property is having a multiplicative inverse one less than itself? Otherwise, what of the silver ratios? Namely, the positive roots of quadratics of the form
x^2 - nx - 1 = 0,
where n is natural.
--Johngalt7777777 05:43, 20 November 2006 (UTC)
replies: text: I don't see how it's misleading.  What follows the "that..." is the equation that defines the unique property.  Dicklyon 06:22, 20 November 2006 (UTC)
thread_title:  Misleading Phrasing 

message: I found this book on the metaphysical meaning of the Golden section in Plato and Pythagorean sources, has anyone else seen it yet? http://www.attan.com/ratio.pdf  -"Pythagoras, Plato, and the Golden Ratio"-
It is a complete book released for download by the author --Attasarna
:I just took a peek. At 23 pages of text, it is more a pamphlet than a "complete book". It has an ISBN number, but that number is neither in the Library of Congress catalog nor in Amazon's database. The first sentence by the author (after the quoted paragraph) contains two errors that any junior copy editor would have caught; they are not the last such errors. The author confuses Phi with phi. I could not, through a few quick searches, find any information about the author; he has no publications in the Library of Congress catalog. The graphics appear to have been cut and pasted from various different sources, including some obviously scanned from printed publications, all without credit. I see nothing that would qualify the pamphlet or its author as a sufficiently reliable source to be cited on Wikipedia. While the pamphlet is available for downloading at the URL that you gave, downloading is inconsistent with the strong copyright notice on the title page; it is therefore not available for "free use". Finell (Talk) 03:11, 22 February 2007 (UTC)
replies: text: Thanks, Finell.  I was about to revert those links when you beat me to it.  This editor likes to link that site, but has denied that it is his own.  Certainly does not appear to be what he says, however. Dicklyon 03:24, 22 February 2007 (UTC)
thread_title:  Free use complete book on Golden Section 

message: Quote from lead:
:At least since the Renaissance, many artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing.
The above claim is easily attributable to numerous reliable-looking texts by well reputed authors; all the same other reliable sources deny it or at least point to an astounding lack of primary sources prior to the time of Theodor Fechner stating or demonstrating that the golden ratio is used in art or architecture. I here take "golden ratio" to mean a specific principle consciously applied, though not neccesarily the specific geometric construction or the resulting irrational ratio. A dynamic balance obtained by placing picture elements a bit off the centre is of course very common, as is pleasing-looking rectangular picture frames and the like. It is well documented that Renaissance architects did use the so-called "harmonic port", a rectangle of proportions one-to-squareroot-of-two, i.e. 1 : 1.41 as opposed to 1 : 1.61. The harmonic port is used today in the European A4 paper format.
Would anyone object to a more careful statement in the lead, perhaps like this:
:At least since the end of the 19th century, many artists and architects have proportioned their works to approximate the golden ratio, e.g. in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio, believing this proportion to be aesthetically pleasing. Golden proportions can be found in works from earlier periods, and many sources claim that such proportions were used deliberately in the Renaissance, or even in Antiquity.
--Niels Ø (noe) 11:07, 15 March 2007 (UTC)
replies: text: I expect you'll get some objections; we'll see.  I would reckon that even "At least since the end of the 19th century, many artists and architects have proportioned their works..." is a stretch.  I haven't seen much evidence for this "many" claim; seems more like a "few".  Do you find some support for this? Dicklyon 23:29, 15 March 2007 (UTC)
thread_title:  Use in the Renaissance 

message: A section was added to state that φ has one of the worst approximation speeds in the rationals. It mentions the successive quotients of Fibonacci numbers to show this. However, it is not explained why there cannot be better approximations than those quotients. −Woodstone 21:05, 22 April 2007 (UTC)
replies: text: It's a well known property of continued fractions and is explained in the linked article on Convergent (continued fraction). Dicklyon 23:13, 22 April 2007 (UTC)
replies: text: That the continued fraction converges slowly may be true, but that does not imply that there cannot be better rational approximations. −Woodstone 19:57, 23 April 2007 (UTC)
replies: text: Yes it does. The continued fraction convergents (and some other fractions derived from them which don't affect the result for the golden ratio) are known to give the best possible rational approximations. See continued fraction, under "semiconvergents". —David Eppstein 20:04, 23 April 2007 (UTC)

text: Also this recent edit actually expands on a remark about rational approximation in "Other interesting properties".  These should be rationalised.  (abysmal pun intended)   Since it is covered elsewhere I would be in favour of reverting it.  The page is already a bit of a mess - far too many random factoids.  Andrew Kepert 02:13, 23 April 2007 (UTC)
replies: text: Go for it.  If it's already mentioned, it should be integrated, at best, or just reverted. Dicklyon 03:15, 23 April 2007 (UTC)

text:  I don't see this specific fact mentioned anywhere else(I checked the article above and some others) but agree this is not the place for it. I will move it to the continued fraction article and make a link to it.Ricardo sandoval 04:08, 23 April 2007 (UTC)

text:  Just changed the link. The link in the "worst case" and the link in the "approximation theorem" seem disconnected. With no reference to φ on the second. Ricardo sandoval 19:14, 24 April 2007 (UTC)
thread_title: Slow approximation by rationals

message: Recently I was playing with Perl on the laptop and started toying with the question of what a closed loop would look like if divided into bands which have sizes according to the golden mean ratio.  So starting with a loop with one black band of size φ and a white band of size 1, divide the black band into 1/φ (black), 1/(φ**2) (white), 1/φ (black), i.e. like one side of a pentagram.  Repeat with for all bands of the next largest size (1), and the next (1/φ), etc.  The result is a figure with all bands of one color being the same size, and all bands of the other color either longer or shorter than that by a factor of φ, and the number of those bands (long, short, long+short) are all Fibonacci numbers.  What's more, the pattern of long and short bands is also the sum of the preceding two steps.  Written as a code (short=0 or 10, long=1 or 110), these form a simple L-system (example 1 or 2 from that article), a string where every interval between integers not occupied by an integral multiple of the golden mean is represented by one character, and the others by the other character.  Taking every kth digit of this string yields a pseudoperiodic tiling, and the closer k is to an even multiple of φ (21, for example), the longer the runs of 0s and 1s.  Could someone point out a reference that leads in this direction?  (not just for curiosity, but also so some of this can be put into the article without violating WP:NOR) Mike Serfas 20:34, 25 April 2007 (UTC)
thread_title: Fibonacci numbers from the golden mean (and back again)

message: What do you guys have against  as a source of digits of golden ratio?  How is this website worse than the other one with only 20000 digits.--BorisFromStockdale 19:11, 5 May 2007 (UTC)
replies: text: It's someone's personal site, essentially anonymous, non-authoritative and unsourced, and contains no information that's encyclopedic or useful in extending the content of this article; we already have way more digits than anyone has a possible use for, as well as a description of how to compute more.  If it was a discussion of how to compute those digits, with code, and said by whose authority we should believe it, then maybe it would be useful. Dicklyon 22:18, 5 May 2007 (UTC)
thread_title: Website:[http://abrau.durso.googlepages.com/mathematicalconstants]. 

message: IANAM, but you can calculate 1/\varphi with the following iteration, which is not in the article:
: x_{n+1} = \frac{1}{1+x_n} (starting with any x != -1)
Starting with x=1, it takes around 34 iterations to converge to 1.61803398874989, while Newton's method on x^2 - x - 1 needs only 6 iterations! 
However, given a crazy starting value like 1e10, this method still requires only 34 iterations to converge (the last digit is corrupted, note), while Newton is only at 1.66707382493846 after 34 iterations.  In fact, it converges from any starting point in the same number of iterations.  Uncoolbob 15:18, 14 May 2007 (UTC)
replies: text: Actually, it also does NOT work if you start with -2, or -1.5, or an infinite number of other negative starting values.  It's also a very expensive calculation to get many digits with, since it requires a full bignum division for each step, which adds only a fraction of a digit each time.  It is much easier to compute big fibonacci numbers, which is quick, and then do a single bignum division. Dicklyon 00:19, 13 May 2007 (UTC)
replies: text: Good call - I had not tried -2 or -1.5.  Also, I guess this iteration is equivalent to the continued fraction at the start of this section of the article, so in a sense this is superfluous. Uncoolbob 15:18, 14 May 2007 (UTC)
thread_title:  Calculation by iteration another way 

message: The reason I took out this tidbit, calling it unsourced, is that I read the refs and only found these two things about the golden ratio in the first and second refs, respectively:
* Enthusiasts for “the golden ratio” φ have claimed to see it in the proportions of classical architecture and art, and it was  very consciously used by the 20th century architect Le Corbusier.
* The series has many interesting features, including the fact that the ratio of each number to the preceding one tends towards 1.618, the so-called golden ratio. You can find this ratio, and shapes and patterns derived from it, everywhere in botany, physiology, architecture and, if you believe Elliott Wave Theory, in the stock market.
And the Elliott wave principle article doesn't say much about it either, just: 
* The Fibonacci sequence is also closely connected to the Golden ratio (1.618). Practitioners commonly use this ratio and related ratios to establish support and resistance levels for market waves, namely the price points which help define the parameters of a trend.
The second ref above, talking about the Batchelor guy mentioned, says: 
* Professor Roy Batchelor, at the Cass Business School, is a braver man than I. Unconvinced by the idea that market movements might be determined by a sequence of numbers uncovered by a thirteenth century mathematician, he crunched all the daily movements in the Dow Jones index from 1914 to 2002 before concluding: forget Fibonacci.
This Elliot wave stuff is much more about Fibonacci numbers, and the golden ratio barely gets a mention.  This snip to go back to where it came from.  Or if the golden ratio really is used in investing, we should find a source that says so, and get some verifiability into what this snip says. Dicklyon 02:22, 13 May 2007 (UTC)
replies: text: But Fibonacci number doesn't have a "disputed sightings" section, and this does... More to the point, on the previous page from the one where you found the bit about Le Corbusier (that is, on p.9 of the Batchelor paper), you will see "All textbooks in technical  analysis devote considerable space to description and discussion of these ratios. For  example, Murphy (2000) asserts that 0.5 and 0.618 are the key ratios for determining  target prices in retracements." Which seems to be almost exactly the claim in the snippet, and relates much more closely to the golden ratio than to Fibonacci. And further the part about "all textbooks" (by someone who doesn't like this theory!) seems a strong claim for notability of such theories. The fact that these other guys mistakenly talk about Fibonacci when they really mean the golden ratio doesn't mean we have to follow them in doing so. —David Eppstein 04:31, 13 May 2007 (UTC)
replies: text: OK, my quick search did miss that 0.618 bit.  But let's be careful and not say anything beyond what the refs support.  It would be better if the support for the ratio being used wasn't coming from the same guys who claim to be debunking it; that's too self-referential, isn't it?  I'll re-check when you rewrite it. Dicklyon 04:36, 13 May 2007 (UTC)
replies: text: Hey, at least I included some sources and skepticism! The guy who put it into Fibonacci number didn't. I'll see what I can find. —David Eppstein 04:56, 13 May 2007 (UTC)

text: I added the disputed paragraph back in again, with more sourcing. If you go to the source I added (Osler), you will discover that she also uses the phrase "Fibonacci number" to refer to a relationship that is more properly described as the golden ratio (the supposed 38.2% and 61.8% pricing support levels). But she does seem to support exactly the claim made in the disputed paragraph. I moved the Elliot wave stuff to a less prominent position as it appears to be related but not quite the same. Please me know what you think of it now. —David Eppstein 16:20, 13 May 2007 (UTC)
replies: text: Thanks.  I tweaked it a bit, too, and I think that now it's OK, since you found those sources. Dicklyon 19:33, 13 May 2007 (UTC)
replies: text: You're welcome, and thanks. I think your tweaks are an improvement, so for now I guess we can leave it as is. —David Eppstein 20:21, 13 May 2007 (UTC)
thread_title: Investing

message: Would anyone be willing to simplify the language in the article? For those who are curious about the golden ration yet are less mathematically inclined, the article is difficult to read and hard to comprehend. I include myself, to be honest. I find the article's math to trying to read through. And at the end of it all, the golden ratio still seems rather elusive. Any help for math laypeople? --Bentonia School 17:19, 23 May 2007 (UTC)
replies: text: Give us a clue where it gets hard.  Do you understand the lead OK?  Do you know what is meant by larger, smaller, and sum?  by ratio? irrational? square root?  Decimal fractions?  Letters standing for quantities in algebraic expressions?  At what point do you think a more elementary explanation would be helpful? Dicklyon 05:02, 24 May 2007 (UTC)
thread_title:  Simplification 

message: This article is 58k, almost double the (theoretical) recommended size.  A split Phi versus Golden ratio was proposed above, but I think that's a bad idea because they're synonymous terms (besides, Phi is taken).  But as the Simplification subsection above suggests, there's a huge difference in audience - is the reader seeking a technical mathematical article, or a culture and history article?  Nearly the entire table of contents is made up of sections split into "mathematics" and "aesthetics".  I'd suggest two articles, Golden ratio (mathematics) and Golden ratio (applications), each referring to the other in summary style.  The latter category would talk about pyramids, biological spirals, paintings, etc. --- any point where the math you need to know is basically that some measurement works out to roughly 1.6.  Since biological applications can involve more complex mathematics if you try to work out plant spirals in terms of morphogens or packing efficiency, and they don't fall into a historical scheme, it's also possible a third article Golden ratio (biology) would turn out to be desirable. Mike Serfas 17:04, 24 May 2007 (UTC)
replies: text: There are already 12 articles in :Category:Golden ratio, so I don't see that one or two more would hurt. And I agree that separating the content will likely better please the users who are there for the aesthetics and put off by the technical math. But I think that, rather than just splitting into two, it might make more sense to use summary style for the main article and split out into separate articles anything long enough to require subsections. I think there's enough material to support as separate articles Golden ratio (architecture) (the main article's architecture and Egyptian pyramid subsections), Golden ratio (aesthetics) (the rest of the aesthetics subsections, with an abbreviated description of the architectural connections), Golden ratio (geometry) (the main article's geometry, Ptolemy's theorem, pentagram, and mathematical pyramid subsections, plus better linkage to Golden rectangle, Golden angle, and Golden spiral); Golden ratio (number theory) (rest of the mathematical content, including the "calculation" section, plus better linkage to Golden ratio base. —David Eppstein 17:46, 24 May 2007 (UTC)
replies: text: I don't think a split into more than two is warranted at this point.  It makes sense for one to be the mathematical aspects, and the other to be all the other stuff, whatever you want to call it.  Separating architecture from aesthetics makes no sense. Dicklyon 18:23, 24 May 2007 (UTC)
replies: text: The point of separating architecture from aesthetics is to deal with the pyramid stuff, which is certainly architecture but not really aesthetics. —David Eppstein 18:33, 24 May 2007 (UTC)
replies: text: Well, that could be argued either way.  There's no evidence that any ancient pyramid was ever architected with the golden ratio in mind, and plenty of evidence to the contrary.  I wrote that section, mostly, and it's mostly mathematical, actually.  That's an example of why it will be difficult to do the split.  Either the mathematical part will be polluted by the pseudo-science stuff, or that aeastetics/architecture stuff will get pretty mathematical.  Dicklyon 18:47, 24 May 2007 (UTC)

text: I agree with Finell, in a preference to not split the article. Dicklyon 22:11, 24 May 2007 (UTC)
thread_title:  Split this article 

message: I tracked the wrong digit to this random act of vandalism.  The next editor, User:Ricardo sandoval should have looked at the edit immediately before his, before doing an edit that masked it from easy discovery; but he didn't, so we missed it. Dicklyon 17:36, 8 June 2007 (UTC)
thread_title: Bad digit

message: The golden ratio here is WRONG!!!
The golden ratio is actually
\varphi = \frac{16}{9}\approx 1.77777\,777\,...
--Onekopaka 04:27, 10 June 2007 (UTC)
replies: text: Well, if by golden you mean causing people to spend lots of money on wide-screen TVs... —David Eppstein 04:46, 10 June 2007 (UTC)
replies: text: Sounds like a good new article topic:  golden rule ratio, 16:9, because he who has the gold makes the rules. Dicklyon 05:38, 10 June 2007 (UTC)
replies: text:  LOL! ≈ jossi ≈ (talk) 05:47, 10 June 2007 (UTC)
thread_title:  WRONG!!!!!!!!!!!!!!!!!!!!!!!!!