# Talk:Rule of thirds

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## Untitled

This page uses the second person, which may be acceptable, but probably isn't. I'm not changing anything because I haven't read the editing guidelines, so I don't know if this really is acceptable or not.—Preceding unsigned comment added by 67.161.35.195 (talkcontribs)

## Golden Ratio?

The rule of thirds has little if anything to do with the golden ratio.

In simple terms: 0.618... != 0.666....

The only reason to cite the golden ratio is for the usual pseudoscientific reasons: trying to find "scientific" or "objective" backing that isn't there. Especially given the wording ("based on the theory of the golden ratio").

It's certainly possible that whoever came up with the rule of thirds was an idiot, but that seems unlikely considering how well it works. So I'm guessing the golden ratio hooey was added later.

At least in the golden ratio page, it says "is said to be roughly...." 69.107.70.159 17:29, 5 March 2006 (UTC)

The rule of thirds is not as such derived from the golden ratio, but it certainly is an approximation of it, It is descirbed as “a sloppy approximation of the Golden Ratio” by Datta, Joshi, Li & Wang, 2006 (¶ 2.3). The golden ratio (√5+1)/2 would demand a 3.23:2 or 4.31:3 ratio rather than the common photograph ratios of 3:2 and 4:3. In fact, a photograph compliant to the 1:((√5+1)/2) ratio can also be divided according to the golden ratio:
You take an image with that ratio and for my convenience, let's say it has a landscape orientation. Draw two vertical lines in the rectangle, one at ((√5+1)/2)-1 and the other at 1. The horizontal lines are successively found by drawing a bisector from a top and a bottom corner, and letting the horizontal line cross through the point where the bisector crossed the nearest vertical line. Hope this makes sense. Either way, that is dividing the image using the golden ratio. If you would draw the rule of thirds over the lines you've just drawn, you'll see that Datta et al. (2006) cited above had put it quite accurately.
Further, I disagree with you on "how well it works" since "anywhere near" the strong points is sufficient; that is not in any case specific enough. The only argument the rule of thirds holds is that it is an excellent guide to help beginners avoid making basic mistakes such as placing the horizon in the vertical middle or a subject in the centre of the image. Eddyspeeder 22:24, 23 May 2007 (UTC)
I don't know how old most of you are, or how much experience you have, but when I grew up with photography well over 50 years ago, the "Rule of Thirds" wasn't even known. The "Golden Ratio" however was WELL known. Whenever discussing with others how to visualize the Golden Ratio to better compose their photos, we'd just tell them, "Imagine a tic-tac-toe grid dividing the image into 3rds, and putting your subject where the lines intersect, that should get you close enough to the Golden Ratio". Surprise!! The origin of the "Rule of Thirds". Camera makers and instructors adopted this as an easy explanation for simpletons.
Retro-interrupt: sorry, rule of thirds was known and used in landscape painting as early as 1845, as new ref in article shows. Your recollection is therefore moot, don't you think? Dicklyon 18:51, 6 July 2007 (UTC)
Sorry, but I cannot find any photographic reference which states that the rule of thirds was based on the Golden Ratio. Your "evidence" fails to qualify as either unreferenced speculation or as original research. You must provide a reference for an unsupported statement other than your vague recollections of something you heard fifty years ago. I have photography books older than you and none says the golden ratio was the origin of the rule of thirds. -- Moondigger 16:11, 6 July 2007 (UTC)
Go ahead, perpetuate some misinformation just because YOU can't find it. For those that know more than you from LIFE EXPERIENCE, here's a better composition layout based on the Golden Ratio (the origin of the Rule of Thirds) to undo all the damage that simpletons have done to art and photography over the years with their simplton's "Rule of Thirds". http://images.wikia.com/scratchpad/images/a/a7/Grids.jpg One of the new compositional overlays available on any Canon camera that supports the programmable CHDK overlay.
I have been doing photography for 20+ years. You can speculate all you want, but that doesn't change the facts. Wikipedia has a policy against unreferenced statements and original research. You'll have to provide an acceptable reference if you want the statement to stand in the article. -- Moondigger 16:28, 6 July 2007 (UTC)
How about this reference then? *I* started that damned "rule of thirds" nonsense because I couldn't explain the Golden Ratio to idiots like you that long ago. And now I'm trying to UNDO that! Got it? (Fool)
Even if that were true, it would still violate Wikipedia's original research policy. And your tone violates other policies as well. -- Moondigger 16:45, 6 July 2007 (UTC)
What a moron. If the Wikipedia rules told you to go out to kill someone every day you'd probably do that too. Try living somewhere other than in cyberspace for a blast of realty some day. You sorely need it. I'm done trying to educate the clueless. (At least here.)
Let me be clear, then. I do not oppose your edits simply based on policy. I believe the statement that the rule of thirds originates from the golden ratio is false. One is a sloppy approximation of the other, to be sure. But a natural consequence of the human talent for pattern recognition makes many people assume causation where there is really only correlation. That's what's going on here. Therefore we'll need something more than speculation that the golden ratio was the origin of the rule of thirds to support its inclusion in the article. -- Moondigger 17:03, 6 July 2007 (UTC)
No, let ME be clear. When I was telling others over 50 years ago how to approximate the Golden Ratio by dividing up their photos by a tic-tac-toe grid, this was NOT some stupid "spectulation" or the plan to get some idiot trying to find cause and effect of pattern recognition on a Wiki page 50 years later, it was MY WORDS. Go find some other "living in your brain" fight. I'm done with you.
You telling people 50 years ago that the rule of thirds approximates the golden ratio is one thing. Stating that the golden ratio is the origin of the rule of thirds is another thing entirely. When you understand the difference between those two statements, stop back and we can continue the discussion -- particularly the parts about original research and unsourced statements. Thanks. -- Moondigger 17:25, 6 July 2007 (UTC)

Wow, you are a clueless twit, aren't you. THERE WAS NO RULE OF THIRDS until people were told how to approximate the Golden Ratio by using that method, because it was easier to try to explain it that way to idiots like you! How f'n dense can they get online? Enyoy your cyberlife. I have better things to do, with people that can actually think logically.
For the record, your replies here are PERFECT example of why we had to invent the "Rule of Thirds", Is it any wonder why we just gave up? It would always go something like this: You, "But I don't understand?" Me. "It's based on the Golden Ratio because everything in nature is based on the Golden Ratio." You, "But how does that relate to the rectangle in my look-through-my-camera thingy?" Me, "You have to put your subject nearer to one side, according to how that rectangle would be divided by the Golden Ratio." You, "But but ... I don't know where that is in my viewfinder thingy!" Me, "Okay, let's play tic-tac-toe, see this shape?" You, "Yes, but how do we play tic-tac-toe?" Me, (now getting enraged and trying to remanin calm with the idiot), "That's not important, what's important is that grid of 2 lines crossing 2 other lines, see where they intersect?" You, "yes, but ..." Me, "Well, now try to imagine that grid over the scene in your camera's 'viewfinder thingy'." You, "But there is no tic-tac-toe game in my camera!!" And so on and so on and so on, until we finally gave up trying to explain something to a moron like you.
More speculation, this time about whether I understand what the golden ratio is. Is there anything you can contribute that isn't unsourced speculation? (For the record, I understood what the golden ratio was before I ever took up photography or learned about the rule of thirds. However I did not make the mistake of assuming the golden ratio was the origin of the rule of thirds when I did.) -- Moondigger 18:02, 6 July 2007 (UTC)

Settle down guys. The only thing that matters here is what you can find sources for. Without a source, the Golden Ratio connection is out. Dicklyon 17:32, 6 July 2007 (UTC)

I hate backing up loudmouthed bigots. Anyway, on a completely unrelated note... I'm pretty sure the rule of thirds is a sight older than the advent of photography. It's not a photographic invention, it's one derived from art and architecture and ultimately, nature (via Fibonacci et al and the Golden Mean, or golden spiral, or phi, or golden ratio or call it what you will, it's nothing new..) the earliest practitioner I can think of was Michaelangelo, but the idea then was heavily contrived and mathematically exacting. Imagine the 19th century photographer, a lazy scientist to start with, out and about with his humongous plate camera and tripod – the last thing he wanted was to be further encumbered with an abacus, slate and chalks, so the approximation of the ratio (eventually) became common compositional practice. I jest, but it's basically like that. With all the time in the world, an easel, canvas and pencil, you can do it mathematically. With just a fraction of a second and one eye shut, it's not so easy to be so precise. A reliable source might be tricky for what is, in effect, casual convention based on a mathematical analysis of the harmony and balance inherent in nature, but I'll have a look. mikaultalk 18:08, 6 July 2007 (UTC)
BTW, the anonymous editor has now violated 3RR. -- Moondigger 18:02, 6 July 2007 (UTC)
You have to give a warning on his talk page before it counts as a violation. Hopefully with my recent edit with reference he'll start to see how this works. Dicklyon 18:04, 6 July 2007 (UTC)
I didn't know exactly how the 3RR enforcement worked. In any case, I like the reference you found to the rule of thirds, and the image you added to the article. I wonder if he'll return now and tell us that he "translated" the golden ratio into the rule of thirds prior to 1845... -- Moondigger 18:12, 6 July 2007 (UTC)
24 hour block applied anyway. Even without the warning, he deserves one for violating WP:CIVIL and WP:NPA. 18:08, 6 July 2007 (UTC)

ah, cross posting, sorry :/ mikaultalk 18:09, 6 July 2007 (UTC)

A connection to Golden Ratio seems to have been posited by this guy in 1986, though the Dondis book he references for it does not mention the rule of thirds, but only the golden ratio (as far as I can tell; I've ordered a copy to look further). I wouldn't mind seeing a mention if it was tied to references and properly attributed, but it probably doesn't belong in the lead if anywhere. I agree with Mick that the term didn't originate with photography, but I'm skeptical as to whether it originated as an approximation to the golden ratio. The 1845 source I added certainly doesn't hint that direction. Dicklyon 18:14, 6 July 2007 (UTC)

This is interesting in that it ties the GR with art and painting, which is the pont I was trying to make. Still nothing in the way of a reliable souce yet. mikaultalk 18:29, 6 July 2007 (UTC)
Based on what I have read on the subject, the connection is correlational when it is mentioned at all -- not causational. Back to the pattern recognition thing. The golden ratio is sorta close to 2:1, therefore they're "related." It's like the folklore about "ring around the rosy" being about smallpox or some other infectious disease. Because one can make a connection between the words of the song and some of the symptoms/characteristics of the disease, people speculated that the song was actually about the disease. Later this came to be accepted as fact in popular culture, even though it's false.
I could be wrong about the rule of thirds... perhaps there is some reliable reference that states the golden ratio as the origin of the rule of thirds. But I haven't seen one, and until one is found that amounts to more than simple speculation, the article should stand without the speculation. Thanks... -- Moondigger 18:36, 6 July 2007 (UTC)
Maybe there is such a ref, but sincerely doubt it. I can find a fair number of perception-based psychological sources, usually in the form of studies like this one, which draw a distinction between the golden ratio and the rule of thirds (or "thirds ratio") and conclude that people prefer the look of the golden ratio in everything from art to basic geometry <sarcasm>(surprise!)</sarcasm>. This would appear to support your contention that there is no direct correlation between the two, which may be the case in terms of written documentation, but I'd say there was ample pictorial evidence to support the claim that the thirds ratio is a dumbed-down golden ratio, informally handed down to photography from the classical arts in a form which was close enough to guide the uninitiated without baffling them with applied mathematics. It's surely fair to say the latter preceded the former and was a means of achieving the same end without all the attenuated scholarly learning and – most importantly – without the use of a calculator. In this respect, the link I posted yesterday may serve as a ref for a watered-down statement to the effect that there is a clear correlation between the two, although no formal link has ever been established. Quite how the rule of thirds spontaneously generated itself with the advent of photography, I guess we'll never know ;o) mikaultalk 19:04, 7 July 2007 (UTC)
We'll never know, because that's not what happened. See the ref I added; the rule of thirds seems to have come from landscape painters, not from photographers. Dicklyon 19:57, 7 July 2007 (UTC)
Sorry, that was yet more sarcasm. I was inferring exactly that, though, in fact my whole point is that there is a heritage, if not a direct traceable lineage, from painting. Maybe I should stick to irony :o/
Interesting that the date of your ref coincides with the advent of photography.. in any event, it's not so much a reference as a "first mention in print". There is no more a good reference for the "rule of thirds" in this article than there is for the golden ratio being the basis for it. Are we supposed to believe this to be the true origin of the rule? There's no mention of intersecting points, in fact it sounds suspiciously like a sloppy approximation of the Golden Ratio. mikaultalk 19:33, 8 July 2007 (UTC)
Also, re your sarcasm, I think you've seriously misunderstood, or misrepresented, the results of that study you linked. It says, to take one simple bit out of context, that "The hypothesis was supported. The golden ratio was not preferred in the more basic patterns." Besides that, a 2:1 rectangle which they used to represent the "thirds" ratio is hardly related to the rule of thirds, which is about a placement at 1/3, or division into 3 parts. A ratio of the large part to the whole (2:3) might be a better way to construct an analogous rectangle, but that's still a stretch. The rectangle divided into 3 similar parts has both of these rectangles in it of course, along with the 3:1 rectangle; but only if it starts square. Dicklyon 20:10, 7 July 2007 (UTC)
I'm not entirely with you here. The study I linked to concluded (just after the part you quoted) "The participants showed a significant preference for the golden ratio in likeability and quality over all other ratios in page designs supporting the hypothesis that the golden ratio would be preferred in context driven environments.". Ok, maybe that particular study didn't fairly compare the GR with the ROT, but the issue here is a concession on my part that the two are often considered to be different things.
OK on page design, but you had said they showed that "people prefer the look of the golden ratio in everything from art to basic geometry" which they in fact contradict as in my quote. Plus, they didn't test any alternatives closer than 1.3 and 2.0, so even the limited preference result is quite weak compared to most earlier studies. But I agree with your point other than that. Dicklyon 20:47, 8 July 2007 (UTC)
What I'm trying to prove is the relationship between the two. Firstly, I think it's an omission in the article to fail to mention the Euclidean/Pythagorean basis for all this. The Greeks worked out that the most aesthetically pleasing point to place a knot in a length of string was "about" a third of the way in. I could probably ref that without too much trouble. It's not a stretch from there to the four points at the intersection of four lines, at "about" a third of the way along each, which forms the basis of the rule of thirds. The Greeks sparked off something which was extrapolated into a mathematical theorem purporting to explain the "divine proportion" in all living things. For thousands of years, artists and architects studied these theorems and created stunning works of intense beauty. Photographers may use the rule of thumb of the rule of thirds and create a raft of unoriginal lookalike pictures, but that's not to say the rules don't have the same origin.
Indeed, a ref to the Greeks doing something related or analogous would be a good step. But your implication that the golden ratio has been involved in aestetics for thousands of years is without basis, as far as I've been able to find. Dicklyon 20:47, 8 July 2007 (UTC)
It's easy enough to ref this within the encyclopedia, the basis for it is very well established. It's easy to ref pretty much all of the examples in the link I posted but I'd suggest this is nowhere near as contentous a claim as the idea that the rule of thirds had no relation to the golden ratio. Look at the entry for Aesthetics; the Parthenon is right there, in this context. Look at the entry for golden ratio and see what links here. mikaultalk 00:09, 9 July 2007 (UTC)
I'm all done researching this and it basically looks like the only decent reference this article could have (apart from the one at the top of this section) is one to classical Greek math. At the moment it's a barefaced cheek to insist on quality references for a link between GR and ROT when the article itself is almost completely devoid of anything but original research, hearsay and perpetuation of an unfounded rule of thumb with no basis in concrete fact. As this post quite pointedly notes, it's a wonder it was never nominated for AfD. Lets bring in some quality examination of it, rather than trot out internet lore and photographic mythology as fact. mikaultalk 19:33, 8 July 2007 (UTC)
I disagree. It's always a good idea to challenge things with citation needed tags when they seem to be wrong, and even if they seem to be right; but the latter is less important and doesn't make the former a "barefaced cheek". And "rule of thirds" appears in over 600 books, so I don't think there's reason to believe that it's not an actual notable topic. Dicklyon 20:47, 8 July 2007 (UTC)
Yeah, maybe I got a bit carried away... but it is incredibly frustrating to see many hundreds of thousands of books, articles and web pages fail to mention this clear relationship, despite the fact that it goes some way to explaining how and why the ROT "works" the way it does and even helps stop people falling into the trap of rigid adherence to the rule. mikaultalk 00:09, 9 July 2007 (UTC)
I find this hilarious, basing "fact" validity on the number of books it is printed in or web-pages it is found on. You might as well start citing the middle-east's bible as factual proof for everything too. Here's another excellent example of how hundreds of thousands or millions of books can be 100% wrong: For nearly 100 years or more everyone thought that moths were attracted to lights because it was assumed they used the lights of the moon and stars as navigational aids. By always keeping one area of their eye lighted they would fly in a circular or straight line. Somehow this was supposed to be beneficial for them finding a mate or food source. I grew up reading this all my life and could only think, "What clap-trap this is!" I re-examined this foolishness printed in millions of books by hundreds of authors, about 20 years ago. I published my findings on the net anonymously. Moths fly to lights to try to induce a sleep-cycle so they will be able to be motionless and safe from predators. The very same reason they evolved their myriad camouflage patterns and even evolved to be awake in the dark -- safe from predators. If the light is on 24 hours a day they will contentedly remain asleep while even laying their eggs on a window screen or wall beneath the light. Surely this being attracted to lights ALL night in NO WAY was beneficial to the continuation of their species. This new idea is now being taken as FACT. Refuting what was written in millions of books by hundreds of authors. As the old saying goes, "If even five billion people are believing or doing (or writing) a foolish thing, it remains a foolish thing."
It's good that you're easily amused. But read Wikipedia:Verifiability. Dicklyon 00:01, 11 July 2007 (UTC)
Er, I was referring to the fact that "hundreds of thousands of books don't mention it, not that they do. The fact is, this whole article seem based on repetition of such "facts" in an equally vast number of decidedly non-scholarly books and webpages. My sense of irony seems destined to be lost on you. Amusing to read about you breakthrough with the sleep behaviour of the moth, though. mikaultalk 00:58, 11 July 2007 (UTC)
What I find hilarious is the idea that anybody could believe that historical fact can be derived through intuition. The example given, about why moths fly towards light, is not a question of historical fact. It is a question of scientific theory. Scientific theories are questioned and updated as new and better information comes available. If it's really the case that the previous theory of moth photo-affinity is wrong, then congratulations... you may well have posited a valid correction.
However this is not a question of scientific theory. It is a question of history. One does not simply declare that one thing was based on another because it sounds good. Questions of historical fact must have answers that can be verified through acceptable references. If somebody asks whether Buster Keaton, Michael Keaton and Diane Keaton are related, one cannot simply answer "Of course they're related! They have the same name, don't they? I've been telling people for 20 years that they're related, therefore they are related." In fact, they're not related, and of the three, the only one born with the last name "Keaton" was Buster. That information is easily found in a variety of acceptable sources. Contrast that with the dearth of references supporting the claim that the rule of thirds was based on the golden ratio, and you'll have some idea of why we can't just take somebody's word for it. -- Moondigger 00:55, 11 July 2007 (UTC)
Then I suggest you question the very first person that published your "Rule of Thirds" and find out where he got the idea from or if he invented it. And if he "invented" it, I'd find it awfully odd that a few millennia of common-knowledge about the Golden Ratio wouldn't have influenced his "new" compositional method in any way. If he was an artist then he would have most certainly known about the "Golden Ratio". I suspect his case to be no different than the one that originator of this conversation ran into repeatedly. He had to dumb-down the Golden Ratio because he too got tired of trying to explain something this all-encompassing to mere morons. And to state that the Golden Ratio is never used in painting composition? That's to laugh at. Even if you painted the Parthenon (its whole construction based on the Golden Ratio), you would have to use the knowledge of it in your painting. You really must stop living in the digital-dark as much as you choose to do.
That you do not understand the criteria required for inclusion of a particular piece of information in a Wikipedia article is evident. That you are resorting to the same personal attacks and poor attitude as the previous Anon editor is a strong indication that you are the same person. Regardless, either or both are good enough reasons to discontinue this discussion with you. -- Moondigger 02:44, 11 July 2007 (UTC)
• First I do not want to fight this war, does not matter to me, just giving my feedback from what I have learned. I learned to take pictures about 30 years ago, I learned the rules of thirds and that it was a aproximation of the golden ratio, which in my opinion makes sense! Obviously this is WP:OWN but it is a fact (that it happened to me). I will see if I can find any old photography books that states this but I doubt it. Look at the golden ratio page, it is pretty well referenced and I do not think it should be argued about, WHY would the golden ration NOT apply to pictures taken by a camera??? And if it does apply and the RoT also applies why does the RoT not apply to art? Or does it? And if both applies does that not mean that they are the same, or one is an aproximation of the other? And if so what is the first ref for golden ration we can find and what is the first ref for RoT? I think golden ratio wins by a few centuries! Dosent it make more sense that the rules of thirds is just a aproximation of the golden ratio? Obviously if we want to follow the wikipedia 'rules' to 100% the relationship to the golden ratio can not be mentioned in this article unless we find a good reference, but I think the relationship is obvious enough for me to beleive it to be the truth no matter if it can be alloed to be mentioned in wikipedia or not :-). Stefan 06:51, 10 July 2007 (UTC)
Stefan, the reasoning you put forth in your comments here is exactly the kind of thing the Wikipedia inclusion rules are designed to address. Arguing "I think the relationship is obvious enough for me to believe it to be the truth..." is a dangerous/sloppy way to go about writing an encyclopedia article. Many causational relationships seem obvious but are in fact false. It seems just as obvious to many people that "Ring Around the Rosie" is about smallpox or the bubonic plague. Yet it's that great human talent/desire to find patterns or relationships that leads us down the false path of assuming a "fact" with nothing to support it. We can see evidence of this even in some of the references Dicklyon found... the author of the 1986 book posited that the rule of thirds derived from the golden ratio, and then cited an earlier book that doesn't mention the rule of thirds at all. The relationship seemed obvious to him as well, but his cite doesn't support it, making his a flawed reference.
The short answer is that really really wanting something to be true doesn't make it true, even if that's what you were told years ago. -- Moondigger 14:35, 10 July 2007 (UTC)
Stefan, if it's true that being closer to golden ratio works better than the rule of thirds, or that someone has said so in print, that would be worth adding and citing. On the other hand, if it's just what you happen to believe, it's not. So "put up or shut up" as they say. Dicklyon 15:38, 10 July 2007 (UTC)
Well this is not science, it is art, nothing is absolute, see [1] it states that G. T. Fechner made a study that concluded that GR is most popular, I would assume that that is in print. But I do not want to argue about that, all I want is that GR should be mentioned in this article! Why not? They are related, look at the 2 pictures in the link I gave, GR and RoT is so close that if one works the other will be pretty good also. This article now is so full of weasel words now that a few more stating that RoT and GR might be related will not hurt anyone. Golden ratio is very well referenced I count more than 50 references, RoT have references (but not many on the page). I think we should mention that another simmilar rule of composition is GR This is a encyclopedia, if I'm interested in RoT dont you think it would be good to mention GR also in the same place? Stefan 16:18, 10 July 2007 (UTC)
The Fechner study is well known, but he looked at rectangle shapes, not compositional rules like the RoT. The Golden ratio article is in good shape and well referenced precisely because I and others took it on to remove the unsupportable crap from it and find and add references; I never came across anything that proposed using it in the way the rule of thirds is used, but it's possible it's out there. The key point again: we're not going to mention it without a reliable verifiable source, and you haven't found us one. Dicklyon 16:27, 10 July 2007 (UTC)
I'd like to add to this. I can't find a single reference that cites the golden ratio as a useful compositional guideline for photography or painting (ala the rule of thirds). I see plenty of references to abstract math, architecture and nature. Furthermore, (and to repeat myself yet again) just because they're "close" doesn't mean one is the origin or source of the other. -- Moondigger 16:51, 10 July 2007 (UTC)

You aren't looking very hard, I ran across these just browsing around in general photography info. The first page references quite a few other pages using it for a photography composition tool.

http://photoinf.com/Golden_Mean/

It must be nice living with blinders on. But then ignorance is bliss, isn't it. You must be very happy.

—Preceding unsigned comment added by 64.61.220.107 (talkcontribs)

Given the largely visual nature of the issue, is [this] not reference enough for you? mikaultalk 00:58, 11 July 2007 (UTC)
If you can point out where in that article the rule of thirds is mentioned, I'd appreciate it. This is the second time I've looked at it and still can't find a reference. ;^) -- Moondigger 01:19, 11 July 2007 (UTC)
Nevermind, I understand what you're saying now. I had lost track of where I was in this huge mess of a discussion, with non-chronological insertions, etc. I looked back to see what your comment was in reference to and thought you were responding to the immediate predecessor, ending "just because they're close doesn't mean one is the origin or source of the other." Looking back, it's obvious you were responding to the previous statement.
Even so, the page you reference (and the most convincing examples therein) most closely relate the golden section to architecture. Several of the painting examples have a tenuous link at best, relying on the way the author of the article superimposed the lines of the triangle or pentagram on the image. The lines are drawn specifically to support the hypothesis, despite the fact that somebody uninterested in the hypothesis might draw the lines differently to incorporate more or less of the figures. Why is a large portion of one person's leg cut off, but not another? That human gift for pattern recognition at work again.
Not to say that certain artists didn't use it. I stand corrected on that point. Nonetheless, I still see nothing supporting the contention that the rule of thirds was derived from the golden ratio. -- Moondigger 01:47, 11 July 2007 (UTC)
We will probably never find a ref to state that RoT is derived from GR so with wikipedia rules I can accept that we do not state that, but you agree that GR is referenced as a compositional rule used for paintings? If so lets at least include it as a see also link or even a sentence that talks about related compositional guidelines in this page? OK with you or will you or anyone else revert that? Stefan 03:53, 11 July 2007 (UTC)
I'd like to see a reference that indicates some relationship between the RoT and the GR before we imply such a relationship in this article. What exactly is the GR compositional rule used for paintings? Is it mentioned in a book along with the RoT as an alternative? If so, let's say so. If not, keep looking; don't add stuff based on your gut or memory. Dicklyon 04:00, 11 July 2007 (UTC)
I'm not stating that there is a relationship or alternative, read what I write! In the GR page it is stated 'Salvador Dalí explicitly used the golden ratio in his masterpiece, The Sacrament of the Last Supper.' and 'Mondrian used the golden section extensively in his geometrical paintings' that alone is enough for we to suggest that it might be a useful see also item in a page about composition. References such as [2], [3], [4] is serious enough for me, there have never been any rule for having written references for see also items as far as I know, please show me, if I'm wrong. Stefan 14:05, 11 July 2007 (UTC)
There are two sources below – one which Dicklyon refers to as the "2003 book" and a paper I found, which make a connection between the two, but there's little or no chance of finding a direct link or lineage there. I think the fairest solution is to recognise that the two are closely related compositional aids. It makes no sense (a) to mention one and not the other ((b) to fail to provide a link from one to the other (a "see also" or whatever) or (c) to refuse to admit a referenced inference that they may be somehow connected. The refs we have for the RoT are no more reliable sources of fact than the ones I've just pointed to here. Lets quit the heel-digging and add the see also for now, then ditch this lengthy debate for a new discussion on the agreed form that connection should take in the article. mikaultalk 16:13, 11 July 2007 (UTC)
Nice to see that power-tripping control-freaks with no lives are the ones ensuring that only their form of information is contained in Wiki pages. I'll be sure to spread the news that the Wiki is as biased as any other informational source online. Destroying any credibility it once was supposed to have.
If you want to engage in the debate, which has by no means concluded in anyone's favour, log on or at least sign and date your contributions. If you simply want to snipe from the sidelines, go ahead, snipe away, and be roundly ignored until your next block. mikaultalk 07:04, 14 July 2007 (UTC)
Thanks for your input Stefan. The reference situation is key because we have no real reference for the origin of the RoT, let alone a connection between this and the GR. There are plenty of refs, however, for the origins of the GR. In this sense, the connection between the two is quite possibly the only firm ref we have for the origins of the RoT at all. It's clearly needed, IMO, to lend any credibility to the article beyond pointing to the repetition of the rule in a plethora of "photography for beginners" books and websites. The RoT/GR refs we do have are outlined in Dick's post immediately below. mikaultalk 10:05, 10 July 2007 (UTC)
Book refs

If you look for book refs that associate "rule of thirds" and "golden ratio", you find a few. One 2003 book goes so far as to say:

• As the golden ratio of 0.618 is approximately two-thirds (0.666), the "rule of thirds" is roughly based on the golden section.

A 1986 book that I mentioned above refers to

• a rule of thirds based on the "golden ratio" of the Greeks (Dondis, 1973)

and a 2004 book copies his exact wording "golden ratio" of the Greeks; but as I pointed out, the referenced Dondis book does not mention the rule of thirds. No doubt these are not the first to invent such a connection, as our anon contributor above mentions he used to teach this connection many years ago. But there's nothing I can find that actually supports the idea that the rule of thirds originated from a rule based on the golden ratio; indeed, the finding in an 1845 book that does not mention the golden ratio suggests otherwise. It's an interesting question, and more research and refs would be welcome. Dicklyon 21:26, 8 July 2007 (UTC)

I'd say you have a ref worth mentioning, if one is needed at all, in the 2003 book. Is it a really a case of "invent a connection"? I'm fairly sure the problem is that sources like the 1845 book simply fail to mention that there was one. Many great discoveries are in fact rediscoveries – old wine in new bottles – primarily for self-glorification purposes. Or maybe, in this case, the fact that correlation to the proportion of ourselves has some mathematical significance seems counter-intuitive enough to opt instead for an arbitrary rule which just "somehow works". I'd certainly like to see some more contributions here and ultimately a consensus on the wording of a reference to the Greek connection. mikaultalk 00:09, 9 July 2007 (UTC)
As this seems as good a place as any to temporarily list links to ref material, this is a link to the Datta et al "sloppy approximation to the golden rule" paper. mikaultalk 10:06, 10 July 2007 (UTC)

### The Greeks, the Golden Ratio and the Rule of Thirds: why there's a link but no lineage

I've put this together to hopefully clarify the relationship between the RoT and GR, but I'll not be about to reply to reponses for a week or so. It's probably too long to stay here and if someone feels it ought to be moved elsewhere, that's fine with me. Neither Thales, the teacher of Pythagoras, nor Pythagoras himself, left a written account of their discoveries. The oral tradition they developed (almost certainly from ancient Egyptian sources) inspired the likes of Plato, Aristotle and particularly Euclid to codify laws and rules of arithmetic, harmonics and geometry, most of which are still valid today, if known by different names and concepts. Pythagoras' key discovery was the harmonic interval which he then translated into harmonious ratios (including the famous theorem. It seems neither he nor the Egyptians worked with irrational numbers but the irrational GR is right there in the geometry of the pyramids and implicit in the Pythagorean harmonic interval. According to tradition, by streching a string and dividing it into twelve, Pythagoras was able to mark intervals corresponding to octave, fifth and fourth by shortening it from 12 parts to 6, 8 and 9, matching the ratios of 2:1, 3:2 and 4:3 respectively. Why this is historically and mathematically significant (if it's not immediately obvious) is probably best explained by a well-sourced online paper which I think would serve as a good reference for the Greek connection.

• Basically, Euclid extrapolated these rational terms into ones, showing how the physical (rational) is connected with the metaphysical (irrational), how the base relates to the sublime, and hence Man to God, just as Plato had taught 250 years earlier. He did this by developing the Pythagorean arithmetic and harmonic ratios into a geometric ratio, the extreme and mean ratio which we know today as the "golden" ratio. I suppose you could say the irrational (GR-type ratio) was therefore derived from the rational (RoT-type ratio), not the other way round, but that's not really how they came to bear on art and architecture.
• The oral tradition wasn't always strong and the lineage with "western" thought, including much of the Greek philpsophers works, all but broke down during the Dark Ages. Arab scholars reintroduced Euclidean geometry to Europe sparking off a renewed passion for classical geometry in architecture, sculpture and painting along Pythagorean lines. For this reason, it wasn't until the early 16th century that Luca Pacioli made the first ever translation of Euclid into Latin.
• Prior to the Renaissance, European art demonstrated no discernable pattern of composition of regularity of form as was evident in Greek art and architecture; afterwards, it was everywhere, expressly in paintings by Da Vinci, Seurat, Dali, Mondrian and casually by many others, in the architectural work of Palladio and Alberti and others after them, in astronomy, music, even the fields of psychology and biology.
• It's about this time that corresponding "rules" became established in these fields, but the terms we use today came much later: "Golden ratio" was coined by Martin Ohm in 19th century, for example. Hence most of these rules, inlcuding the GR and RoT, cannot be referred to retrospectively. There is no way of identifying either in antiquity except by their common ratios, expressed in either rational (RoT – 1:2, 2:3) or irrational (GR – 1:618…) proportion. They are distinct, but in art, design and architecture as with Canons of page construction, were almost always used together.
• The connection with the Greeks is a connection with geometry. The difference between the RoT and the GR is one of geometrical points and geometrical proportion. My conjecture based on all this, which (for now) is probably too WP:OR to include, is that the RoT is a subject positional guide, while the GR is a proportional layout guide. It's way too easy, and AFAICS practically universal, to conflate the two into one Rule of Thirds. They belong together, grew up together, and IMO you can't properly understand, mention or use the Rule of thirds without first understanding something of the divina proportione.

A nice quote from Plato:

There exists first, the unchanging form, uncreated and indestructible, admitting no modification and entering no combination; second, that which bears the same name as the form and resembles it; third, space, which is eternal and indestructible, which provides a position for everything that comes to be. (Timaeus)

Timeline according to Priya Hemenway (from Golden ratio)[1].
mikaultalk 07:04, 14 July 2007 (UTC)

## Image

The comment about the image being excellent is unnecessary and a more classical example (and simpler) example of the rule would be good with possibly a human.—Preceding unsigned comment added by 206.191.28.13 (talkcontribs)

New image
Reduced saturation version
I wouldn't agree that it's an "excellent" example, simply because as currently marked up and shaded, it's difficult to tell what's depicted. (Shameless self-promotion to follow...) I believe a better choice from a licensing and pedagogical perspective would be one of my images, shown at right. I'd be happy to overlay a grid on it and make it a replacement for the existing image. -- Moondigger 15:09, 23 August 2006 (UTC)

Since the current image does not have a valid license for wikipedia, I support the replacement. A rewrite of the article will be needed as it talks mostly about the current image. HighInBC 16:08, 23 August 2006 (UTC)

I have reduced the current image in size, it should now qualify as fair use(as a commentary of the style of the art). However I agree that it is too cluttered to properly illustrate the concept. I still prefer Image:Rivertree_1_md.jpg(once the diagram is layed ontop and the text of the article is changed to reflect it). HighInBC 16:18, 23 August 2006 (UTC)

Any comments about the changes I made? I ended up going with an animated GIF as I thought the previous graphic was too busy. I can change the timing on the animated GIF to be longer if need be. It's changing every 3.5 seconds right now, but maybe it needs to change less often? I wouldn't want it to change any faster, as I want to avoid a "blinking" look. -- Moondigger 04:49, 24 August 2006 (UTC)

Perhaps instead of going completely greyscale you could just reduce the saturation a bit. I think this will have the same effect with a less blinky feel. However perhaps the technical constraints of animated gifs prevent that. I certainly think it is far better than the other one. HighInBC 04:55, 24 August 2006 (UTC)

Here's one as you suggested, with reduced saturation instead of black & white. It is less blinky, but I think the other one looks better for some reason. Thoughts? -- Moondigger 05:20, 24 August 2006 (UTC)

Your right, the one that goes completely black and white is better, good job. HighInBC 01:22, 4 September 2006 (UTC)

-- (Passing comment by a user who learned) : The tree/grid image is really most excellent for explaining the idea. I read the text, looked at the image, and instantly 'got it'. Thanks, great work.

It's a great photo to use as an example, but I think the animation is a mistake - you're forcing the reader to look at particular aspects at particular times, to wait 3.5 seconds if they were examining some aspect of the grid when it disappeared. I think a static version of the colour image, with the white grid overlaid, would be equally illustrative (and more suitable for printing). --McGeddon 20:05, 2 April 2007 (UTC)

The image actually needs to be replaced. Image use policy and guidelines indicate that animated images should not be used in article space as you can't print them or save a particular version of the image. This needs to be broken into separate images to illustrate the point.--Crossmr (talk) 03:48, 15 November 2008 (UTC)

### Size

The picture's size should be a 3:2 aspect ratio like most photographic pictures instead of 1:1. At the very least, there should be a 4:3 ratio. --68.239.240.144 01:37, 27 January 2007 (UTC)

Why? The rule of thirds applies to photographs of any common aspect ratio. In any case this particular image was square from the start (taken with a Mamiya C220f on a 6x6cm square chunk of film). If you have or know of a better image demonstrating the rule of thirds, then post a link here. However unlike with most articles, changing the photo on this one necessitates changing large chunks of the article text to match. -- Moondigger 19:40, 5 February 2007 (UTC)
Agree with Moondigger; the rule of thirds is not limited to any specific aspect ratio. By the way, nice to know what camera you used for it; I also used it on the Dutch page nl:Regel van derden because it is a highly appropriate example. Eddyspeeder 22:30, 23 May 2007 (UTC)