Talk:Golden ratio

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The Theorem of the Golden Mean[edit]

Add a reference to Thean'so "The Theorem of the Golden Mean" in the Pythagorean school? it would be useful to show works on the golden mean at that time. — Preceding unsigned comment added by 78.137.177.20 (talk) 10:06, 20 August 2014 (UTC)

Egyptian Pyramids[edit]

"Adding fuel to controversy over the architectural authorship of the Great Pyramid, Eric Temple Bell, mathematician and historian, claimed in 1950 that Egyptian mathematics would not have supported the ability to calculate the slant height of the pyramids, or the ratio to the height, except in the case of the 3:4:5 pyramid, since the 3:4:5 triangle was the only right triangle known to the Egyptians and they did not know the Pythagorean theorem, nor any way to reason about irrationals such as π or φ."

"the 3:4:5 triangle was the only right triangle known to the [ancient] Egyptians" is unverifiable and illogical. If an individual can create two measured lines (sharing an endpoint) and make them perpendicular to one another, then that person can construct any right triangle.

"they did not know the Pythagorean theorem, nor any way to reason about irrationals such as π or φ." is unverifiable.

AnonymousAuthority (talk) 05:51, 15 November 2013 (UTC)

Take it up with Eric Temple Bell's ghost. We are merely reporting what he said. —David Eppstein (talk) 06:05, 15 November 2013 (UTC)
The word "since" divides what he claimed from what is implied as some known facts. The sentence either needs to be rephrased to clarify that it is not a known fact, or a direct quote needs to be provided. AnonymousAuthority (talk) 20:07, 16 November 2013 (UTC)

That the Ancient Egyptians did know about irrationals, and that they did base their entire number system and way of doing mathematics on them, as grounding principles is outlined in detail in R A Schwaller de Lubicz's The Temple of Man - 2 Vols - Trans. Lawlor & Lawlor - ISBN 978-0892815708. Your article should take the timeline back far enough to include this information.86.160.8.214 (talk) 21:18, 17 January 2014 (UTC)

This article is neither about irrational numbers in general nor about fringe theories of Egyptian mathematics published by woo astrology/tarot publishers. That material does not belong here. —David Eppstein (talk) 21:56, 17 January 2014 (UTC)

Do you need pi in order to know about the Golden Section?? I don't think so. The Timeline section of this article arguably must start with the Egyptians, in any case, as it has been fairly well established that the proportional ratio is <ital>present</ital>in the pyramids, regardless of any controversy about their mathematical prowess. see for instance math.iit.edu/~mccomic/420/presentations/goldenRatio.ppt; see http://milan.milanovic.org/math/english/golden/golden3.html notwithstanding the poor English, it is written by a Serbian engineer with decent credentials; see also http://goldenratio.wikidot.com/egyptian-art, and http://jwilson.coe.uga.edu/EMAT6680/Parveen/ancient_egypt.htm, excerpts here: "The Egyptians thought that the golden ratio was sacred. Therefore, it was very important in their religion. They used the golden ratio when building temples and places for the dead. If the proportions of their buildings weren't according to the golden ratio, the deceased might not make it to the afterlife or the temple would not be pleasing to the gods. As well, the Egyptians found the golden ratio to be pleasing to the eye. They used it in their system of writing and in the arrangement of their temples. The Egyptians were aware that they were using the golden ratio, but they called it the "sacred ratio."" Cesca1910 (talk) 09:13, 3 July 2014 (UTC)

Golden Ratio on Architecture[edit]

For some reason, a good image showing the use of the golden ratio as a proportion rule in modern architecture has been removed twice by Binksternet. Though at first he removed it under the pretence that the architect himself had nothing much to do with the page, it was once again removed after his suggestions were met.

The topic is very well discussed on the page, and after a talk with David Eppstein, it was provided strong reference backing up the image. I think it is DISGRACEFUL that Binksternet is so arrogant as to prevent people to CONTRIBUTE to the page. His reasoning being 'original research' is an excuse for his large ego, since the reference I provided, being a doctoral dissertation, is the most reliable, though anyone with basic knowledge on Mid-Century modernism would know about the use of proportion rules.

Stop being a child. I am a new editor, and your actions are discouraging me from contributing or even learning further on how to. — Preceding unsigned comment added by RPFigueiredo (talkcontribs) 23:01, 20 June 2014 (UTC)

RP, you are free to question and discuss the decisions of other editors, but to call their actions "disgraceful", call them "arrogant", say they have a "large ego", and tell them to "stop being a child" are actions that are unlikely to advance your position, and probably transgress WP:NPA, and may lead to sanctions against you. And there's no evidence of your claimed discussion with David Eppstein, the other editor who reverted you. So calm down and explain what you've got. It looks to me like you added material from a 2012 primary source, to a mature article based mostly on secondary sources, which are the preferred sources for wikipedia. See WP:WPNOTRS. That's probably why the material was removed. Dicklyon (talk) 02:10, 21 June 2014 (UTC)
The only interaction with me was what you can see on the edit summaries in the article edit history. —David Eppstein (talk) 03:11, 21 June 2014 (UTC)

────────────────────────────────────────────────────────────────────────────────────────────────────I would be happy to see an analysis of Niemeyer's use of the golden ratio brought into this article. Such an analysis should be a representative summary of multiple writings about Niemeyer, all of which agree that he used the golden ratio for one his buildings. In that case, we could also show the reader an image of Niemeyer's golden ratio work. It would also be best for the encyclopedia to have even more detailed information at the Niemeyer biography. However, none of this should be brought into the article if there is only one little-known paper describing Niemeyer as employing the golden ratio. This topic is very broad, and we should tell the reader the major themes, not a minor sidebar. — Preceding unsigned comment added by Binksternet (talkcontribs)


The image is an example of the use of the GR in modern architecture. But I see your thought - examples must be cited on the text. Then I believe adding a image of Corbusier's work would be fine then, since it is mentioned?

I don't intend to 'advance my position' here, as opposed to what other users seem to be trying to do. I want to share knowledge. It's not helpful to remove representative information. But it is helpful to get in touch and try to help people in validating it. Just because someone is high rank on wikipedia doesn't mean they know all subjects, and that's were humbleness should kick in - Believe me, though I cited a doctoral dissertation, any first year architecture student could provide you secondary sources. But someone just don't seem to care about that...

I'm sorry for the term I've used about the interaction with David Eppstein - but his reversion was helpfully explained, I have no objections to it.

I would suggest someone adding an image of the regulating lines of the Parthenon - that would be much more explanatory to readers. But I won't dare to do any alterations after all that went through here... Just hope someone would.RPFigueiredo (talk) 05:24, 21 June 2014 (UTC)

Per WP:BRD, you need not hesitate to make a bold edit. Just don't get upset when/if it gets reverted; it can be a good discussion starter. Now, if you could find sources that actually support the idea the the Parthenon was designed with the golden ratio, as opposed to the myriad of sources that just blindly repeat it even though there's no evidence for it, we'd have something interesting to talk about. A Corbusier image is a good idea, if you can find one that's freely available and illustrates a use of GR. Dicklyon (talk) 05:43, 21 June 2014 (UTC)


The issue I have is that people revert it before they even try to include it in the article. The approach is the opposite of what en encyclopedia should be. But that's fine.

Sourcing the use of GR in the Parthenon would be like sourcing F=ma. It's there for everyone to measure. Same with Niemeyer's congress building. But apparently I need secondary source for common knowledge.

Anyway, I could look for it, but I just don't care anymore. I hoped Binksternet would have encouraged my to do that on the first place, rather than instantaneously discarding contribution. — Preceding unsigned comment added by RPFigueiredo (talkcontribs) 06:20, 21 June 2014 (UTC)

Niemeyer at least probably left some documentation of his design choices, beyond the buildings themselves, unlike the designers of the Parthenon. And (without having researched the matter myself) it doesn't seem unlikely that he would have deliberately used the golden ratio. But there's a reason we're quick on the trigger with this article, more than a lot of others on WP: there's so much credulous repetition of bad information and not-even-close matches even in published sources (say, for example, the supposed occurrence of the golden spiral in the nautilis shell — it's a log spiral but with completely different parameters) that we need to sift through them to find the examples that bear up under scrutiny. —David Eppstein (talk) 07:23, 21 June 2014 (UTC)

Semi-protected edit request on 29 June 2014[edit]

Near the end of the section "Relationship to Fibonacci sequence", immediately before the sentence and paragraph beginning "However, this is no special property...", please insert the following (I.e., right after the 3-line equation sequence):

The reduction to a linear expression can be accomplished in one step by using the relationship
\varphi^k=F_k \varphi +F_{k-1},
where F_k is the kth Fibonacci number.

208.50.124.65 (talk) 23:14, 29 June 2014 (UTC)

Red information icon with gradient background.svg Not done: please provide reliable sources that support the change you want to be made. — {{U|Technical 13}} (etc) 15:04, 1 July 2014 (UTC)
This standard equation appears as the second equation in Fibonacci number#Decomposition of powers of the golden ratio. That article gives no source for it, probably because it is so standard and easy to verify. However, one source that states it without proof is Mitchell, Douglas. "Powers of \varphi as roots of cubics", Mathematical Gazette 93, November 2009, 481-482. 208.50.124.65 (talk) 15:33, 1 July 2014 (UTC)

not well fleshed-out[edit]

I understand the rejection of my edit, especially given the general style of mathematical articles. First though - are there any other such numbers, whose inverted value plus one equals the value before inversion ? I'm not a mathematician, but I have though read (and used) more maths than most other people, including at university level. Although it was some years ago now. I just find the math-related articles perhaps could be a bit easier to read, and sometimes give more "hard" examples of complicated formulas. I don't believe my rejected edit helped very much there, but I though it might get some reader more interested. (and if so, necessaraly early in the article) However I agree it could be better fleshed-out. Boeing720 (talk) 23:25, 25 September 2014 (UTC)

There is no prohibition on the lead including material covered later on, but I don't think your addition belonged for two reasons. First it was not encyclopaedic. It is not for us to say what we find interesting, or to comment on facts. We should simply state the facts and let them speak for themselves. There is nothing to stop you making them interesting, with good writing, presentation, layout. In fact that's of the main things distinguishes our best articles from the merely good ones. But you should not say so. Second the lead section is the place to say what something is (so a definition), say why it's important (so put it in context), and say how it is used/what it relates to. It's not the place for more detailed properties and examples, which can go in their own section and expand on the definition. The lead is the wrong place for this.--JohnBlackburnewordsdeeds 23:48, 25 September 2014 (UTC)
(ec) But this is exactly the content of the first paragraph of the calculation section, is it not? That 1+1/\phi=\phi is just a quadratic equation. This has two roots: one is the golden ratio \phi and the other is -1/\phi. So there are exactly two numbers with that property. Sławomir Biały (talk) 23:54, 25 September 2014 (UTC)
Thanks ! Boeing720 (talk) 20:34, 26 September 2014 (UTC)

Section on Irrationality[edit]

The picture and caption under "irrationality" does not prove that the golden ratio is irrational. It states that: "If φ were rational, then it would be the ratio of sides of a rectangle with integer sides. But it is also a ratio of sides, which are also integers, of the smaller rectangle obtained by deleting a square. The sequence of decreasing integer side lengths formed by deleting squares cannot be continued indefinitely, so φ cannot be rational."

But I fail to see how the fact that the side lengths stop being integers implies irrationality. — Preceding unsigned comment added by 130.245.221.218 (talkcontribs) 11:13, 23 November 2014

Because it's not possible to have an infinite descending sequence of positive integers. If the first number in a sequence is n, then any descending sequence starting from that number can run at most n steps. —David Eppstein (talk) 18:57, 23 November 2014 (UTC)
I think the OP has a point here - that simply means that the sides won't be integers; it doesn't entail that their ratio cannot be rational (i.e. that the ratio cannot be expressed as a ratio of integers). The proof seems to be missing something. -- Scray (talk) 19:23, 23 November 2014 (UTC)
Huh? Read the first line the OP quoted: if the ratio were rational, there would exist a rectangle with integer sides. For instance, one side can be the numerator and the other the denominator of this supposed rational number. And if this rectangle existed, there would exist a smaller rectangle that still had integer sides. And so on into an impossible infinite descent. There is nothing missing from a careful reading of the text that's already there. —David Eppstein (talk) 20:22, 23 November 2014 (UTC)
I'm sure I'm missing something, so let me explain where I'm coming from and you can tell me what I'm missing (and note that I'm not arguing that φ is rational - I'm just asking if the proof is compelling): let's take a classic 3-4-5 (side length) right triangle. The ratio of any pair of side lengths is rational. If one takes similar triangles of progressively smaller area, their side lengths are not integers but their side length ratios remain rational (and constant, of course). That the side length of the triangle (or in the case of this proof, the rectangle) are not integers does not mean the ratio is not rational. I think the proof lacks evidence that the side length ratios cannot remain rational, which has to do with the way the side lengths shrink (rather than their resepective absolute lengths). What am I missing? -- Scray (talk) 21:08, 23 November 2014 (UTC)
What you are missing is that in this case the side lengths remain integers, as the caption already states — see the phrase "which are also integers" in the quote given by the OP. Specifically, when you delete a square, one of the sides of the new rectangle is also a side of the old rectangle (an integer) and the other side is the difference of the old rectangle's sides (a difference of two integers is always an integer). —David Eppstein (talk) 22:11, 23 November 2014 (UTC)
Ok, thanks. -- Scray (talk) 22:29, 23 November 2014 (UTC)
Ah, I see. What I was missing was the "which are also integers" bit. The placement of that clause in the sentence is a bit awkward and breaks up the sentence in an unexpected way that threw me off. But you're right--the sentence as written is perfectly correct and a careful reading reveals no problem in the proof..