Talk:Golden ratio: Difference between revisions

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	:Also over-aggressive insertions and comments by Achim1999 are a problem. Let's talk here about what improvements are proposed, instead of warring in the article. This article attracts an awful lot of well-intentioned changes, but lots of editors watch and care, so don't expect to just put in whatever you want without some pushback. And maintain politeness even if someone is objecting, please, per ] and ]. ] (]) 21:01, 13 June 2012 (UTC)		:Also over-aggressive insertions and comments by Achim1999 are a problem. Let's talk here about what improvements are proposed, instead of warring in the article. This article attracts an awful lot of well-intentioned changes, but lots of editors watch and care, so don't expect to just put in whatever you want without some pushback. And maintain politeness even if someone is objecting, please, per ] and ]. ] (]) 21:01, 13 June 2012 (UTC)

			:I have rolled back all of your contributions to the article of today, which started with a large expansion of a section on a property, and came with a new section heading with improper capitalization. This is not German; please respect that the article is in good shape by carefully adhere to both style and content guidelines. And it's already pretty large, so major additions need to be carefully considered. ] (]) 21:08, 13 June 2012 (UTC)

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"At least since the Renaissance"

"At least since the Renaissance" is in dispute. In fact, there is no concurrent evidence of Renaissance artists using this ratio; everything is line-drawing and measuring after the fact, which is notably vulnerable to selection bias. Matthew Miller (talk) 23:02, 13 March 2012 (UTC)

You don't think Pacioli counts as concurrent evidence? —David Eppstein (talk) 23:19, 13 March 2012 (UTC)

It doesn't appear to. He describes the geometric properties, and delves into its relationship to the Platonic solids, not its use in art. The part about the divinity of numbers is more mystical than aesthetic. And there's no evidence of anyone — even Da Vinci, who illustrated the book! — having followed up with actual art or architecture devised around the golden ratio, until at least the 19th century. Matthew Miller (talk) 19:54, 16 March 2012 (UTC)

From http://www.emis.de/journals/NNJ/Frings.html#anchor656497: "Neither in the text nor in the illustrations is the Golden Ratio recommended for practical use." Matthew Miller (talk) 20:53, 16 March 2012 (UTC)

The German WP article has some sourced information on that. According to that there's a number of renaissance artwork in which the golden section "appears numerically" (da Vinci among others). The notion that this was designed and influenced by Pacioli and there there was a cooperation on that between Pacioli and da Vinci was promoted by the philosopher and golden section guru Zeising the 19th century. However Zeising's arguments are merely speculative and have not substantiated by direct/hard evidence ever since. There has been actually some systematic x-ray analysis of those renaissance paintings by some art expert to verify actual construction sign of the golden section among the paint, but they haven't turned up anything. The explicit, verified use of the golden section doesn't seem to take off before the 19th century.--Kmhkmh (talk) 01:56, 18 March 2012 (UTC)

Removal of Pacioli woodcut

The image http://en.wikipedia.org/File:Divina_proportione.png does not illustrate the golden ration, despite its caption. None of the lines or rectangles appear to illustrate the golden ratio! It appears to illustrate a system of integer division — 1, 1, 2, 2 for the horizontal divisions, and then a ratio of 6:7 for the box as a whole. 6:7 is not a very good approximation of phi. The horizontal division is clearly by half. So even if this image is well-sourced, it does not appear to be an appropriate illustration. http://www.emis.de/journals/NNJ/Frings.html#anchor656497 confirms that this image illustrates the Vitruvian section, not phi. Matthew Miller (talk) 20:55, 16 March 2012 (UTC)

I agree. I had looked for sources connecting it to phi, and found none; but I hadn't found that source with "Vitruvian section". Good find. Dicklyon (talk) 15:24, 17 March 2012 (UTC)

Two Platonic solids

Please, no more non-actionable commentary, see WP:TALK and WP:NOTFORUM. Johnuniq (talk) 11:07, 27 March 2012 (UTC)
The following discussion has been closed. Please do not modify it.
Platonic dodecahedron and icosahedron. In green, red, blue and yellow, the succession of four lengths is a geometric progression with common ratio φ, the golden ratio. Top view. Platonic dodecahedron placed on a horizontal puzzle with golden triangles. Elevation view. Same Platonic dodecahedron with same notations. Regular pentagons and decagons. The ten thick semi-transparent lines are the sides of a stellated regular decagon: an image under a vertical othogonal projection of ten segments, which extend ten edges of the Platonic dodecahedron. Three unfolded faces of Platonic dodecahedron The same partial net is visible in the top view, with vertex L. Here is a geometric sequence of five lengths with common ratio φ, that begins with the term denoted by b: the difference between the diagonal length and the side length of a face of the Platonic solid. The fifth term of the sequence equals (3 φ + 2) b. The right bottom image shows a geometric progression of five areas with common ratio φ, that begins with the area of the green triangle. The fifth area is the total area of the four triangles in green, pink and blue, that form "a golden triangle" similar to the green or blue one. There is no image about regular polyhedra in the current article. In my opinion, we have to talk about the two dual Platonic solids. For example, two opposite edges of a Platonic icosahedron are two smaller sides of a golden rectangle. — Aughost (talk) 11:59, 17 March 2012 (UTC) Good idea; though this one is awful busy, and the "yellow" is not really recognizable as such. Dicklyon (talk) 15:25, 17 March 2012 (UTC) About the good idea, thank you. About colours, how might we name the golden tint associated to the fourth and last length of the increasing sequence? Weak ocher? This is depending on our screens and our eyes and our terminology. Anyway, stripes have to draw our attention all the more when they take up less space in the image. Actually, we find the weakest colour because it is the one of the largest length, equal to the sum of some lengths very well marked, and because of this equality written within the image: /_φ + a = φ a. In the current section that is entitled Geometry, the first image shows two spirals. The text deals with pentagon and icosahedron… — Aughost (talk) 09:16, 19 March 2012 (UTC) The two following images show the same twelve points built through a stellation of a Platonic dodecahedron. More informations in several images, of course. — Aughost (talk) 16:01, 20 March 2012 (UTC) Those images look extremely busy and confusing to me. —David Eppstein (talk) 17:11, 20 March 2012 (UTC) These are extraordinary images, but they are too complex for use in an article. The Platonic solids are wonderful and have many interesting properties, but this level of detail only makes sense after intense study. Johnuniq (talk) 01:46, 21 March 2012 (UTC) An article is not a course page. In the current article, for example, what does everybody understand in the first image of section "Geometry"? Actually, this current first image does not correspond to the first paragraph. And we cannot explain everything about an interesting 3D image. — Aughost (talk) 11:00, 21 March 2012 (UTC) The idea of illustrating the presence of the golden ratio in a platonic solid seems a good one, but how about starting with the simplest illustration of a single such relation for a single solid, rather than the superposition as in these figures? The icosahedron in the first figure seems to play almost no role in the relations. Tkuvho (talk) 16:16, 21 March 2012 (UTC) Through a stellation of a Platonic dodecahedron, we build a great dodecahedron, a Platonic icosahedron, and twelve stellated regular pentagons. Each face of the great dodecahedron is a duplicate of a face of the initial dodecahedron, to scale φ or φ + 1. Two opposite edges of a great dodecahedron are the smaller sides of a golden rectangle. — Aughost (talk) 18:47, 21 March 2012 (UTC) Whew. Let's start with something simple. Let a denote the distance between two opposite edges of a dodecahedron. The first figure suggests that the edgelength is then $(2-\phi )a$ . Is this correct? Something that can be stated in English rather than Coxeterish may be appropriate for this page. Tkuvho (talk) 18:54, 21 March 2012 (UTC) $2\,-\,\varphi$ is the multiplicative inverse of $\varphi ^{\,2}.$ — Aughost (talk) 19:14, 21 March 2012 (UTC) Very good then, we see that phi^2 appears as the ratio of the edge to the distance between opposite edges of a dodecahedron. That seems like an English sentence that could be added here. Any comment, David? Tkuvho (talk) 15:14, 22 March 2012 (UTC) How to yield a geometric sequence with common ratio φ from two consecutive terms? From (1, φ), for example, we can yield (2 φ – 3, 2 – φ, φ – 1, 1, φ, 1 + φ, 2 φ + 1), through a few additions and subtractions. More generally, given two positive values a and b that fulfill ${\tfrac {\,a\,}{\,b\,}}\,=\,\varphi ,$ we can yield a geometric sequence from (b, a ), either through successive additions or through successive subtractions, depending on the sense of the extension, right or left. Is it an article or a book that we are trying to write? — Aughost (talk) 17:26, 22 March 2012 (UTC) If two opposite faces of a Platonic dodecahedron are not distorted under an orthographic projection, the outline of the regular polyhedron is a convex regular decagon. Through a stellation of a Platonic dodecahedron and such a projection, we obtain eleven points, that are the common center of regular decagons and their ten common vertices. In the top view, five black crosses are the images of five of the twelve vertices of the icosahedron, which are in the upper horizontal face plane of the dodecahedron. The current rubric "Architecture" presents the only occurrence of "decagon" in the article. Someone that plays with this puzzle can discover some properties of regular pentagons and decagons, notably that /_a = φ and /_a = φ + 1, by denoting a, r and s three lengths in a convex regular decagon: sides, radius of circumcircle, and some diagonals. — Aughost (talk) 09:29, 23 March 2012 (UTC)

Please, no more non-actionable commentary, see WP:TALK and WP:NOTFORUM. Johnuniq (talk) 11:07, 27 March 2012 (UTC)

The following discussion has been closed. Please do not modify it.

There is no image about regular polyhedra in the current article. In my opinion, we have to talk about the two dual Platonic solids. For example, two opposite edges of a Platonic icosahedron are two smaller sides of a golden rectangle.
— Aughost (talk) 11:59, 17 March 2012 (UTC)

Good idea; though this one is awful busy, and the "yellow" is not really recognizable as such. Dicklyon (talk) 15:25, 17 March 2012 (UTC)

About the good idea, thank you. About colours, how might we name the golden tint associated to the fourth and last length of the increasing sequence? Weak ocher? This is depending on our screens and our eyes and our terminology. Anyway, stripes have to draw our attention all the more when they take up less space in the image. Actually, we find the weakest colour because it is the one of the largest length, equal to the sum of some lengths very well marked, and because of this equality written within the image: /_φ + a = φ a.

In the current section that is entitled Geometry, the first image shows two spirals. The text deals with pentagon and icosahedron…
— Aughost (talk) 09:16, 19 March 2012 (UTC)

The two following images show the same twelve points built through a stellation of a Platonic dodecahedron. More informations in several images, of course.
— Aughost (talk) 16:01, 20 March 2012 (UTC)

Those images look extremely busy and confusing to me. —David Eppstein (talk) 17:11, 20 March 2012 (UTC)

These are extraordinary images, but they are too complex for use in an article. The Platonic solids are wonderful and have many interesting properties, but this level of detail only makes sense after intense study. Johnuniq (talk) 01:46, 21 March 2012 (UTC)

An article is not a course page. In the current article, for example, what does everybody understand in the first image of section "Geometry"? Actually, this current first image does not correspond to the first paragraph. And we cannot explain everything about an interesting 3D image.
— Aughost (talk) 11:00, 21 March 2012 (UTC)

The idea of illustrating the presence of the golden ratio in a platonic solid seems a good one, but how about starting with the simplest illustration of a single such relation for a single solid, rather than the superposition as in these figures? The icosahedron in the first figure seems to play almost no role in the relations. Tkuvho (talk) 16:16, 21 March 2012 (UTC)

Through a stellation of a Platonic dodecahedron, we build a great dodecahedron, a Platonic icosahedron, and twelve stellated regular pentagons. Each face of the great dodecahedron is a duplicate of a face of the initial dodecahedron, to scale φ or φ + 1. Two opposite edges of a great dodecahedron are the smaller sides of a golden rectangle.
— Aughost (talk) 18:47, 21 March 2012 (UTC)

Whew. Let's start with something simple. Let a denote the distance between two opposite edges of a dodecahedron. The first figure suggests that the edgelength is then

(2-\phi )a

. Is this correct? Something that can be stated in English rather than Coxeterish may be appropriate for this page. Tkuvho (talk) 18:54, 21 March 2012 (UTC)

2\,-\,\varphi

is the multiplicative inverse of

\varphi ^{\,2}.

— Aughost (talk) 19:14, 21 March 2012 (UTC)

Very good then, we see that phi^2 appears as the ratio of the edge to the distance between opposite edges of a dodecahedron. That seems like an English sentence that could be added here. Any comment, David? Tkuvho (talk) 15:14, 22 March 2012 (UTC)

How to yield a geometric sequence with common ratio φ from two consecutive terms? From (1, φ), for example, we can yield (2 φ – 3, 2 – φ, φ – 1, 1, φ, 1 + φ, 2 φ + 1), through a few additions and subtractions. More generally, given two positive values a and b that fulfill

{\tfrac {\,a\,}{\,b\,}}\,=\,\varphi ,

we can yield a geometric sequence from (b, a ), either through successive additions or through successive subtractions, depending on the sense of the extension, right or left. Is it an article or a book that we are trying to write?
— Aughost (talk) 17:26, 22 March 2012 (UTC)

If two opposite faces of a Platonic dodecahedron are not distorted under an orthographic projection, the outline of the regular polyhedron is a convex regular decagon. Through a stellation of a Platonic dodecahedron and such a projection, we obtain eleven points, that are the common center of regular decagons and their ten common vertices. In the top view, five black crosses are the images of five of the twelve vertices of the icosahedron, which are in the upper horizontal face plane of the dodecahedron.

The current rubric "Architecture" presents the only occurrence of "decagon" in the article. Someone that plays with this puzzle can discover some properties of regular pentagons and decagons, notably that /_a = φ and /_a = φ + 1, by denoting a, r and s three lengths in a convex regular decagon: sides, radius of circumcircle, and some diagonals.
— Aughost (talk) 09:29, 23 March 2012 (UTC)

The last picture looks less busy than the others and may actually be accessible to the uninitiated. It looks like there may be aspects of the dodecahedron related to the golden ratio that are not already present in the regular pentagon. If so, these could be included in the article in addition to the discussion of the pentagon (perhaps in the same section). Tkuvho (talk) 11:09, 27 March 2012 (UTC)

John, I think you are overreacting (see previous message). Tkuvho (talk) 11:11, 27 March 2012 (UTC)

Sorry, but I did check the history and at the time of my edit the last comment made by someone other than the user posting the images which are not useful for this page was on March 22. Do you think something useful for this article may come from these deliberations? If so, please undo my change and feel free to remove my comments here. Johnuniq (talk) 11:16, 27 March 2012 (UTC)

As I mentioned above, the last figure may be usable. What do you think? Tkuvho (talk) 11:26, 27 March 2012 (UTC)

I was hoping to not be forced to say anything more because there is obviously an enormous effort behind creating the images. However, I saw the new image and, no, I do not think it is useful in an article. This talk page usually attracts fast attention from several editors, if they feel a comment is needed. I think that given the time that has elapsed, the lack of discussion regarding how an image like these might be used indicates that it is unlikely there is much support for their use. I will stop commenting for a while, and wait for others to offer an opinion. Johnuniq (talk) 11:45, 27 March 2012 (UTC)

Golden Ratio in atomic nuclei

The chemist Jan Boeyens has noted what appears to be a limit for neutrons versus protons in atomic nuclei with a value of Phi, as atomic number increases (see his Number Theory and the Periodicity of Matter, coauthored with Levendis, Demetrius C.).

In fact, the N/P ratio starts out at 0 (for H), is 1 (for D), and 2 (for T), but after, for stable nuclei, hovers around 1 until Ca (20N,20P). But Ca also has a very stable isotope with 28 neutrons (20 and 28 are 'magic' numbers)- this gives an N/P of 1.4 This seems to be approximately the start of the part of the N/P nuclide curve that hovers around 1.6. It continues out past 82, Pb, the last stable element.

However, it may be that what is really going on here is a shift between Metallic Means- with 1.000 for the first stable part of the nuclear periodic system, 1.6 as Golden Mean for the second stable part, and then finally the Silver Mean for the last- never seen because even supernova neutron fluxes are too low to produced such nuclei. Thus we would have, it this were true, a multitrack system, with stability shifting between the three tracks. — Preceding unsigned comment added by 69.121.117.192 (talk) 05:38, 4 June 2012 (UTC)

over-aggressively deletions by User:Kmhkmh

I want to ask what can be done to avoid such kind of revertions see History between 20:00 & 22:20. Three times he simply deleted my added content -- should I/he start a revision war? :-(

First time he deleted the word instead of correcting it to the preciser/informative adjective.
Second time, I gave no reference, so one may discuss the issue (or move it to the later in the article) -- but not totally delete the information. Else we (and even I) may delete much if all articles.
Third time he deletes a remark which I want to have in a footnote. This remark also includes a high-quality reference, which now is gone!

This user, Kmhkmh, is also involved in an article fight in wikipedia-de in "goldener-Schnitt" where I withdraw (like others) to continue to help because of the too chaotic discussion. Now it looks like he must also look after the english article "golden ratio", which is a way better designed article (IMHO) because in the german article about the same topic the "arts" aspect is degraded to a minor aspect -- it seems effectively to be reworked to become a mathematical article with some applied facts. Achim1999 (talk) 20:36, 13 June 2012 (UTC)

Also over-aggressive insertions and comments by Achim1999 are a problem. Let's talk here about what improvements are proposed, instead of warring in the article. This article attracts an awful lot of well-intentioned changes, but lots of editors watch and care, so don't expect to just put in whatever you want without some pushback. And maintain politeness even if someone is objecting, please, per WP:AGF and WP:BRD. Dicklyon (talk) 21:01, 13 June 2012 (UTC)

I have rolled back all of your contributions to the article of today, which started with a large expansion of a section on a property, and came with a new section heading with improper capitalization. This is not German; please respect that the article is in good shape by carefully adhere to both style and content guidelines. And it's already pretty large, so major additions need to be carefully considered. Dicklyon (talk) 21:08, 13 June 2012 (UTC)

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