![]() | This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 | ← | Archive 3 | Archive 4 | Archive 5 | Archive 6 | Archive 7 | → | Archive 9 |
That religious stuff is nonsensical enough and was removed in the past already. If anyone insist on including this under dipsuted claims, then to the very least you need to provide proper citations (no citation needed stuff). Furthermore a consent on the discussion page is needed as well.-- Kmhkmh ( talk) 23:55, 28 October 2011 (UTC)
(indent pushed <---- thataways, sorry). For the proponents of the measurements of such cities: This is stepping away from mathematics and toward numerology. Given any number, you can look and find items that closely resemble it. If not a city, then a mountain range. If not that, then the trees. There is no point whatsoever in visiting each of these. IF A NEW ARTICLE ENTITLED (words to the effect of) "Matching items to the golden ratio", then perhaps. Tgm1024 ( talk) 21:30, 7 February 2012 (UTC)
who is the writer of this arcticle, im doing a work on the golden ratio in the pyramids so please help. — Preceding unsigned comment added by 192.115.130.253 ( talk) 11:58, 9 February 2012 (UTC)
From WP:RS, "Self-published material may be acceptable when produced by an established expert on the topic of the article whose work in the relevant field has previously been published by reliable third-party publications." That seems to fit the situation to a tee. He has a masters in Mathematics Education, and his book "A Beginner's Guide To Constructing The Universe: The Mathematical Archetypes Of Nature, Art and Science" has been published by a non-vanity press (HarperPerennial). Further, we are giving it as his POV, as with some of the other examples (e.g. Roy Howat). Superm401 - Talk 07:27, 14 February 2012 (UTC)
I made an edit which made several improvements to this article. [1] The edit was reverted with an enigmatic edit summary of "An edit that removes the numeric value from the lede is unacceptable," I'm putting the improvements back in. If anyone would like to make additional improvements, please feel free to do so, but don't simply revert a major, good-faith edit containing several changes without discussing it here first. (If that edit summary comment was about moving the equations from the introduction, please read WP:MOSINTRO before making any further edits.) Sparkie82 ( t• c) 05:01, 2 March 2012 (UTC)
I feel the article would be improved by moving the equations from the intro. If this were only a mathematics article, then the equations would be appropriate in the introduction, however, this article covers a broad number of disciplines, including the arts, music, nature and many others. Readers will be coming to this article from many differing areas and with a variety of levels of understanding of mathematics. If there was no other way to introduce the subject and explain what the ratio is, then the equations would be needed, however, the prose, along with the graphical representation to the right of the intro adequately explain the ratio. Plus, the equations are revealed in the very next section of the article. Sparkie82 ( t• c) 05:41, 2 March 2012 (UTC)
I find it very difficult to imagine anyone who would find Sparkie82's proposed replacement lede easier to understand than the one that was there before. The phrase "the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one" does not communicate anything that is not communicated by "(a+b)/a = a/b", and it does so in a way that is much harder to understand. I am doubtful that there is anyone who will understand phrases of the form "the ratio of the quantity… to …" who will not also understand a simple division sign, and I cannot believe that there is anyone who will understand the phrase "is equal to" but not the = sign.
In fact, I think Sparkie82's change, and the rationale for it, is is completely misconceived. The phrase "the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one" is in fact an equation—that is, it is an assertion of the equality of two quantities. Sparkie82 has not removed the equations from the lede; instead, this user has removed one of the equations, and the one that was most clearly expressed. — Mark Dominus ( talk) 15:42, 3 March 2012 (UTC)
I'm testing a proposed new introduction for the article and requested those who are unfamiliar with the topic to comment on it. Those of you who are already familiar with the Golden ratio can continue to comment here. Sparkie82 ( t• c) 05:24, 5 March 2012 (UTC)
This is a proposed replacement for the introduction of the Golden ratio article. If you are unfamiliar with the golden ratio, please add a comment at the bottom of this section. Your comments will be used to help improve this article.
In mathematics and the arts, two quantities are said to have the golden ratio when the ratio between the larger and the smaller quantity is equal to the ratio between their sum and the larger quantity.
Expressed graphically,
When it is calculated, the ratio is 1.61803398...
The symbol for the golden ratio is the Greek letter phi(). The golden ratio is often called the golden section (Latin: sectio aurea) or golden mean. [1] [2] [3] Other names include extreme and mean ratio, [4] medial section, divine proportion,divine section (Latin: sectio divina), golden proportion,golden cut, [5]golden number, and mean of Phidias. [6] [7] [8]
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 (see Applications and observations below). Mathematicians have studied the golden ratio because of its unique and interesting properties. The golden ratio is also used in the analysis of financial markets, in strategies such as Fibonacci retracement.
Please add your comments below. (If you are already familiar with the golden ratio, or want to comment on the usability test itself, please use another section.) Thank you. Sparkie82 ( t• c) 05:15, 5 March 2012 (UTC)
How are you going to find people unfamiliar with the golden ratio to come here and take the test? And how are you going to compare the usability with the usability of what we have already? And why not express the ratio by using the aspect ratio of rectangles, as is pretty typical? Dicklyon ( talk) 05:23, 5 March 2012 (UTC)
"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)
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)
The image http://en.wikipedia.org/wiki/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)
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. |
![]() In green, red, blue and yellow, the succession of four lengths is a geometric progression with common ratio φ, the golden ratio. ![]() Platonic dodecahedron placed on a horizontal puzzle with golden triangles. ![]() Same Platonic dodecahedron with same notations. ![]() 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. ![]() 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.
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.
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 r / a = φ and s / a = φ + 1, by denoting a, r and s three lengths in a convex regular decagon: sides, radius of circumcircle, and some diagonals. |
OK, I'll bite. What is the relevance of Roses of Heliogabalus? Aldenrw ( talk) 16:30, 21 April 2012 (UTC)
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)
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? :-(
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)
Achim: Actually I left most of your edits untouched aside from fixing citations (despite considering all of them bit problematic) and just deleted one completely unsourced paragraph regarding the golden section only appearing "in popular and didactic math". Also I already outlined in de.wp why this opinion of yours is at least questionable. So if you can't source it, it stays out. Another thing is that you cannot mess up the display of featured article and asking others to fix it. If you have a problem with the wiki format make a text suggestion here and ask somebody to incorporate it into the article in proper format.-- Kmhkmh ( talk) 22:14, 13 June 2012 (UTC)
Sorry, I did asking for formating-help immediately, but see Wikipedia:Help_desk#sorry, need a quick help to place foot note and look at the time-stamps. You was too eager to delete, IMHO, and provocate this developemnt, IMHO. :-( Achim1999 ( talk) 22:35, 13 June 2012 (UTC)
I don't really see much in the added material that is worth keeping. The article already appears to state the rational approximation properties concisely, and I don't think there is much that we should add to that, aside from pointing the reader to the relevant articles. Sławomir Biały ( talk) 00:33, 14 June 2012 (UTC)
Note:
Since additional editors have reverted most of the edits as well (and addition removed an additional edit by Giufra9396 (newly introduced cinema section) the current version essentially matches the state before Achim's edits.The exact state version in the version history is: [2]
additional paragraph:
An often occuring misunderstanding is, that this golden ratio must be a number, but effectively it should and shall "only" be a ratio. This explains why also many people call the value , its reciprocal, the golden ratio. Moreover, popular science need not to be unique or consistent.
additional footnote(?):
There is a remarkable, high quality mathematical monograph by a leading authority in computer-science and mathematics which uses the wording golden-ratio, but (almost?) only in the book-index. The notable exception in his well-known book is the paragraph on pages 80-81, where a short historic overview about is given. The author also says why he uses this notation and where it is used mainly! See D. E. Knuth, The Art of Computer Programming, Vol 1, Fundamental Algorithms, 3rd Edition, Addison-Wesley 1997, chapter 1.2.8
The golden ratio (considered as ratio, but see below) has the simplest expression (and slowest convergence) as a continued fraction expansion of any irrational number (see Alternate forms above). [9] It is, for that reason, one of the (infinite many) worst cases of Lagrange's approximation theorem. For all integers , the numbers form the set of the worst possible approximable real numbers by rational numbers.
In reality if one considers a ratio a:b of two lengths or general two physical sizes of the same type, you are free also to consider the reciprocal value of b:a. But if a certain phenomen is identified or discovered to be caused by a special numeric ratio a:b then the explanation must also provide exactly the same phenomen for the numeric value of b:a. E.g. either one considers the typical angle by which handles are rotated around a certain pole, or look at the average number of handles needed for having a full rotation around this pole. Each explanation which reasons a value a:b will also lead to the value b:a from the "exchanged point" of view of the same phenomen.
Two important examples (in nature) are: the angles close to the golden ratio often show up in phyllotaxis (the growth of plants) [10] and the discovery in 1964, that sufficient irrational ratios for orbits are prefered in survive-duration and maximal stabilizing if they have the value 1:φ. Such orbits are called KAM-orbits (siehe see Kolmogorov–Arnold–Moser theorem). [11] [12] According to the just said, as well the ratio a:b as the ratio b:a should be maximal bad for approximation by rational numbers in these natural occuring cases. Because practical measured sizes must be positive, their values can only be or to be a value of worst possible approximability. In this sense, this is an important unique distinction of the golden ratio among all (positive) real numbers. Therefore this number is sometimes denoted in mathematical literature as the most irrational number. [13]
I like to cite the last reason for revision (Revert again to pre-today version. Ungrammatical and misspelled ("recursivly expansion"), unsourced (failure to converge for the other expansion), badly organized (phyllotaxis in rational approximation), etc.)
The phyllotaxic was in rational approximation integrated by purpose! Why did noone delete this unsourced statements prior to my given two sources there? :-/
Did you say anything about the convergence of these two given expansions? No, but I did! And the sqrt-expansion was not unique, you can also make a quadratic expansion from the given formula with doesn't convergent. I pointed this out, you not, but deleted my valuable hint -- (a good lecturer who knows the facts, would maybe formulated this differently, but not delete it).
As I just pointed very precisely out, you measure really subjective and to your personal likelyness (restricted knowledge), this is by far not scientific, as I like to work. But we will see what will have happened with my valuable contributions in say 1 month. There is a proverb: "It gets dangerous, if silly people get busy!" Sorry, but interpretation is still up to you. Achim1999 ( talk) 11:26, 14 June 2012 (UTC)
Diagram shows "a" x "a" as a rectangle with about 35% greater width than height. The adjacient text says it is a square which is what "a x a" signifies. Tiddy ( talk) —Preceding undated comment added 13:38, 24 July 2012 (UTC)
Monitor set at 1024x768 but looks like aspect ratio must be wrong for screens we are using. Thanks. Tiddy ( talk) —Preceding undated comment added 04:22, 10 September 2012 (UTC)
"Proportion Control" by Steven Strogatz, September 24, 2012... AnonMoos ( talk) 13:19, 26 September 2012 (UTC)
The text of the article stated that artists and architects used the golden ratio "at least since the Renaissance" for several years starting in 2006, if not before. This was changed, apparently without discussion, to "at least since the 20th Century" in March 2012. The comment on the edit was that there is "no evidence" for Renaissance use. However, the article itself gives examples. Even if the editor is correct, "at least since the 20th Century" is silly, and it would have been better simply to have removed claims as to the length of time the golden ratio has been used, rather than have it say that it is only since the 20th Century. I am reverting this change back to what the article stated before March 2012, namely "Renaissance". 98.229.134.2 ( talk) 16:28, 11 November 2012 (UTC)
The March 2012 discussion is at Talk:Golden_ratio/Archive_5#.22At_least_since_the_Renaissance.22. Dicklyon ( talk) 19:11, 11 November 2012 (UTC)
![]() | This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 | ← | Archive 3 | Archive 4 | Archive 5 | Archive 6 | Archive 7 | → | Archive 9 |
That religious stuff is nonsensical enough and was removed in the past already. If anyone insist on including this under dipsuted claims, then to the very least you need to provide proper citations (no citation needed stuff). Furthermore a consent on the discussion page is needed as well.-- Kmhkmh ( talk) 23:55, 28 October 2011 (UTC)
(indent pushed <---- thataways, sorry). For the proponents of the measurements of such cities: This is stepping away from mathematics and toward numerology. Given any number, you can look and find items that closely resemble it. If not a city, then a mountain range. If not that, then the trees. There is no point whatsoever in visiting each of these. IF A NEW ARTICLE ENTITLED (words to the effect of) "Matching items to the golden ratio", then perhaps. Tgm1024 ( talk) 21:30, 7 February 2012 (UTC)
who is the writer of this arcticle, im doing a work on the golden ratio in the pyramids so please help. — Preceding unsigned comment added by 192.115.130.253 ( talk) 11:58, 9 February 2012 (UTC)
From WP:RS, "Self-published material may be acceptable when produced by an established expert on the topic of the article whose work in the relevant field has previously been published by reliable third-party publications." That seems to fit the situation to a tee. He has a masters in Mathematics Education, and his book "A Beginner's Guide To Constructing The Universe: The Mathematical Archetypes Of Nature, Art and Science" has been published by a non-vanity press (HarperPerennial). Further, we are giving it as his POV, as with some of the other examples (e.g. Roy Howat). Superm401 - Talk 07:27, 14 February 2012 (UTC)
I made an edit which made several improvements to this article. [1] The edit was reverted with an enigmatic edit summary of "An edit that removes the numeric value from the lede is unacceptable," I'm putting the improvements back in. If anyone would like to make additional improvements, please feel free to do so, but don't simply revert a major, good-faith edit containing several changes without discussing it here first. (If that edit summary comment was about moving the equations from the introduction, please read WP:MOSINTRO before making any further edits.) Sparkie82 ( t• c) 05:01, 2 March 2012 (UTC)
I feel the article would be improved by moving the equations from the intro. If this were only a mathematics article, then the equations would be appropriate in the introduction, however, this article covers a broad number of disciplines, including the arts, music, nature and many others. Readers will be coming to this article from many differing areas and with a variety of levels of understanding of mathematics. If there was no other way to introduce the subject and explain what the ratio is, then the equations would be needed, however, the prose, along with the graphical representation to the right of the intro adequately explain the ratio. Plus, the equations are revealed in the very next section of the article. Sparkie82 ( t• c) 05:41, 2 March 2012 (UTC)
I find it very difficult to imagine anyone who would find Sparkie82's proposed replacement lede easier to understand than the one that was there before. The phrase "the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one" does not communicate anything that is not communicated by "(a+b)/a = a/b", and it does so in a way that is much harder to understand. I am doubtful that there is anyone who will understand phrases of the form "the ratio of the quantity… to …" who will not also understand a simple division sign, and I cannot believe that there is anyone who will understand the phrase "is equal to" but not the = sign.
In fact, I think Sparkie82's change, and the rationale for it, is is completely misconceived. The phrase "the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one" is in fact an equation—that is, it is an assertion of the equality of two quantities. Sparkie82 has not removed the equations from the lede; instead, this user has removed one of the equations, and the one that was most clearly expressed. — Mark Dominus ( talk) 15:42, 3 March 2012 (UTC)
I'm testing a proposed new introduction for the article and requested those who are unfamiliar with the topic to comment on it. Those of you who are already familiar with the Golden ratio can continue to comment here. Sparkie82 ( t• c) 05:24, 5 March 2012 (UTC)
This is a proposed replacement for the introduction of the Golden ratio article. If you are unfamiliar with the golden ratio, please add a comment at the bottom of this section. Your comments will be used to help improve this article.
In mathematics and the arts, two quantities are said to have the golden ratio when the ratio between the larger and the smaller quantity is equal to the ratio between their sum and the larger quantity.
Expressed graphically,
When it is calculated, the ratio is 1.61803398...
The symbol for the golden ratio is the Greek letter phi(). The golden ratio is often called the golden section (Latin: sectio aurea) or golden mean. [1] [2] [3] Other names include extreme and mean ratio, [4] medial section, divine proportion,divine section (Latin: sectio divina), golden proportion,golden cut, [5]golden number, and mean of Phidias. [6] [7] [8]
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 (see Applications and observations below). Mathematicians have studied the golden ratio because of its unique and interesting properties. The golden ratio is also used in the analysis of financial markets, in strategies such as Fibonacci retracement.
Please add your comments below. (If you are already familiar with the golden ratio, or want to comment on the usability test itself, please use another section.) Thank you. Sparkie82 ( t• c) 05:15, 5 March 2012 (UTC)
How are you going to find people unfamiliar with the golden ratio to come here and take the test? And how are you going to compare the usability with the usability of what we have already? And why not express the ratio by using the aspect ratio of rectangles, as is pretty typical? Dicklyon ( talk) 05:23, 5 March 2012 (UTC)
"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)
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)
The image http://en.wikipedia.org/wiki/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)
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. |
![]() In green, red, blue and yellow, the succession of four lengths is a geometric progression with common ratio φ, the golden ratio. ![]() Platonic dodecahedron placed on a horizontal puzzle with golden triangles. ![]() Same Platonic dodecahedron with same notations. ![]() 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. ![]() 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.
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.
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 r / a = φ and s / a = φ + 1, by denoting a, r and s three lengths in a convex regular decagon: sides, radius of circumcircle, and some diagonals. |
OK, I'll bite. What is the relevance of Roses of Heliogabalus? Aldenrw ( talk) 16:30, 21 April 2012 (UTC)
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)
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? :-(
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)
Achim: Actually I left most of your edits untouched aside from fixing citations (despite considering all of them bit problematic) and just deleted one completely unsourced paragraph regarding the golden section only appearing "in popular and didactic math". Also I already outlined in de.wp why this opinion of yours is at least questionable. So if you can't source it, it stays out. Another thing is that you cannot mess up the display of featured article and asking others to fix it. If you have a problem with the wiki format make a text suggestion here and ask somebody to incorporate it into the article in proper format.-- Kmhkmh ( talk) 22:14, 13 June 2012 (UTC)
Sorry, I did asking for formating-help immediately, but see Wikipedia:Help_desk#sorry, need a quick help to place foot note and look at the time-stamps. You was too eager to delete, IMHO, and provocate this developemnt, IMHO. :-( Achim1999 ( talk) 22:35, 13 June 2012 (UTC)
I don't really see much in the added material that is worth keeping. The article already appears to state the rational approximation properties concisely, and I don't think there is much that we should add to that, aside from pointing the reader to the relevant articles. Sławomir Biały ( talk) 00:33, 14 June 2012 (UTC)
Note:
Since additional editors have reverted most of the edits as well (and addition removed an additional edit by Giufra9396 (newly introduced cinema section) the current version essentially matches the state before Achim's edits.The exact state version in the version history is: [2]
additional paragraph:
An often occuring misunderstanding is, that this golden ratio must be a number, but effectively it should and shall "only" be a ratio. This explains why also many people call the value , its reciprocal, the golden ratio. Moreover, popular science need not to be unique or consistent.
additional footnote(?):
There is a remarkable, high quality mathematical monograph by a leading authority in computer-science and mathematics which uses the wording golden-ratio, but (almost?) only in the book-index. The notable exception in his well-known book is the paragraph on pages 80-81, where a short historic overview about is given. The author also says why he uses this notation and where it is used mainly! See D. E. Knuth, The Art of Computer Programming, Vol 1, Fundamental Algorithms, 3rd Edition, Addison-Wesley 1997, chapter 1.2.8
The golden ratio (considered as ratio, but see below) has the simplest expression (and slowest convergence) as a continued fraction expansion of any irrational number (see Alternate forms above). [9] It is, for that reason, one of the (infinite many) worst cases of Lagrange's approximation theorem. For all integers , the numbers form the set of the worst possible approximable real numbers by rational numbers.
In reality if one considers a ratio a:b of two lengths or general two physical sizes of the same type, you are free also to consider the reciprocal value of b:a. But if a certain phenomen is identified or discovered to be caused by a special numeric ratio a:b then the explanation must also provide exactly the same phenomen for the numeric value of b:a. E.g. either one considers the typical angle by which handles are rotated around a certain pole, or look at the average number of handles needed for having a full rotation around this pole. Each explanation which reasons a value a:b will also lead to the value b:a from the "exchanged point" of view of the same phenomen.
Two important examples (in nature) are: the angles close to the golden ratio often show up in phyllotaxis (the growth of plants) [10] and the discovery in 1964, that sufficient irrational ratios for orbits are prefered in survive-duration and maximal stabilizing if they have the value 1:φ. Such orbits are called KAM-orbits (siehe see Kolmogorov–Arnold–Moser theorem). [11] [12] According to the just said, as well the ratio a:b as the ratio b:a should be maximal bad for approximation by rational numbers in these natural occuring cases. Because practical measured sizes must be positive, their values can only be or to be a value of worst possible approximability. In this sense, this is an important unique distinction of the golden ratio among all (positive) real numbers. Therefore this number is sometimes denoted in mathematical literature as the most irrational number. [13]
I like to cite the last reason for revision (Revert again to pre-today version. Ungrammatical and misspelled ("recursivly expansion"), unsourced (failure to converge for the other expansion), badly organized (phyllotaxis in rational approximation), etc.)
The phyllotaxic was in rational approximation integrated by purpose! Why did noone delete this unsourced statements prior to my given two sources there? :-/
Did you say anything about the convergence of these two given expansions? No, but I did! And the sqrt-expansion was not unique, you can also make a quadratic expansion from the given formula with doesn't convergent. I pointed this out, you not, but deleted my valuable hint -- (a good lecturer who knows the facts, would maybe formulated this differently, but not delete it).
As I just pointed very precisely out, you measure really subjective and to your personal likelyness (restricted knowledge), this is by far not scientific, as I like to work. But we will see what will have happened with my valuable contributions in say 1 month. There is a proverb: "It gets dangerous, if silly people get busy!" Sorry, but interpretation is still up to you. Achim1999 ( talk) 11:26, 14 June 2012 (UTC)
Diagram shows "a" x "a" as a rectangle with about 35% greater width than height. The adjacient text says it is a square which is what "a x a" signifies. Tiddy ( talk) —Preceding undated comment added 13:38, 24 July 2012 (UTC)
Monitor set at 1024x768 but looks like aspect ratio must be wrong for screens we are using. Thanks. Tiddy ( talk) —Preceding undated comment added 04:22, 10 September 2012 (UTC)
"Proportion Control" by Steven Strogatz, September 24, 2012... AnonMoos ( talk) 13:19, 26 September 2012 (UTC)
The text of the article stated that artists and architects used the golden ratio "at least since the Renaissance" for several years starting in 2006, if not before. This was changed, apparently without discussion, to "at least since the 20th Century" in March 2012. The comment on the edit was that there is "no evidence" for Renaissance use. However, the article itself gives examples. Even if the editor is correct, "at least since the 20th Century" is silly, and it would have been better simply to have removed claims as to the length of time the golden ratio has been used, rather than have it say that it is only since the 20th Century. I am reverting this change back to what the article stated before March 2012, namely "Renaissance". 98.229.134.2 ( talk) 16:28, 11 November 2012 (UTC)
The March 2012 discussion is at Talk:Golden_ratio/Archive_5#.22At_least_since_the_Renaissance.22. Dicklyon ( talk) 19:11, 11 November 2012 (UTC)