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Archive 5 | Archive 6 | Archive 7 | Archive 8 | Archive 9 |
Regarding this removal: this isn't one of those cases where there is an unresolved difference of legitimate opinion in the field (like when Physicist A uses a particular approximation that Physicist B thinks is inapplicable). Davies just screwed up. XOR'easter ( talk) 13:08, 26 July 2019 (UTC)
spinning parameter). It's not reliable either. XOR'easter ( talk) 00:07, 27 July 2019 (UTC)
Whoops, I must have missed this notification in my watchlist. There's a box in Gravitation dedicated to the topic on page 36. But pretty much any field theory textbook will discuss the subject at least a little in the course of establishing its notational conventions. Tony Zee's Quantum Field Theory in a Nutshell does so in the preface (p. xxv), for example. XOR'easter ( talk) 21:03, 8 August 2019 (UTC)
I find the mathworld explanation much clearer and more intuitive. My mental picture is of a piece of paper from which you keep cutting squares from the longest size, and the ratio of the sides is always φ.
As it is, it takes several steps to get from the a+b relationship to the one just for φ whereas if you directly make the sides 1 and φ then this relationship "can immediately be seen".— Preceding unsigned comment added by 2A01:CB15:8010:2F00:ECF5:C24C:4992:6347 ( talk) 07:56, 7 February 2020 (UTC)
The Reference 9, while covering the first clause of the sentence does not mention financial markets, thus a separate reference for this clause is necessary. Also, I am interested if indeed phi does show up in financial markets. — Preceding unsigned comment added by 2603:3005:BE6:C000:8DF:D9BE:2C86:6D0 ( talk) 22:42, 24 February 2020 (UTC)
So be skeptical the next time you see the golden ratio being used to sell blue jeans, stock tips or the perfect smile.
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I found a new property of the Golden ratio:
1 / x = 1 + x
Where (x = 1,618...(Golden ratio) - 1)
thx Ricerca Veritas ( talk) 01:49, 22 August 2020 (UTC)
Should it be mentioned that the flag of Togo has a proportion of 1:φ? – Hydrogenation ( talk) 18:55, 16 January 2021 (UTC)
It's meaningless and a bit confusing when viewed in a mobile context. Bunglero ( talk) 00:23, 14 February 2021 (UTC)
For what n,m is this claimed? It fails for n=3 and m=2 (and most others) [Why not say: sqrt 5 is irrational hence phi is irrational?] 74.81.88.122 ( talk) 15:40, 25 March 2020 (UTC)
Equation * is said to be an identity. It is certainly not true for all m an n. What is the claim? In my view Eq * does not prove phi is irrational. If you feel that it does please supply some detail to support you view. If not just go with your next paragraph which, as you note, says that it is irrational because sqrt 5 is irrational. 74.81.88.122 ( talk) 01:03, 26 March 2020 (UTC)
The most beautiful equation for golden ratio was discovered by the Indian Mathematician Srinivasa Ramanujan. The equation is as follows: Golden ratio = [2*3/1*4]*[7*8/6*9]*[12*13/11*14]* ... — Preceding unsigned comment added by Ashutoshpise ( talk • contribs) 08:56, 2 March 2021 (UTC)
in the music section, it says that: "The musicologist Roy Howat has observed that the formal boundaries of Debussy's La Mer correspond exactly to the golden section." what is a formal boundary of a music composition? how can it be a number or a ratio? Please tell me if I should put this question somewhere else. Thank you! Bumpf ( talk) 15:06, 24 March 2021 (UTC)
I used my ruler to measure the proportions of the Parthenon face shown here: https://www.shutterstock.com/editorial/image-editorial/art-places-various-5850841gq
using the large version shown here, I got 22.2 mm wide measured across the top frame, and 13.7 mm deep from the tip of the triangle to the foundation. The proportion is 16.2. Using the smaller version of this image I saw on google images, I measured 10.5 mm divided by 6.5, or 1.615. So it seems you can find the golden proportion in the Parthenon front face if you include what appears to be the foundation. Eameece ( talk) 23:06, 11 April 2021 (UTC) [1]
This author Gary Meisner (2013) finds golden proportion ratios in The Parthenon as well. https://www.goldennumber.net/parthenon-phi-golden-ratio/ Meisner's article points out that the fact that the Greeks in the 5th century BC did not know about this proportion and thus did not intentionally design the building in accordance with it, does not disprove that the proportion appears. Meisner says that the proportions may be present since the appearance of the Golden Ratio in nature and the human body influences human aesthetics. Eameece ( talk) 23:18, 11 April 2021 (UTC)
The ratio of the width of 101′ 3.75″ to revised height of 62.491′ is 1.621, close to the golden ratio of 1.618. Any measure of the Parthenon should include it's base, since that's what observers see as "The Parthenon" Gary Meisner, 2020. [1] Perhaps this represents another view on this subject. Eameece ( talk) 06:41, 12 April 2021 (UTC)
OK. Thanks for reading my suggestion. I think this Meisner website is well documented and accurate, despite that one review. There may be others who hold this opinion, but that's all for now 2600:1700:BEF0:1BB0:5D6F:5F58:45F8:E304 ( talk) 20:23, 12 April 2021 (UTC)
I went and checked the actual journal article and "the golden ratio is present at the atomic scale in the magnetic resonance of spins in cobalt niobate crystals" is not what the article found.
Specifically, the journal article states:
"Figure 4D shows how the ratio of the energies of those peaks varies with increasing field and approaches closely (near 5 T just below the 3D critical field of 5.5 T) the golden ratio m2/m1 = (1 + sqrt(5))/2 = 1.618 predicted for the E8 masses. [1]
I'm not sure about admissible evidence (it is locked behind a paywall). And the source the wiki article links is quoted correctly. The source is just pop science and doesn't understand the word "approaches". I mean its nifty but so would approaching pi or sqrt(2) be. Mediocracy ( talk) 19:54, 1 July 2021 (UTC)
References
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Please add this subsection to the "Applications and observations" section of the current Golden Ratio wiki page
Human Physical Beauty
Some believe that the golden ratio may serve as the underlying foundation of an attractive human physical appearance. American plastic surgeon Andrew J. Hayduke, M.D. proposed that human physical beauty can be objectively tested via analysis for golden ratio anatomic relationships within the physical anatomic features of human faces and breasts. Hayduke describes a series of golden ratio based anatomic test grids within his treatise entitled The Golden Ratio Within the Human Face and Breast: A Plastic Surgeon's Method of Analyzing Beauty.
[1] JohnEdit45 ( talk) 14:01, 13 August 2021 (UTC)
References
I spent like 2 hours cleaning up this article’s 5 different inconsistent ways of writing inline math (sans serif italics, sans serif Roman, serif italics, serif Roman, LaTeX serif italics). Apparently David Eppstein really preferred the extremely inconsistent version / is too busy to bother with the details, so insists on trashing that effort. To be honest I don’t understand what he is trying to say. The explanation given in reverts were:
(1) Math tags should always be preferred to math templates
(2) Blackboard bold should be left alone
(3) Supposedly looks impossibly different from φ, φ, or φ, so the latter forms should be avoided/eliminated
Cheers. – jacobolus (t) 23:33, 21 September 2021 (UTC)
Why 1:φ ratio is so special? I mean, of course φ has its properties such as 1,618.. & 0,618...; but in everyday life only one of them is used, the one that allows to create a paper page (A format) with the same ratio upon dividing it in half on the longer side. But, you know what? a 1:√2 ratio has exactly the same property because √2/2:1 |*2/√2| = 1:2/√2 |*√2/√2| = 1:2√2/2 = 1:√2. — Preceding unsigned comment added by 31.182.229.99 ( talk) 20:43, 30 December 2021 (UTC)
Even though display="block" adds too much white space, {{ block indent}} completely cuts off text at the edge of the screen with no scrolling capabilities. Especially a problem on mobile screens. Text gets wrapped, but since <math> is rendered as an image anything to the right of a boundary is lost Hellacioussatyr ( talk) 23:25, 28 July 2022 (UTC)
If you test for convergence for sequences 1,1 1,2 2,1 2,2; 1,2 will converge faster, as you are already one step along the Fibonacci sequence. 1,1 converges faster than 2,1. Therefore, bringing the concept of Lucas numbers, and giving a specific example starting 2,1 could be misleading as to suggest that Lucas series beginning with numbers other than 1,1 possess special properties not found in the Fibonacci number when it comes to dividing consecutive numbers and the golden ratio.
I suggest the section on Lucas numbers should be slimmed down, Lucas examples removed, and a note that: In the Fibonacci sequence, each number is equal to the sum of the preceding two, starting with the base sequence 1,1. As you move along the Fibonacci sequence, dividing two consecutive numbers, the closer you move to the golden ratio. Lucas numbers begin with a base sequence other than 1,1 and will similarly converge towards the golden ratio. Nick Hill ( talk) 11:42, 8 June 2022 (UTC)
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In the section labeled Music, the third paragraph says, “ The musicologist Roy Howat has observed that the formal boundaries of Debussy's La Mer correspond exactly to the golden section.[119] Trezise finds the intrinsic evidence "remarkable", but cautions that no written or reported evidence suggests that Debussy consciously sought such proportions.[120]”
This is incorrect. In fact, Trezise’s actual quote is, “ The precise significance of these findings is hard to assess, but the intrinsic evidence is remarkable; there is, however, no material proof (letters, sketches, anecdotes, for example) other than the finished works that Debussy consciously contrived such proportional schemes.
There is, in fact, a quote from Debussy himself, in Debussy’s published letters, titled ‘Debussy’s Letters’, in a letter to his publisher, referencing “the divine number”. I’m quoting Debussy word for word. This is taken from letter #108, to Jacques Durand: “I was just getting ready to send you the proofs…. You’ll see, on page 8 of ‘Jardins sous la pluie’, there’s a bar missing; my fault, in fact, as it’s not in the manuscript. Even so, it’s necessary from the point of view of number; the divine number,…”
I would suggest you amend the third paragraph, by quoting Debussy and adding a reference to the ‘letters’ book. There’s speculation that Debussy may have been influenced by a particular group of artists and poets in France he was spending time with. Regardless, that is a direct quote from his letters, and the piece of music mentioned has been analyzed for use of the golden ratio and checks out. If you’d like I’ll send you the findings in that score. I believe Roy Howat may have also discussed this in his book, ‘Debussy in Proportion.’ I would need to get a new copy of that book to verify, which I’d be happy to do.
You may contact me directly at email@stevesteele.com.
Regards, Steve Steele Andromeda Expat ( talk) 05:37, 4 August 2022 (UTC)
Is there a reason for these two as separate categories? – jacobolus (t) 07:38, 18 August 2022 (UTC)
may contain any or all of the following: Explanatory footnotes ... Citation footnotes ... Full citations to sources, ... General references (full bibliographic citations to sources that were consulted in writing the article but that are not explicitly connected to any specific material in the article).This seems to perfectly well include everything currently in the "further reading" section of this article. To be honest I don’t get the point of a "further reading" section, for which it recommends
a reasonable number of publications that would help interested readers learn more about the article subject.... This section is not intended as a repository for general references or full citations that were used to create the article content....To me the separation into two sections seems not that helpful. It creates extra work for anyone adding or removing footnotes (need to check which section the source is in and move it if necessary) and potential confusion for readers (is one of the two types being more recommended than the other? Are there any model articles where both of these sections appear and seem to have particularly clear/helpful content and structure? – jacobolus (t) 05:43, 19 August 2022 (UTC)
— Preceding unsigned comment added by 46.39.54.40 ( talk) 18:44, 28 May 2022 (UTC)
I made the bit about 5th roots of unity a bit more explicit in golden ratio#Other properties. Does that cover what folks here were looking for? – jacobolus (t) 05:45, 23 August 2022 (UTC)
The formula for phi can be reduced to a positive exponent, multiplication, and addition:
This is clear and easy to remember, demonstrates interesting relationships, and is less obtuse than the formula as shown in the article. This can also improve computational efficiency (of admittedly marginal importance). Here is an example for javascript:
const phi = Math.pow(5, 0.5) * 0.5 + 0.5;
I placed this under computation, but Ovinus reverted it. Placing it here in the event someone else sees it as useful. Myndex talk 00:45, 23 August 2022 (UTC)
sqrt
in preference to pow
for practical computation, though it doesn’t really matter in this case because Javascript JIT compilers are smart enough to evaluate the constant expression one time and save the result then not bother repeating the computation. The definitional “formulas” in the article are or and they do not seem “obtuse”. –
jacobolus
(t)
01:35, 23 August 2022 (UTC)
sqrtsd
/vsqrt
is a single instruction; powf
is usually a complex beast to get faithful rounding (e.g.,
[1]).) In any case, that's still OR, and I agree with jacobolus that it's no easier to remember. recalls the beloved quadratic formula, while this formula uses unsightly decimals.
Ovinus (
talk)
04:45, 23 August 2022 (UTC)
phi approximates the Fibonacci ratio starting with the 5th Fibonacci number pair– this is starting to sound suspiciously like numerology. – jacobolus (t) 19:07, 23 August 2022 (UTC)
Hello!
I hope my edits have been pleasant (and thank you to those who have pitched in to mine and prior), if you need me to add/remove or change anything I've done in a similar style, please let me know or feel free to further improve the article yourself. Since the mathematics content was expanded by a relatively large amount, I am going to also help update Applications and observations and Disputed observations to balance the length of Mathematics (maybe expand History, too). If you'd like to join me in this effort, please feel free, there is plenty more that can be added, almost everywhere. If you also have ideas on minor unmentioned golden ratio topics for the article under Mathematics that could be added inside a larger heading of Other properties let me know too, I can work on them if you don't feel inclined. I am going to expand Other properties with sections detailing:
That way we have a proper Other properties section that flows into Applications and observations. Thank you for reading
and/or helping the article!
Radlrb (
talk)
13:11, 24 June 2022 (UTC)
Is there any reason why this article shouldn't be changed from using the mathematically-rare curly phi (LaTeX \varphi) to the historically-accurate straight phi (LaTeX \phi)? D.keenan ( talk) 04:46, 14 September 2022 (UTC)
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Please allow me to edit this page.I am currently a college student and i have spotted a gramatical error SoopBruv ( talk) 08:22, 14 October 2022 (UTC)
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Justification for change: There is no reason, to my understanding, that content that is not sky-is-blue obvious should be allowed to appear, unsourced, without a reader warning. To do so violates WP:VERIFY and/or WP:ORIGINAL RESEARCH. (As a former professor of the physical sciences, I state without reservation, the content of this section is not obvious, rather, it needs to have been taught to the editor placing it, and therefore is derived, ultimately, from some authoritative source.) The "Calculation" section certainly must appear so-derived in a wide variety of reputable sources. Find an autoritative source, edit the content to that source, and place the citation. Until then, I ask the following reader warning edit, in keeping with clear WP policies and guidelines.
Change from:
Change to:
If rejecting this request, please state the applicable WP policies and guidelines that trump the clear statements in WPVERIFY and WP:ORIGINAL RESEARCH. Thank you. 2601:246:C700:2:8D90:7012:872:558C ( talk) 20:01, 27 October 2022 (UTC)
Mathematical literacy may be necessary to follow a "routine" calculation, particularly for articles on mathematics or in the hard sciences. In some cases, editors may show their work in a footnote.This calculation is decidedly "routine", in the context of this sentence of CALC (assuming mathematical "literacy", a higher standard than what you suggest). What is certainly not routine: medium-sized proofs, rarely used or opaque techniques, judgments on the nature of proofs (simplicity, beauty). To be honest, I've never seen people using footnotes for work, although I think it's a nice idea.
articles are beyond the pale with regard to being verifiable content– You can certainly find examples that push (or exceed) the boundary of WP:CALC, but this is not one of them.
you ... and I ... can follow it, and are sure it is true, is not the test given us– Yes it is, more or less. More concretely, anyone with a reasonable background (introductory middle school / high school algebra, and a reasonably careful effort) can follow the steps here; if your undergraduate technical students are having a problem following this line of reasoning something is going very wrong with their background preparation. Adding a source is not going to make basic algebraic manipulations easier to follow for someone who has not yet been through a year or two of introductory algebra courses, but teaching elementary algebra can’t be expected of every technical article, even those aimed at a broad audience. You can trivially find some sources for these specific manipulations if you need to (e.g. by skimming through a few of the cited books about the golden ratio), but even if you couldn’t, these are well within the scope of WP:CALC for this article. – jacobolus (t) 02:09, 28 October 2022 (UTC)
{{
Edit semi-protected}}
template. —
Paper9oll (
🔔 •
📝)
14:25, 29 October 2022 (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 5 | Archive 6 | Archive 7 | Archive 8 | Archive 9 |
Regarding this removal: this isn't one of those cases where there is an unresolved difference of legitimate opinion in the field (like when Physicist A uses a particular approximation that Physicist B thinks is inapplicable). Davies just screwed up. XOR'easter ( talk) 13:08, 26 July 2019 (UTC)
spinning parameter). It's not reliable either. XOR'easter ( talk) 00:07, 27 July 2019 (UTC)
Whoops, I must have missed this notification in my watchlist. There's a box in Gravitation dedicated to the topic on page 36. But pretty much any field theory textbook will discuss the subject at least a little in the course of establishing its notational conventions. Tony Zee's Quantum Field Theory in a Nutshell does so in the preface (p. xxv), for example. XOR'easter ( talk) 21:03, 8 August 2019 (UTC)
I find the mathworld explanation much clearer and more intuitive. My mental picture is of a piece of paper from which you keep cutting squares from the longest size, and the ratio of the sides is always φ.
As it is, it takes several steps to get from the a+b relationship to the one just for φ whereas if you directly make the sides 1 and φ then this relationship "can immediately be seen".— Preceding unsigned comment added by 2A01:CB15:8010:2F00:ECF5:C24C:4992:6347 ( talk) 07:56, 7 February 2020 (UTC)
The Reference 9, while covering the first clause of the sentence does not mention financial markets, thus a separate reference for this clause is necessary. Also, I am interested if indeed phi does show up in financial markets. — Preceding unsigned comment added by 2603:3005:BE6:C000:8DF:D9BE:2C86:6D0 ( talk) 22:42, 24 February 2020 (UTC)
So be skeptical the next time you see the golden ratio being used to sell blue jeans, stock tips or the perfect smile.
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I found a new property of the Golden ratio:
1 / x = 1 + x
Where (x = 1,618...(Golden ratio) - 1)
thx Ricerca Veritas ( talk) 01:49, 22 August 2020 (UTC)
Should it be mentioned that the flag of Togo has a proportion of 1:φ? – Hydrogenation ( talk) 18:55, 16 January 2021 (UTC)
It's meaningless and a bit confusing when viewed in a mobile context. Bunglero ( talk) 00:23, 14 February 2021 (UTC)
For what n,m is this claimed? It fails for n=3 and m=2 (and most others) [Why not say: sqrt 5 is irrational hence phi is irrational?] 74.81.88.122 ( talk) 15:40, 25 March 2020 (UTC)
Equation * is said to be an identity. It is certainly not true for all m an n. What is the claim? In my view Eq * does not prove phi is irrational. If you feel that it does please supply some detail to support you view. If not just go with your next paragraph which, as you note, says that it is irrational because sqrt 5 is irrational. 74.81.88.122 ( talk) 01:03, 26 March 2020 (UTC)
The most beautiful equation for golden ratio was discovered by the Indian Mathematician Srinivasa Ramanujan. The equation is as follows: Golden ratio = [2*3/1*4]*[7*8/6*9]*[12*13/11*14]* ... — Preceding unsigned comment added by Ashutoshpise ( talk • contribs) 08:56, 2 March 2021 (UTC)
in the music section, it says that: "The musicologist Roy Howat has observed that the formal boundaries of Debussy's La Mer correspond exactly to the golden section." what is a formal boundary of a music composition? how can it be a number or a ratio? Please tell me if I should put this question somewhere else. Thank you! Bumpf ( talk) 15:06, 24 March 2021 (UTC)
I used my ruler to measure the proportions of the Parthenon face shown here: https://www.shutterstock.com/editorial/image-editorial/art-places-various-5850841gq
using the large version shown here, I got 22.2 mm wide measured across the top frame, and 13.7 mm deep from the tip of the triangle to the foundation. The proportion is 16.2. Using the smaller version of this image I saw on google images, I measured 10.5 mm divided by 6.5, or 1.615. So it seems you can find the golden proportion in the Parthenon front face if you include what appears to be the foundation. Eameece ( talk) 23:06, 11 April 2021 (UTC) [1]
This author Gary Meisner (2013) finds golden proportion ratios in The Parthenon as well. https://www.goldennumber.net/parthenon-phi-golden-ratio/ Meisner's article points out that the fact that the Greeks in the 5th century BC did not know about this proportion and thus did not intentionally design the building in accordance with it, does not disprove that the proportion appears. Meisner says that the proportions may be present since the appearance of the Golden Ratio in nature and the human body influences human aesthetics. Eameece ( talk) 23:18, 11 April 2021 (UTC)
The ratio of the width of 101′ 3.75″ to revised height of 62.491′ is 1.621, close to the golden ratio of 1.618. Any measure of the Parthenon should include it's base, since that's what observers see as "The Parthenon" Gary Meisner, 2020. [1] Perhaps this represents another view on this subject. Eameece ( talk) 06:41, 12 April 2021 (UTC)
OK. Thanks for reading my suggestion. I think this Meisner website is well documented and accurate, despite that one review. There may be others who hold this opinion, but that's all for now 2600:1700:BEF0:1BB0:5D6F:5F58:45F8:E304 ( talk) 20:23, 12 April 2021 (UTC)
I went and checked the actual journal article and "the golden ratio is present at the atomic scale in the magnetic resonance of spins in cobalt niobate crystals" is not what the article found.
Specifically, the journal article states:
"Figure 4D shows how the ratio of the energies of those peaks varies with increasing field and approaches closely (near 5 T just below the 3D critical field of 5.5 T) the golden ratio m2/m1 = (1 + sqrt(5))/2 = 1.618 predicted for the E8 masses. [1]
I'm not sure about admissible evidence (it is locked behind a paywall). And the source the wiki article links is quoted correctly. The source is just pop science and doesn't understand the word "approaches". I mean its nifty but so would approaching pi or sqrt(2) be. Mediocracy ( talk) 19:54, 1 July 2021 (UTC)
References
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Please add this subsection to the "Applications and observations" section of the current Golden Ratio wiki page
Human Physical Beauty
Some believe that the golden ratio may serve as the underlying foundation of an attractive human physical appearance. American plastic surgeon Andrew J. Hayduke, M.D. proposed that human physical beauty can be objectively tested via analysis for golden ratio anatomic relationships within the physical anatomic features of human faces and breasts. Hayduke describes a series of golden ratio based anatomic test grids within his treatise entitled The Golden Ratio Within the Human Face and Breast: A Plastic Surgeon's Method of Analyzing Beauty.
[1] JohnEdit45 ( talk) 14:01, 13 August 2021 (UTC)
References
I spent like 2 hours cleaning up this article’s 5 different inconsistent ways of writing inline math (sans serif italics, sans serif Roman, serif italics, serif Roman, LaTeX serif italics). Apparently David Eppstein really preferred the extremely inconsistent version / is too busy to bother with the details, so insists on trashing that effort. To be honest I don’t understand what he is trying to say. The explanation given in reverts were:
(1) Math tags should always be preferred to math templates
(2) Blackboard bold should be left alone
(3) Supposedly looks impossibly different from φ, φ, or φ, so the latter forms should be avoided/eliminated
Cheers. – jacobolus (t) 23:33, 21 September 2021 (UTC)
Why 1:φ ratio is so special? I mean, of course φ has its properties such as 1,618.. & 0,618...; but in everyday life only one of them is used, the one that allows to create a paper page (A format) with the same ratio upon dividing it in half on the longer side. But, you know what? a 1:√2 ratio has exactly the same property because √2/2:1 |*2/√2| = 1:2/√2 |*√2/√2| = 1:2√2/2 = 1:√2. — Preceding unsigned comment added by 31.182.229.99 ( talk) 20:43, 30 December 2021 (UTC)
Even though display="block" adds too much white space, {{ block indent}} completely cuts off text at the edge of the screen with no scrolling capabilities. Especially a problem on mobile screens. Text gets wrapped, but since <math> is rendered as an image anything to the right of a boundary is lost Hellacioussatyr ( talk) 23:25, 28 July 2022 (UTC)
If you test for convergence for sequences 1,1 1,2 2,1 2,2; 1,2 will converge faster, as you are already one step along the Fibonacci sequence. 1,1 converges faster than 2,1. Therefore, bringing the concept of Lucas numbers, and giving a specific example starting 2,1 could be misleading as to suggest that Lucas series beginning with numbers other than 1,1 possess special properties not found in the Fibonacci number when it comes to dividing consecutive numbers and the golden ratio.
I suggest the section on Lucas numbers should be slimmed down, Lucas examples removed, and a note that: In the Fibonacci sequence, each number is equal to the sum of the preceding two, starting with the base sequence 1,1. As you move along the Fibonacci sequence, dividing two consecutive numbers, the closer you move to the golden ratio. Lucas numbers begin with a base sequence other than 1,1 and will similarly converge towards the golden ratio. Nick Hill ( talk) 11:42, 8 June 2022 (UTC)
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In the section labeled Music, the third paragraph says, “ The musicologist Roy Howat has observed that the formal boundaries of Debussy's La Mer correspond exactly to the golden section.[119] Trezise finds the intrinsic evidence "remarkable", but cautions that no written or reported evidence suggests that Debussy consciously sought such proportions.[120]”
This is incorrect. In fact, Trezise’s actual quote is, “ The precise significance of these findings is hard to assess, but the intrinsic evidence is remarkable; there is, however, no material proof (letters, sketches, anecdotes, for example) other than the finished works that Debussy consciously contrived such proportional schemes.
There is, in fact, a quote from Debussy himself, in Debussy’s published letters, titled ‘Debussy’s Letters’, in a letter to his publisher, referencing “the divine number”. I’m quoting Debussy word for word. This is taken from letter #108, to Jacques Durand: “I was just getting ready to send you the proofs…. You’ll see, on page 8 of ‘Jardins sous la pluie’, there’s a bar missing; my fault, in fact, as it’s not in the manuscript. Even so, it’s necessary from the point of view of number; the divine number,…”
I would suggest you amend the third paragraph, by quoting Debussy and adding a reference to the ‘letters’ book. There’s speculation that Debussy may have been influenced by a particular group of artists and poets in France he was spending time with. Regardless, that is a direct quote from his letters, and the piece of music mentioned has been analyzed for use of the golden ratio and checks out. If you’d like I’ll send you the findings in that score. I believe Roy Howat may have also discussed this in his book, ‘Debussy in Proportion.’ I would need to get a new copy of that book to verify, which I’d be happy to do.
You may contact me directly at email@stevesteele.com.
Regards, Steve Steele Andromeda Expat ( talk) 05:37, 4 August 2022 (UTC)
Is there a reason for these two as separate categories? – jacobolus (t) 07:38, 18 August 2022 (UTC)
may contain any or all of the following: Explanatory footnotes ... Citation footnotes ... Full citations to sources, ... General references (full bibliographic citations to sources that were consulted in writing the article but that are not explicitly connected to any specific material in the article).This seems to perfectly well include everything currently in the "further reading" section of this article. To be honest I don’t get the point of a "further reading" section, for which it recommends
a reasonable number of publications that would help interested readers learn more about the article subject.... This section is not intended as a repository for general references or full citations that were used to create the article content....To me the separation into two sections seems not that helpful. It creates extra work for anyone adding or removing footnotes (need to check which section the source is in and move it if necessary) and potential confusion for readers (is one of the two types being more recommended than the other? Are there any model articles where both of these sections appear and seem to have particularly clear/helpful content and structure? – jacobolus (t) 05:43, 19 August 2022 (UTC)
— Preceding unsigned comment added by 46.39.54.40 ( talk) 18:44, 28 May 2022 (UTC)
I made the bit about 5th roots of unity a bit more explicit in golden ratio#Other properties. Does that cover what folks here were looking for? – jacobolus (t) 05:45, 23 August 2022 (UTC)
The formula for phi can be reduced to a positive exponent, multiplication, and addition:
This is clear and easy to remember, demonstrates interesting relationships, and is less obtuse than the formula as shown in the article. This can also improve computational efficiency (of admittedly marginal importance). Here is an example for javascript:
const phi = Math.pow(5, 0.5) * 0.5 + 0.5;
I placed this under computation, but Ovinus reverted it. Placing it here in the event someone else sees it as useful. Myndex talk 00:45, 23 August 2022 (UTC)
sqrt
in preference to pow
for practical computation, though it doesn’t really matter in this case because Javascript JIT compilers are smart enough to evaluate the constant expression one time and save the result then not bother repeating the computation. The definitional “formulas” in the article are or and they do not seem “obtuse”. –
jacobolus
(t)
01:35, 23 August 2022 (UTC)
sqrtsd
/vsqrt
is a single instruction; powf
is usually a complex beast to get faithful rounding (e.g.,
[1]).) In any case, that's still OR, and I agree with jacobolus that it's no easier to remember. recalls the beloved quadratic formula, while this formula uses unsightly decimals.
Ovinus (
talk)
04:45, 23 August 2022 (UTC)
phi approximates the Fibonacci ratio starting with the 5th Fibonacci number pair– this is starting to sound suspiciously like numerology. – jacobolus (t) 19:07, 23 August 2022 (UTC)
Hello!
I hope my edits have been pleasant (and thank you to those who have pitched in to mine and prior), if you need me to add/remove or change anything I've done in a similar style, please let me know or feel free to further improve the article yourself. Since the mathematics content was expanded by a relatively large amount, I am going to also help update Applications and observations and Disputed observations to balance the length of Mathematics (maybe expand History, too). If you'd like to join me in this effort, please feel free, there is plenty more that can be added, almost everywhere. If you also have ideas on minor unmentioned golden ratio topics for the article under Mathematics that could be added inside a larger heading of Other properties let me know too, I can work on them if you don't feel inclined. I am going to expand Other properties with sections detailing:
That way we have a proper Other properties section that flows into Applications and observations. Thank you for reading
and/or helping the article!
Radlrb (
talk)
13:11, 24 June 2022 (UTC)
Is there any reason why this article shouldn't be changed from using the mathematically-rare curly phi (LaTeX \varphi) to the historically-accurate straight phi (LaTeX \phi)? D.keenan ( talk) 04:46, 14 September 2022 (UTC)
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Please allow me to edit this page.I am currently a college student and i have spotted a gramatical error SoopBruv ( talk) 08:22, 14 October 2022 (UTC)
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Justification for change: There is no reason, to my understanding, that content that is not sky-is-blue obvious should be allowed to appear, unsourced, without a reader warning. To do so violates WP:VERIFY and/or WP:ORIGINAL RESEARCH. (As a former professor of the physical sciences, I state without reservation, the content of this section is not obvious, rather, it needs to have been taught to the editor placing it, and therefore is derived, ultimately, from some authoritative source.) The "Calculation" section certainly must appear so-derived in a wide variety of reputable sources. Find an autoritative source, edit the content to that source, and place the citation. Until then, I ask the following reader warning edit, in keeping with clear WP policies and guidelines.
Change from:
Change to:
If rejecting this request, please state the applicable WP policies and guidelines that trump the clear statements in WPVERIFY and WP:ORIGINAL RESEARCH. Thank you. 2601:246:C700:2:8D90:7012:872:558C ( talk) 20:01, 27 October 2022 (UTC)
Mathematical literacy may be necessary to follow a "routine" calculation, particularly for articles on mathematics or in the hard sciences. In some cases, editors may show their work in a footnote.This calculation is decidedly "routine", in the context of this sentence of CALC (assuming mathematical "literacy", a higher standard than what you suggest). What is certainly not routine: medium-sized proofs, rarely used or opaque techniques, judgments on the nature of proofs (simplicity, beauty). To be honest, I've never seen people using footnotes for work, although I think it's a nice idea.
articles are beyond the pale with regard to being verifiable content– You can certainly find examples that push (or exceed) the boundary of WP:CALC, but this is not one of them.
you ... and I ... can follow it, and are sure it is true, is not the test given us– Yes it is, more or less. More concretely, anyone with a reasonable background (introductory middle school / high school algebra, and a reasonably careful effort) can follow the steps here; if your undergraduate technical students are having a problem following this line of reasoning something is going very wrong with their background preparation. Adding a source is not going to make basic algebraic manipulations easier to follow for someone who has not yet been through a year or two of introductory algebra courses, but teaching elementary algebra can’t be expected of every technical article, even those aimed at a broad audience. You can trivially find some sources for these specific manipulations if you need to (e.g. by skimming through a few of the cited books about the golden ratio), but even if you couldn’t, these are well within the scope of WP:CALC for this article. – jacobolus (t) 02:09, 28 October 2022 (UTC)
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Paper9oll (
🔔 •
📝)
14:25, 29 October 2022 (UTC)