Talk:Fibonacci sequence/Archive 3

Citation to Binet's vs. Abraham de Moivre's formula
In paragraph Fibonacci_number citation is needed for disambiguation that closed-form formula was introduces by Abraham de Moivre and not Jacques Philippe Marie Binet. It can be found in the book The_Art_of_Computer_Programming and I think this book should be cited. — Preceding unsigned comment added by Milikicn (talk • contribs) 18:30, 19 August 2011 (UTC)

Simple is best
To initially demonstrate the relationship between the Fibonacci sequence and the Golden Ratio, the Kepler solution is clearly the best. It is the simplest, clearest and most obvious therefore the most elegant solution. The other solutions are definitely worthy of mention but they are needlessly complex answers where a direct answer to a very simple question is already available. The Kepler solution should be the first listed followed by the Binet. Wading through the Binet solution only to find the obvious and to the point Kepler solution leads the reader to conclude that he has stumbled upon an Asperger's self stroking fest rather than an encyclopedia.74.178.137.190 (talk) 11:00, 4 September 2011 (UTC)


 * Editors here are unlikely to take your suggestions seriously if you cannot express them without throwing in gratuitous playground insults. Gandalf61 (talk) 12:47, 4 September 2011 (UTC)

Identities and combinatorial interpretations
There are two problems with the beginning of the "Identities" section. (1) The first sentence of this section asserts that "Most identities involving Fibonacci numbers draw from combinatorial arguments." This statement sounds subjective; unless reinforced by strong evidence I would remove it. In any case it's irrelevant to the statement of identities. (2) The first identity cannot be proved, as it is the definition. The proper way to handle it is to prove the "interpretation" given (without proof) in the previous section. That should be in a separate section on "Combinatorial interpretations of the Fibonacci numbers". Zaslav (talk) 01:29, 24 October 2011 (UTC)

1/89
The linked page misleadingly suggests that a certain Cody Birsner discovered the relationship between the series and the fraction, whereas it had been known for a considerable time before. Perhaps it would be better to link to another page, e.g. http://www.goldennumber.net/Number89.htm or http://www.fibonacci.name/1-89.html or http://www.mathpages.com/home/kmath108.htm Dadge (talk) 20:50, 31 December 2011 (UTC)


 * I agree. Thanks for pointing this out. I changed it to:
 * which in turn cites some earlier papers from FQ. —Mark Dominus (talk) 22:04, 31 December 2011 (UTC)
 * which in turn cites some earlier papers from FQ. —Mark Dominus (talk) 22:04, 31 December 2011 (UTC)

add some formulas and proofs
put the even,odd,odd,even pattern on the article.and proofs.and before you do this:is there a pattern like this?yes or no and why?John kaiser (talk) 06:08, 30 January 2012 (UTC)


 * This pattern is mentioned in the section headed "Divisibility properties" and is described more generally in our article on Pisano periods. Gandalf61 (talk) 08:53, 30 January 2012 (UTC)

Recognizing Fibonacci Number
According to the Fibonacci number article "a positive integer $$ z $$ is a Fibonacci number if and only if one of $$ 5z^2 + 4 $$ or $$ 5z^2 - 4 $$ is a perfect square."

However, the statement $$ 5z^2+4=25^2 $$ or $$ 5z^2-4=25^2 $$ does not imply that $$ z $$ is a Fibonacci number. — Preceding unsigned comment added by Yonizilpa (talk • contribs) 19:10, 30 January 2012 (UTC)


 * You are starting at the wrong end. If z is an integer such that $$5z^2+4$$ or $$5z^2-4$$ is a perfect square then z is a Fibonacci number. So 5x1^2+4 =9, 5x2^2-4=16 and 5x3^2+4=49. It doesn't say there is a Fibonacci number corresponding to every square. Gandalf61 (talk) 19:31, 30 January 2012 (UTC)


 * In fact, the only squares that give Fibonacci numbers in the reverse direction are the squares of Lucas numbers. 1,2,3,4 and 7 are Lucas numbers, but 5 and 6 are not, so we have
 * $$\frac{1^2+4}{5}=1=1^2$$
 * $$\frac{2^2-4}{5}=0=0^2$$
 * $$\frac{3^2-4}{5}=1=1^2$$
 * $$\frac{4^2+4}{5}=4=2^2$$
 * $$\frac{7^2-4}{5}=9=3^2$$
 * which are all squares of Fibonacci numbers, but $$\frac{5^2 \pm 4}{5}\, $$ and $$\frac{6^2 \pm 4}{5}\, $$ are not squares of Fibonacci numbers. Gandalf61 (talk) 09:04, 31 January 2012 (UTC)

Thanks for the explanation I now realize my mistake. — Preceding unsigned comment added by Yonizilpa (talk • contribs) 13:10, 11 February 2012 (UTC)

A pyramid relating the golden ratio and the tetrahedron
If you take a regular tetrahedron and truncate(cut) it so that you keep the three original 60degree angles at one vertex but change the three lengths from that vertex to any three successive terms of the Fibonacci series then the base of the new pyramid will be the two internal diagonals of a pentagon and the corresponding side.The face with the corresponding side has the other sides Fib(n)and Fib(n+1),the angle opposite Fib(n) is 37.76124degrees and opposite Fib(n+1) is 82.23876degrees. One face of the pyramid with one of the internal diagonals as a side has other sides Fib(n+1) and Fib(n+2) and is similar to the previously mentioned face. The third face having the other internal diagonal as a side has other sides Fib(n)-angle opposite being 22.23876degrees- and Fib(n+2)-angle opposite being 97.76124degrees. Sabastianblak (talk) 23:20, 12 February 2012 (UTC)Bradley J. Grantham February 12,2012

The fibonacci numbers used for multiplication
The Fibonacci numbers are meso-American multiplication method. It may use any type of numbers I think.... — Preceding unsigned comment added by 203.126.140.131 (talk) 01:26, 29 March 2012 (UTC)

Nobel Prize ?
Excuse me but, i win a nobel prize if i say that the fibonacci phenomenon is due to rotation of earth "plus" growth factor ???

for example... for the spiral of sunflowers, and sea animal shells, just draw a straight line...very slowly...maybe following the sun light... and the rotation of earth make (plus growth factor) it become a spiral... does anybody before me understand it ???

thank you.

M.G. — Preceding unsigned comment added by 79.25.124.250 (talk) 15:39, 11 June 2012 (UTC)


 * See golden spiral. Gandalf61 (talk) 15:47, 11 June 2012 (UTC)

ty i read..but..no mention to relate it to the rotation of earth? (or taking the sun as a polar star)? — Preceding unsigned comment added by 79.25.124.250 (talk) 16:09, 11 June 2012 (UTC)


 * Well, you have a hypothesis, which is that phyllotaxis is caused by the movement of the sun across the sky. But that is just the first part of the scientific method. Next you need to make a prediction - for example, if the sun did not move across the sky, then plants would not show phyllotaxis. Then you need to devise and carry out an experiment that tests your prediction - for example, you could grow plants under artificial sun lamps so that the light under which they grow comes from a constant direction. If you did all this, and got a positive result from the experiment, then it would be interesting, but I really doubt it would qualify for a Nobel Prize. Gandalf61 (talk) 08:56, 12 June 2012 (UTC)

aaaa!! ty Gandalf61!! :) mmm i already have a certain idea..:) but i will make some experiment anyway. ty so much for your interest on my topic anyway! thank you. and...if i suppose is due to the earth magnetic field..? kinda like make grow a broccoflower inside a solenoid? i will try.

-mmm..nice reading Phyllotaxis..it comes out that golden ratio have something to do with pentagon, and pentagon with dodecahedron, a platonic solid.(and the that-time-believed shape of universe). Bye. — Preceding unsigned comment added by 79.11.127.63 (talk) 18:34, 12 June 2012 (UTC)

first list of fibonacci numbers
in the image https://upload.wikimedia.org/math/c/a/b/cabe91689f6a1af616ace02827c6e89c.png shouldn't the 7 be an 8? — Preceding unsigned comment added by JaysnArr (talk • contribs) 18:55, 5 October 2012 (UTC)


 * It says 8 for me but I see 7 in http://upload.wikimedia.org/math/7/3/8/73824f3b44e0a4920a70ae1ff1820fcd.png. The article was recently changed to a wrong sequence with 7. It was fixed 10 minutes later. PrimeHunter (talk) 19:02, 5 October 2012 (UTC)

Initial Fibonacci numbers
The original Fibonacci numbers began 1, 1, as everyone knows. In modern times mathematicians have often found it useful to start with 0, 1, 1, but often they have not found that useful and still begin with 1, 1. The article ought not to be prescribing usage to mathematicians, and I have revised the introduction accordingly. Some time ago, a person objected to any use of the beginning 1, 1, so I provide a reference for the 1, 1 sequence:
 * Matthias Beck and Ross Geoghegan, The Art of Proof: Basic Training for Deeper Mathematics. New York: Springer, 2010.

Zaslav (talk) 06:46, 9 October 2012 (UTC)


 * Addendum (not merely beating a dead horse, I'm sorry to say): In applications of Fibonacci numbers in science, the initial numbers seem to be 1, 1, not 0, 1, 1 (0 being inappropriate for them).  That is certainly true in biology.  Users of Fibonacci numbers in science (or anywhere else), not only professional mathematicians, ought to be taken account of in deciding what "the" initial numbers are.  Zaslav (talk) 06:16, 23 October 2012 (UTC)


 * Starting with 0 makes both the generating function and the closed-form expression in terms of the golden ratio nicer.


 * It's not really an issue, though, since the mathematics and computer science references I see tend to refer to F_0=0, F_1=1, F_2=1, F_3=2, etc. That makes terms 1,2 of the sequence 1,1 for the life sciences, and "term 0" is there for those who want to start with 0. Husoski (talk) 18:45, 25 January 2013 (UTC)

mAtrA-vr.ttas
From the page:


 * Variations of two earlier meters [is the variation]... For example, for [a meter of length] four, variations of meters of two [and] three being mixed, five happens. [works out examples 8, 13, 21]... In this way, the process should be followed in all mAtrA-vr.ttas (prosodic combinations).

I assume "mAtrA-vr.ttas" is some sort of transliteration, but I've never seen it before (and originally interpreted it as vandalism). I think we should mention what transliteration was used to make this a little less confusing. Cheers, — sligocki (talk) 15:44, 21 October 2012 (UTC)


 * Looks like a seven-bit way of writing mātrā-vṛttas, though I don't know if that's a word. —Tamfang (talk) 17:04, 21 October 2012 (UTC)


 * Looking at these (mātrā-vṛttas) seem to be Metre used in Sanskrit poetry. There seem to be a few character conversion errors in the references both numbers 11 and 12 look dodgy. --Salix (talk): 18:09, 21 October 2012 (UTC)

Gopala
The article Gopala (mathematician) redirects here (presumably because there is little to no (easily locatable) information regarding him, other than that he was involved in the development of the "Fibonacci" numbers. However, wouldn't it be intuitively better (controversial as it may be) to permit Gopala his own stub (given that it would likely be a complete article in terms of available information)? Additionally, the sources mentioned in the article, [4] and [5], may contain more information on him - perhaps someone with access to these could confirm this, and if so whether there is sufficient information available to justify a separate article for Gopala. - R160K (talk) 19:45, 3 November 2012 (UTC)

Origins
The photo in the icon (with the page from Liber Abaci) is broken. However, when is clicked, the original photo is right. Can someone restore the photo in the icon? (I don't know how to do this). Thanks. — Preceding unsigned comment added by 223.27.210.130 (talk) 03:39, 24 November 2012 (UTC)

Article name
It seems to me the current name "Fibonacci number" is not the best option. Wouldn't "Fibonacci numbers" (note the s), "Fibonacci series" or specially "Fibonacci sequence" be a better alternative? --Götz (talk) 04:43, 2 July 2013 (UTC)
 * What's wrong with the current title? "Not the best option" is too vague to be helpful. I suspect that "number" better fits WP:COMMONNAME than "series" or "sequence" (which you also haven't provided any specific reason for preferring). "Numbers" does not match WP:SINGULAR. —David Eppstein (talk) 04:49, 2 July 2013 (UTC)
 * I was not aware of WP:SINGULAR, although I find it odd that when describing a series/sequence, the page title is in singular, and the rest of the article is in plural. But there is also WP:PLURAL, under the Exceptions section, "Similarly, one is much more likely to mention the Bernoulli numbers than a particular Bernoulli number."
 * Then, following WP:Search engine test and considering WP:SINGULAR, it seems that "sequence" fits better with WP:COMMONNAME, as it can be seen in Google Ngram and Google Trends. But, what should we do regarding WP:SINGULAR and WP:PLURAL? --Götz (talk) 17:42, 2 July 2013 (UTC)
 * I agree that Fibonacci sequence is a better name. Google Trends (Thanks Götz!) supports the idea that "fibonacci sequence" is most common. And when recently doing research on the Fibonacci sequence (how I got here), I always searched for the more familiar "fibonacci sequence." Are there any good reasons or precedents for leaving the title as Fibonacci number? Tedsanders (talk) 03:07, 21 August 2013 (UTC)
 * Most Wikipedia articles about an individual sequence of integers are named "X number" rather than "X sequence". An article named "X sequence" is usually about a family of integer sequences with similar characteristics (examples are Hofstadter sequence, fractal sequence, complete sequence). But there are exceptions to this "rule" - for example, Padovan sequence, Golomb sequence and Euclid–Mullin sequence are all articles about individual sequences. Renaming this article to Fibonacci sequence (which is currenctly a redirect) has been occassionally suggested in the past - see this talk page archive - but never actioned AFAIK. Gandalf61 (talk) 09:54, 21 August 2013 (UTC)

Divisibility properties Error
It look like there is an Error Displayed under the Section "Divisibility properties" which is under "Primes and divisibility"

Check it out here: Fibonacci_number

I don't know to code "math" so if anyone how knows whats going on in that section please fix it immediately!

If there is no Error displayed it might have been fixed or removed.

Thanks in advance,

GideonWanna talk? 04:51, 12 October 2013 (UTC)
 * Can you state exactly what is the error? The only one that I have found is the "it follows" of the second paragraph: the result does not follows immediately from the previous one, but is an easy consequence of the basic recurrence relation. I have corrected this. On the other hand, if the error lies in the math display, it is possible that it is not an error in the article, but in the data transmission; it seems that Internet did not work correctly yesterday. D.Lazard (talk) 07:53, 12 October 2013 (UTC)
 * hey D.Lazard I', sorry I think its the internet problem (My Fault!) Really sorry, I should have reloaded the webpage!! Sorry, Thanks though... GideonWanna talk? 10:17, 12 October 2013 (UTC)

"Vandalization" of MacTutor history of Mathematics reference
User:Wcherowi removed my so-called "tongue in cheek" reference to a publication from the MacTutor history of Mathematics archive, claiming that it is not published. This is absurd. The url was given to the publication itself. MacTutor publishes refereed articles ONLINE! MacTutor is a reputable archive of mathematical history. I want to put this material back. It is instructive.TonyMath (talk) 01:40, 21 March 2014 (UTC)
 * FYI, I would also like to point out that this published refereed paper is linked to the very biography of Fibonacci himself at the MacTutor historical archive in St-Andrews University. It's at the top of the list of "Additional material". I Also note that Ron Knott's material on the Fibonacci numbers is also online and cited in this very article.  So what is this egregious comment "tongue-in-cheek" all about?
 * This preprint was submitted to MacTutor in March 2014. I hardly think it has been refereed in this short period. While I generally respect the MacTutor material, it can be of uneven quality. At best this could be considered an opinion piece (advancing a hypothesis) and would not be published in a legitimate scholastic journal. Its appearance on-line does not make it a reliable source. Even if I am wrong about it being a hoax, it is clearly a case of WP:TOOSOON. Bill Cherowitzo (talk) 04:51, 21 March 2014 (UTC)
 * I happen to know that the article had been seen long before the March date and was refereed by the editors themselves. Edmund F. Robertson had seen this article as far back as September 2013 i.e. several months before in fact.  What is this stuff about MacTutor not being a legitimate scholastic journal?  The editors of MacTutor material would not have linked the biography of Fibonacci to this paper had they not considered it acceptable.TonyMath (talk) 08:54, 21 March 2014 (UTC)
 * BTW, Reference to MacTutor appears in the Wikipedia site for Al-Karaji namely Note no. 3 and References_and_external_links. MacTutor is also cited in the general references of the Wikipedia site on the great Mathematicians Muḥammad ibn Mūsā al-Khwārizmī and Abū Kāmil Shujāʿ ibn Aslam.  MacTutor is intensely involved in studying Mathematics of the middle-ages.  So explain something to me: if MacTutor is an acceptable reference in these sites, then why not here?TonyMath (talk) 09:02, 21 March 2014 (UTC)
 * I checked the Wikipedia site MacTutor History of Mathematics archive and if you use the tools on the left and find what cites to that archive: you find a HUGE number of Wikipedia articles that cite MacTutor! It is so big, they have to be categorized in alphabetical order. I am all the more amazed at the claim that MacTutor is not a sufficiently credible citation for Wikipedia herein.TonyMath (talk) 10:03, 21 March 2014 (UTC)
 * You have to be careful with MacTutor. Their biographies are reliable but some of their other stuff is just student essays that should not be considered reliable. In particular, I do not believe that the source in question,, should be considered reliable. It is not one of the biographies, is labeled as a preprint, does not seem to have been reliably published, and contains what looks to me like decidedly fringey speculation. —David Eppstein (talk) 12:46, 22 March 2014 (UTC)
 * What I have to be careful about is this kind of bias but you and your colleagues will have your way, rest assured. Yes, the article was submitted as a preprint (of course, for the review process) but MacTutor would not have put it online and linked it to their very biography of Fibonacci even it had not been accepted for publication.  I cannot buy these claims about MacTutor or some of MacTutor not being "reliable" subject to your evaluation.  MacTutor is mentioned in the very Wikipedia site for Pythagoras.  FYI, Do you know how many people out there insist that Wikipedia itself is not authoritative? But we can all get through this with discernment and objectivity.   I can understand that something of an obscure speculative history from a recent publication might be premature for this site which focusses on the Mathematics of the Fibonacci sequence.  I get that and I will no longer insist on mentioning this recent MacTutor content on this particular Wikipedia site but you and your colleagues can do yourself a favor by avoiding this ad-hominem bashing of the reliability of MacTutor's content (against Wikipedia's guidelines I might add). It is an affront to its editors and its authors especially since Wikipedia does cite MacTutor in so many cases.  Moreover, I don't really believe that the true objection is really the Publisher of the material but rather its content and its implications.  Some of the editors simply don't appreciate the content and its controversial implications e.g. how much Fibonacci virtually plagiarized Muslim scholarship.   It would have been more honest to simply admit that. At any rate, I will no longer pursue the matter.TonyMath (talk) 03:36, 23 March 2014 (UTC)

Why are the sequence examples images?
The two examples at the top of the page are images, rather than simply text. Why is this preferable? Images with text are generally considered bad from a usability standpoint. Unlike Unicode characters with distant code points, these reside in ascii (except for the trailing ellipsis) so there's no compatibility issue. — Preceding unsigned comment added by Preinheimer (talk • contribs) 15:45, 8 September 2014 (UTC)
 * You mean the lists of numbers at the top of the article? It's because of Wikimedia's continued poor handling of mathematics markup. They are coded using the &lt;math&gt; tag in the source code of the article, and by default Wikimedia turns that into an image. If you turn on mathjax rendering in your preferences it will be formatted better. As for why they're coded that way: to make them look consistent with the other mathematical formulas in the article. —David Eppstein (talk) 16:15, 8 September 2014 (UTC)

Starting points
Can there be some explanation about the starting points 1,1 versus 0,1? Right now I am confused which one to pick, and why the "0,1" is called modern starting point. 84.113.183.242 (talk) 11:48, 29 October 2014 (UTC)


 * They are both common and both have F1=1, F2=1, F3=2, F4=3, .... The only difference is whether you also have a term F0=0 before F1. That term is practical in many situations such as some formulas which would get more cumbersome without having F0. In some applications it is logical to include F0=0, while it can easily be omitted in others. Fibonacci himself started at 1 but that was in 1202. Modern mathematical texts usually include F0=0 which has no downside for mathematicians, but less formal presentations for lay people often omit it. PrimeHunter (talk) 12:34, 29 October 2014 (UTC)

New MacTutor Bio on Fibonacci's colleague Michael Scot
Fibonacci's Liber Abaci was dedicated in 1227 to Michael Scot. Mactutor has a new bio, on Michael Scot which actually cites as a reference the aformentioned "fringy MacTutor speculative material" on the origin of the Fibonacci sequence, a reference that connects it to the bee reproduction system and was rejected here. This new bio and the authors of that so-called "fringy material" are the same. Apparently MacTutor does not reject this reference as fringy because both its bios for Fibonacci and Michael Scot cite it. For that matter, the wikipedia bios for both Fibonacci and Michael Scot cite their MacTutor counterparts. The French version of this current site on the Fibonacci sequence also cites this "fringy MacTutor material". Will the editors here now accept this reference? Naturally I fully expect people to stand their ground (I regret to say too much ego entered the earlier discussion) but I humbly submit this currently represents an inconsistency within wikipedia. However inconsistency is not new to wikipedia. Just look at the account of the six day war, wikipedia gives a different account if you look at it from the history of Syria :-) TonyMath (talk) 05:29, 25 November 2014 (UTC)

Adding the fact that Fibonnaci series is also known as the Hemachandra Series and was invented by him 50 years before Fibonacci.
I edited the article to include this fact. The source: It is pretty well known but the source I cited was an interview of Manjula Bhargava, the Fields Medal winner of 2014. My first change was undone saying I can not cite Youtube as a source even though it was his interview. I then included a transcript of his interview in the source but that again was undone. I fail to understand why some people are hesitant to accept this fact that the series was actually "invented" not by Fibonacci but by the Indian mathematician Hemachandra,and include it in the article? — Preceding unsigned comment added by G upadhyay (talk • contribs) 05:59, 4 June 2015 (UTC) Here is another source: http://people.sju.edu/~rhall/Multi/rhythm2.pdf — Preceding unsigned comment added by G upadhyay (talk • contribs) 06:02, 4 June 2015 (UTC)
 * Re the history: It was known in India long before Hemachandra (likely as far back as Pingala), and it is already in the article in the appropriate place. Re the name: to include it as an alternative name in the article, you will need to make an effort to convince us that this name is actually in wide use. Youtube is not acceptable as a reliable source and in any case that link shows only that one person uses that name, not that it is widely used. —David Eppstein (talk) 07:05, 4 June 2015 (UTC)

"That one person" you refer to is the Fields Medal winner, a prize which is believed to be the Nobel of Mathematics. OK? So he is far more knowledgeable than you and me in these matters. He knows what he is talking about. In fact, the class that he takes at Princeton he starts with the Hemachandra Theorem and refers the "Fibonacci" series by that name only. That it is not widely popular by that name is because of Eurocentricism. Many of the things west has borrowed from China and Asia and given them their name. It is an attempt to correct this distorted picture. Please make appropriate changes if you have the humility and intellectual courage to accept this fact. — Preceding unsigned comment added by G upadhyay (talk • contribs) 10:44, 4 June 2015 (UTC)
 * It is a common mistake to assume that a person with demonstrated abilities in one area is an authority in some other area. When a Fields medalist talks about his area of mathematics, I listen, he is an authority; but when he talks about something else he is expressing an opinion which must be compared to other opinions. With that said, in this interview he explicitly says that the sequence is called the Fibonacci sequence in India, and is only referred to as the Hemachandra sequence in (ancient?) Sanskrit, so your insistence in providing this alternate name is not supported by this citation. Furthermore, there is no attempt in this article to claim that Fibonacci discovered the sequence and the article talks about its Indian roots (long before Hemachandra). I would not claim that Eurocentrism has not had a role in misnaming mathematical ideas, but Wikipedia is not the venue for correcting this bias - we report what is in the (English) literature, not what should be there! Bill Cherowitzo (talk) 17:03, 4 June 2015 (UTC)
 * If there really is a growing movement in the English-speaking world for the name "Hemachandra series" (or similar) then mention of this might be appropriate in the Origins section. We would need a citation or few that speaks of the growing movement.  Leegrc (talk) 19:13, 4 June 2015 (UTC)

Assessment comment
Substituted at 21:15, 4 May 2016 (UTC)

Notation discrepancy
In section https://en.wikipedia.org/wiki/Fibonacci_number#In_nature is the constant phi, not referenced elsewhere in the article. What is this constant?199.116.73.108 (talk) 03:26, 14 January 2016 (UTC)
 * It's the golden ratio. It is referenced heavily in the "Relation to the golden ratio" section. —David Eppstein (talk) 04:11, 14 January 2016 (UTC)

Use in Mathematics Section
The "Use in Mathematics" is absolutely ridiculous. I really needn't say more, but the entire idea of Fibonacci numbers is of mathematical origin. smh 137.124.161.17 (talk) 23:44, 25 January 2016 (UTC)

OEIS links
What's with the inline OEIS links? I find them confusing and distracting. Shouldn't they be footnotes? Jkshapiro (talk) 19:16, 5 February 2016 (UTC)

Demoted to Category:C-Class_mathematics_articles
Lots of pending improvements requested in the talk page. Also the general structure of the article is unprofessional in comparison to other mathematics articles on Wikipedia, especially granted the centrality of Fibonacci numbers in mathematics.

24.97.221.50 (talk) 18:21, 9 February 2016 (UTC)


 * I have returned the rating to B. Your criticism of the page is very vague. I do not see improvements requested on the talk page. I do see a lot of pleading for special POVs. The Fibonacci numbers are not a central item in mathematics, but they may be perceived that way by the popular press and those without much knowledge of mathematics. To justify your downgrading of the rating you would need to be much more specific as to what needs to be changed. Bill Cherowitzo (talk) 19:22, 9 February 2016 (UTC)
 * To be fair, the article doesn't have a lot of structure — it reads liike a randomly ordered collection of subtopics rather than an organized article. And large parts of it are poorly sourced. So I could see a case for C-class rating on that basis. It's definitely not GA-class. —David Eppstein (talk) 19:35, 9 February 2016 (UTC)
 * I agree that this is definitely not a GA-class article, and it does need work. However, I'll stick with my evaluation that this is closer to a B than a C rated article. Reorganizing this behemoth will not be an easy task, there is a lot of disparate material here and I don't see a clear organizing backbone that we can hang its parts on. One of the issues here is that there are very different audiences interested in this article; number theorists, computer scientists, combinatorialists, and Jainists, not to mention the golden ratio crowd. That is probably the reason that the article is in the state it is in. Bill Cherowitzo (talk) 22:33, 9 February 2016 (UTC)

Collatz conjecture link
I'm as much a fan of the Collatz sequences as anyone, but what does it have to do with the Fibonacci numbers? There is no mention in the article, so I suggest the reference link be removed. Walt (talk) 20:05, 13 September 2016 (UTC)
 * Link removed. You could done it yourself. D.Lazard (talk) 20:26, 13 September 2016 (UTC)
 * Thanks. Just wanted to get some more eyes on it in case there was a relevance I didn't recall. Walt (talk) 00:31, 14 September 2016 (UTC)

"Limit of consecutive quotients" section appears to be mistaken
It has the first elements of the sequence listed, it says "generate the sequence 3, 2, 5, 7, 12, 19, 31, 50", but I think that 7 should be an 8. Honestly my head hurts and I don't want to screw up. 187.200.88.60 (talk) 01:03, 17 September 2016 (UTC)
 * It's a sequence where each term is the sum of the two previous terms so 7 = 2+5 is correct. PrimeHunter (talk) 01:30, 17 September 2016 (UTC)

What happened to the Latin-based languages?
There used to be versions of this wiki site on the Fibonacci numbers in French, Italian, Portuguese, Spanish... I found them but they are not linked to this particular site. What happened? These links should be restored.TonyMath (talk) 06:01, 27 September 2016 (UTC)
 * Wikidata made a stupid split between and  depending on how the article happens to be titled in each language. The articles are about exactly the same and no language has two separate articles so there is no reason for the split. They should be merged. PrimeHunter (talk) 11:55, 27 September 2016 (UTC)
 * I'm not sure about Wikidata merge policies when has statements that may not apply to, but I have moved all the language links to the latter. Let's hope they stay there. PrimeHunter (talk) 12:21, 28 September 2016 (UTC)
 * They were quickly split again and I got no support at wikidata:User talk:Infovarius. I haven't found a Wikidata process for proposed mergers. PrimeHunter (talk) 11:02, 3 October 2016 (UTC)
 * The numbers of the Fibonacci sequence are related to each other via the (famous) recursion formula $$ a_{n+1} = a_n + a_{n-1}$$ with $$ a_0 = 0 $$ and $$ a_1 =1$$.  You cannot have the numbers without the sequence and you cannot have the sequence without the numbers.  There should be no split. TonyMath (talk) 19:48, 5 October 2016 (UTC)

Fibonacci in Nature
Any more elaboration on this topic? Shyla Kannambadi (talk) 04:58, 3 January 2017 (UTC)

Closed form and Binet formula
The formula given for the Binet formula is not the same as the one given on Binet's page.

$$F_n = \frac{\varphi^n-\psi^n}{\varphi-\psi} \neq \frac{(1 + \sqrt{5})^n - (1 - \sqrt{5})^n}{2^n \sqrt{5}}$$

And also $$\varphi-\psi = 1 \neq 2 \sqrt{5}$$ — Preceding unsigned comment added by 84.226.134.142 (talk • contribs) 09:27, 14 January 2017 (UTC)


 * Please sign your posts in talk page with four tildes ( ~ ).
 * If you substitute $$\varphi$$ and $$\psi$$ for their values, a very simple transformation allows passing from the first formula to the second one (factoring the denominators 2 out of the exponentiations, and putting them as a common denominator). Also $$\varphi-\psi = \sqrt{5},$$ not $1$, nor $$2\sqrt 5.$$ So the two given formulas are correct and equivalent. D.Lazard (talk) 10:43, 14 January 2017 (UTC)

Shallow Diagonal
The definition of "Shallow Diagonal" seems to be undefined. There is a picture, which is helpful, but no definition (or clarification). Wolfram has a page but with no added definition http://mathworld.wolfram.com/ShallowDiagonal.html. — Preceding unsigned comment added by Scuilion.scuilion (talk • contribs) 21:47, 2 July 2017 (UTC)
 * The reason you can't find a definition most likely has to do with the fact that there is no "standard" way to write Pascal's triangle–spacing between numbers in a row, spacing between rows, left justified, written as a pyramid, etc. Formulas can be found for writing Fibonacci numbers in terms of binomial coefficients that correspond to these "shallow diagonals", but if you are looking for a quick and dirty description with geometric overtones those formulas just don't appeal. If you insist on a geometric description of a shallow diagonal (in this setting) you could try this ... if the lines through the triangle that are parallel to the sides of the triangle and intersect each row are called diagonals, then a shallow diagonal would be a line with half the slope of a diagonal that intersects every other row. This isn't really precise enough to be a definition and there are special cases to consider (say the diagonals are vertical for instance). If you want precision, use the formula, otherwise you need to settle for the imprecise visualization. --Bill Cherowitzo (talk) 03:19, 3 July 2017 (UTC)

Pareto distribution and Fibonacci sequence
Haven't you notice that Fibonacci's sequence are basically the same thing? When I type it in excel and sum first 4/5 and last 1/5 separately I get something around 0,2. I think that this should be mentioned here.

If I discovered it first please call it "KGD's observation". — Preceding unsigned comment added by 89.71.45.86 (talk) 17:16, 13 April 2018 (UTC)


 * The Pareto distribution is a continuous function that depends on a parameter $$\alpha$$ and takes its value between 0 and 1. The Fibonacci sequence is a sequence of integers, which grow exponentially. They cannot be basically the same thing. It may be some connexion between them, but this does not results immediately from the definitions, and, if such a connexion exists, it needs more explanation. In any case, even if your observation is correct, the rules of Wikipedia (WP:NOR) makes that it cannot be mentioned here, unless it is regularly published in a mathematics journal. D.Lazard (talk) 17:53, 13 April 2018 (UTC)

Intelligent Design
Why is there nothing in this article discussing the theory that, FN is possible proof of a creator? I find that troubling. Is there another article about this topic? Jsderwin (talk) 17:05, 28 April 2018 (UTC)
 * This article is about mathematics, not about theology. D.Lazard (talk) 17:12, 28 April 2018 (UTC)
 * So maybe there should be a disambiguation page. Jsderwin (talk) 17:24, 28 April 2018 (UTC)
 * Perhaps Jsderwin should be redirected to a relevant but made-up anecdote. —David Eppstein (talk) 17:39, 28 April 2018 (UTC)
 * David, can you stick to the point? Thanks. Jsderwin (talk) 18:27, 28 April 2018 (UTC)
 * The point is that numerology and proof by amazement at the beauty of mathematical formulae have no place here, especially with no published reliable sources. —David Eppstein (talk) 18:29, 28 April 2018 (UTC)
 * Do you know if there is an article about the topic I mentioned? It seems there's uninformed people spreading the idea that Wikipedia is part of a conspiracy to hide the truth about it.--Jsderwin (talk) 18:37, 28 April 2018 (UTC)


 * btw, quick question, if you don't mind, where does the number sit in with people who study chaos theory? --Jsderwin (talk) 18:39, 28 April 2018 (UTC)


 * Do you mean something like this? Anyway, you'd better ask WP:RELIGION. Boris Tsirelson (talk) 18:48, 28 April 2018 (UTC)


 * Ok thank you all. --Jsderwin (talk) 19:20, 28 April 2018 (UTC)

Why?
At least somebody guess as to why? What does it mean?,the disadvantage with anything not fibonacci or why it alone works perfect. That's what I want to know. — Preceding unsigned comment added by 23.120.254.61 (talk) 00:39, 7 November 2018 (UTC)
 * I can't make heads nor tails of your comment, but Wikipedia talk pages should only be used for suggestions for improvement of the article. They are not for broad philosophical questions like "what are we here for" and "what does it all mean anyway". —David Eppstein (talk) 00:49, 7 November 2018 (UTC)

Fibonacci number edit
I added this section but is disapeared

In 2018 Ondrej Janicko from Slovakia derived reverse Fibonacci sequence. The reverse Fibonacci sequence starts with numbers 0, 1, 8, 56, 384, 2624, 17920, 122368, ... . The reverse Fibonacci sequence Jn is defined by the recurrence relation:
 * $$J_n=8*(J_{n-1} - J_{n-2}),$$

Consecutive numbers in reverse Fibonacci sequence aproximate to number j = 6,828427112475… wich is reverse Fibonaccio ratio. Exact calculation of reverse Fibonaccio ratio is j = 4 + sqrt(8) = 6,828427112475… — Preceding unsigned comment added by Ondrejjanicko (talk • contribs) 09:47, 24 November 2018 (UTC)


 * The removal was correct; please see Wikipedia's policy about no original research. You've picked out some linear second-order recurrence with constant coefficients that otherwise had nothing to do with the Fibonacci sequence, but apparently given it a related name. –Deacon Vorbis (carbon &bull; videos) 10:45, 24 November 2018 (UTC)


 * Edit from contributor -I wanted publish article on Wikipedia about full steps about derivation of reversal Fibonacci sequence. Reverse Fibonacci sequence is derived from Fibonacci sequence. I can show it.
 * (Please indent your replies – see WP:THREAD for info). Wikipedia is not the place to publish original research.  Read the link I provided above.  –Deacon Vorbis (carbon &bull; videos) 11:42, 24 November 2018 (UTC)


 * I agree about the original research. Bubba73 You talkin' to me? 17:43, 25 November 2018 (UTC)


 * That research is self-published here. As far as I understand, it is about decimal digits, not quite about the numbers. Fibonacci sequence is not related to any particular numeral system. Boris Tsirelson (talk) 19:12, 25 November 2018 (UTC)

Jaime and Cersei
Someone has replaced the rabbits with Jaime and Cersei from Game of Thrones.

Okay, someone fixed this already. — Preceding unsigned comment added by 161.53.138.248 (talk) 10:58, 26 February 2015‎ (UTC)

Extracting closed-forms from generating function's power series
Another approach to computing Fn, suggested by Paul Hankin, is to extract Fn from the generating series s(x). http://paulhankin.github.io/Fibonacci/

Given n, we can extract the value of fib(n) from this expansion by picking an integer A large enough that there is no such overflow (strictly speaking, it's A(n), since it depends on n), multiplying by A**n, and extracting the unit term by considering the rest modulo A: A**n*G(1/A) = A**n*Sum(0<=k)(fib(k)*A**-k) = Sum(0<=k)(fib(k)*A**(n-k)) = Sum(0<=k<=n)(fib(k)*A**(n-k)) + Sum(n<k)(fib(k)*A**(n-k)) = fib(0)/A**(n-0) + fib(1)/A**(n-1) + ... + fib(n)*A**0 + Sum(n<=k)(fib(k)*A**(n-k)) A**n*G(1/A) = A**n*(1/A)/(1-(1/A)-1/(A**2)) = A**n*(1/A)*A**2/(A**2*((1-(1/A)-1/(A**2)))) = A**(n+1)/(A**2-A-1) = Assuming for now that the last term will be less than 1, we have the euclidian division (where the euclidian division div is the lisp operator FLOOR): Sum(0<=k<=n)(fib(k)*A**(n-k)) = A**(n+1) div (A**2-A-1)

Then, modulo A, all the terms of the sum disappear except for k=n, and we find this surprising closed formula: fib(n) = (A**(n+1) div (A**2-A-1)) mod A

In practice, A=10**n works. Where div is euclidian division: fib(n) = (10**(n*(n+1)) div (10**(2*n)-10**n-1)) mod 10**n

The above is remarkable because it's a closed form formula: it has no explicit recursion; all the recursion is done implicitly in the exponent function. Another remarkable thing is that before it extracts fib(n) from the low digits, it computes all the earlier fib(i) in the higher digits in a big expansion, a very large number with about n*(n+1) digits. This gives exact answers, but is very inefficient.

For a little bit of efficiency improvement, we see that A=2**n also works, at least for n>=2. Exponents of 2 can be computed cheaply with ASH, and modulo A becomes bit access using LDB. We add a fudge term to fix the computation for n=1. fib(n) = ((2**(n*(n+1))+1) div (2**(2*n)-2**n-1)) mod 2**n

How small can we make A?

For the terms after n to sum under 1, we need to choose A large enough that s = Sum(n<k)(fib(k)*A**(n-k)) < 1

We can check manually that the minimum A's for small n are: A(0)=3, A(1)=3, A(2)=4, A(3)=5, A(4)=7, A(5)=10, A(6)=15, A(7)=23...

From the previous closed formula (see function rfib), we know that Therefore, with k=n+1+l, we have s = Sum(n= phi**(n+1)/sqrt(5)   A >= phi + phi**(n+1)/sqrt(5)

But to get A=2**k, and k>=4, it's easier to approximate A from above with: A >= phi**(n+1)/sqrt(5)/(1-phi/16) > phi**(n+1)/sqrt(5)/(1-phi/A) k >= log(phi**(n+1)/sqrt(5)/(1-phi/16))/log(2) k >= n*log(phi)/log(2) + log(phi/(sqrt(5)*(1-phi/16)))/log(2) k >= n*log(phi)/log(2) + B with B = log(phi/(sqrt(5)*(1-phi/16)))/log(2) = -0.31291115520113505... then we can approximate k from above by using a rational number C/D that is strictly larger than log(phi)/log(2), at which point we use k = ceiling((n*C+ceiling(B*D))/D) A = 2**k

Now, we've optimized the number of bits of precision needed, but we still have this very unwieldly division of an overly large number that contains way more digits than needed. Wouldn't it be nice to simplify the formula so that we don't have to do that much computations, using only modular operations?

First note that when we have a euclidian division, Sum(0<=k<=n)(fib(k)*A**(n-k)) = A**(n+1) div (A**2-A-1) and we call the quotient q and the remainder r, then we have the exact formula: A**(n+1) = q * (A**2-A-1) + r then modulo A, we have 0 = q*-1 + r (mod A) or  q = r (mod A) and since q = fib(n) (mod A), we find the closed formula: fib(n) = (A**(n+1) mod (A**2-A-1)) mod A

This is once again a remarkable closed formula, and this time, we only need modular exponentiation, and this formula, in addition to being closed, leads to an efficient algorithm with the correct asymptotic behavior!

See http://fare.tunes.org/files/fun/fibonacci.lisp

Golden ratio in lead
The Fibonacci sequence is intimately connected with the golden ratio and needs this represented in the lead. I tried doing this but kept getting reverted for the perception of edit-warring, though never made the same edit twice. I think this was the best version, as it links the GR pretty high but not before thoroughly defining the article's subject. UpdateNerd (talk) 16:01, 7 December 2018 (UTC)


 * Mostly sounds good to me, maybe modulo a little tweaking. We have a whole section on the relationship to phi, so a short note giving one basic way in the lead seems reasonable.  –Deacon Vorbis (carbon &bull; videos) 16:20, 7 December 2018 (UTC)
 * I agree also that the relationship with the golden ratio has its place in the lead, but this should be after the definition, and should not be restricted to a property that is less important than Binet's formula. I have added a sentence about this in the lead. D.Lazard (talk) 19:06, 7 December 2018 (UTC)
 * Works for me, for now. But I still think it's more relevant to the Fibonacci numbers than a lot of the maths preceding it, which an average reader wouldn't understand. For future reference, all additive sequences eventually converge on the golden ratio (per Scott Olsen's book); the Fibonacci sequence just does it the fastest. UpdateNerd (talk) 19:24, 7 December 2018 (UTC)

One or two Fibonacci sequence?
One of the reverted edits of was to remove one of the two displayed sequences of the lead. This deserved to be reverted, because the two forms appear in the literature, and this must be reported.

Thinking again about this, it appears to me that the lead is confusing, as suggesting that there are two sequences called "Fibonacci sequence". Also this hides the fact that $$F_n$$ is the same in both cases, because, in modern version the sequence starts from its "0th element".

Also the proper definition that is given later in the lead is too technical as using concepts of the theory of recurrence relations, which are not really useful here.

So, I'll be bold and try another lead. If you disagree, feel free to revert me in view of further discussions. D.Lazard (talk) 10:55, 8 December 2018 (UTC)


 * I've made a bold edit to put some of the more technical information into a note. Thanks, UpdateNerd (talk) 19:09, 8 December 2018 (UTC)
 * I disagree with this edit (except for the grammar correction), for the following reasons. This edit would be fine if WP were a textbook, which it is not. More precisely, it must be adapted to readers with different backgrounds, and must, as far as possible, follow the principle of least astonishment. More specifically, many readers may already know the Fibonacci sequence starting with 1. They must not have to open a footnote for understand why this is not the sequence they know. Also, although the concept of the 0th element is common for experimented mathematicians, it is confusing and possibly strange for the layman. So, by the same principle of least astonishment, this must be explained. In summary, the content that has been pushed to a footnote is not technical information, but explanation for people who do not have any technical ability. So, I'll restore my version. However, if you are not convinced, we must wait for other advices.
 * I am not fully happy with the parentheses around the 0th element, but I have not found anything better. Maybe a short explanation could be useful. D.Lazard (talk) 09:50, 9 December 2018 (UTC)
 * Here's an idea: leave the parenthesis, which help the reader to understand that the zero is "optional". Then, we include the information in question in a footnote immediately following the zero. That way, it will not be delegated to the end of the sequence like a standard reference. The reader will be more likely to understand that the note relates to the 0, which is the only entry with parentheses.
 * I think it's important for the sequence to come earlier, rather than the explanation of the zero inclusion, which may not be "technical" per se, but it is definitely not useful to those readers who only spend about 5 minutes on a page. UpdateNerd (talk) 21:46, 9 December 2018 (UTC)
 * Extra punctuation such as parentheses and footnote marks in the middle of sequences of numbers are a bad idea. They are likely to mislead readers into thinking they have a mathematical rather than textual meaning. —David Eppstein (talk) 21:54, 9 December 2018 (UTC)

Move to Fibonacci sequence
I propose moving the page, as Fibonacci sequence is the more general term for the sequence of numbers. It is also more common in the lexicon with more than twice the Google results. Since the article is about the properties of the series as a whole, and how the numbers within it relate (as opposed to by themselves, which are of little interest), the new name would match the common reader's expectation. UpdateNerd (talk) 22:29, 19 December 2018 (UTC)


 * I oppose that move. "Fibonacci number" is the predominant term in books and sources such as Mathworld.  Bubba73 You talkin' to me? 02:08, 20 December 2018 (UTC)


 * While not quite as perennial an argument as whether we should start with 0 or 1, this has been discussed quite a few times already. See Talk:Fibonacci number/Archive 2, Talk:Fibonacci number/Archive 2, Talk:Fibonacci number/Archive 2, and Talk:Fibonacci number/Archive 3. The general consensus seems to be (as stated at the most recent earlier discussion) "Most Wikipedia articles about an individual sequence of integers are named "X number" rather than "X sequence"." —David Eppstein (talk) 02:16, 20 December 2018 (UTC)

Inappropriate cosmetic changes
Please avoid making wholesale changes like the capitalization of template names (inconsistently no less), and of article names used in piped links. You seem to be using to be using the excuse of a small content change in order to enforce your own version of how wikicode should be formatted. Moreover, the smaller changes you wanted to make are completely hidden in the enormous resulting diff, thus making it virtually impossible for other people to check. It might very well be totally fine, but it's extremely difficult to find amidst all the other stuff. –Deacon Vorbis (carbon &bull; videos) 20:19, 29 August 2019 (UTC)

New Leaf Publishing Group
Please look closer at the source, as well as its publisher (a division of Institute for Creation Research "Master Books"). These books include early school textbooks that are a front for creationism, etc. You may also want to participate at this RSN thread. Thanks, — Paleo Neonate  – 15:47, 19 January 2020 (UTC)

"Binet's fibonacci number formula" listed at Redirects for discussion
A discussion is taking place to address the redirect Binet&. The discussion will occur at Redirects for discussion/Log/2020 July 3 until a consensus is reached, and readers of this page are welcome to contribute to the discussion. D.Lazard (talk) 10:02, 3 July 2020 (UTC)

New Definition for Generalized Fibonacci Sequence
Hi All,

I have a new generalization for Fibonacci numbers. Let $ f(x) = \sum_{i=0}^{k} a_i x^{k-i} = 0 $ be a monic polynomial of degree $k \ge 2 $ with roots $ \{x_i| i=1,...,k \}$. We assume that $ f(x)$ has simple roots $ \{x_i| i=1,...,k \}$ and $a_k \ne 0$. Let $f'(x)$ be the derivative of $f(x)$.

Let $P_{n}$ be defined by the equation

\begin{equation} P_{n} = \sum_{i=1}^{k} \frac{x_i^{n}}{f'(x_i)}. \end{equation}

If $f(x) = x^2 -x-1$, then $P_{n}$ is the Fibonacci numbers $F_{n}$.

Can this be included in this article? — Preceding unsigned comment added by Kaiwang45 (talk • contribs) 15:31, 27 July 2020 (UTC)


 * No. See WP:NOR. –Deacon Vorbis (carbon &bull; videos) 15:37, 27 July 2020 (UTC)
 * On a side note, this also isn't anything new, as it simply describes the solution of a linear recurrence relation with constant coefficients subject to some further restrictions with a given characteristic equation (the one given being that for the Fibonacci sequence's recurrence). –Deacon Vorbis (carbon &bull; videos) 16:04, 27 July 2020 (UTC)


 * are you expert? — Preceding unsigned comment added by Kaiwang45 (talk • contribs) 21:57, 27 July 2020 (UTC)


 * Please sign all your talk page messages with four tildes ( ~ ) and indent the messages as outlined in wp:THREAD and wp:INDENT — See Help:Using talk pages. Thanks.
 * Expertise from Wikipedia contributors is irrelevant. What we need, are wp:reliable sources, (1) to provide a way to verify new content, and (2) to establish whether new content is noteworthy to be included. - DVdm (talk) 22:07, 27 July 2020 (UTC)

History
Article suggests that Fibonacci learned of the sequencecdirect from India which seems highly unlikely. Did hecdiscover itvfor himself? (I think not) or was it mediated through the Islamic World? — Preceding unsigned comment added by 90.154.71.175 (talk) 10:23, 12 October 2019 (UTC)
 * Where do you think the article suggests that? I assume he discovered it himself and that's what I thought the article implied. But I don't think we have information beyond his book itself and we can't write from ignorance and guesses. If we knew of instances of the same sequence in the Islamic world we should report it but I don't think we do. —David Eppstein (talk) 15:40, 12 October 2019 (UTC)
 * Agree. When I read the article, it implies causality between the Indian and European discovery of pattern recognition. Attempting to grok the article, it appears the use of the sequence came about formally in the 19th Century and was linked to Fibonacci. The Indian use of the pattern shows that others were aware of it, but it is not linked historically. According to the article, the linking of the Indian discovery with Fibonacci came a century later. The link to Indian mathematics does not show any reference to Fibonacci numbers or sequencing. However, in that article there is a reference to efforts to address eurocentrism. While we may infer some transfer of concepts, but to that article, there is no evidence. So, this history section may better be introduced by showing that the notion of sequencing came about in two regions independently without causality. That the use of the sequence formalized in Europe and was attributed to Fibonacci reflects that period in history. BenWilson (talk) 12:08, 19 August 2020 (UTC)

The first diagram in the History section and its explanation wrt Fibonacci numbers and Indian prosody make no sense to me at all. I see no 1,2,3,5,8 sequence. Even my binary brain can't make sense of it. (Apologies, I'm only a Physicist 😃) 92.237.196.75 (talk) 20:18, 2 November 2019 (UTC)


 * It involves the Fibonacci numbers 5, 8, and 13. It takes all combinations of 1-square and 2-square dominoes that add up to n=6 in a line.  The number of combinations is 13, the $$n+1$$th Fibonacci (13).  Then 5 of them end in one type and 8 end in the other type.  Bubba73 You talkin' to me? 20:31, 2 November 2019 (UTC)


 * The above response is basically correct, but let me add some refinement to it. The diagram does not represent the sequence, only one member of the sequence (13 = F7). Other members of the sequence are obtained by using different lengths of the strip (n) that is to be covered by the 1-square (gray) and 2-square (red) tiles (or dominoes). Since order matters, we are counting sequences (not combinations). The fact that 5 and 8 have interpretations in this diagram is an expression of a general principle that falls out of the proof that this count of coverings gives a Fibonacci number. However, I think that this is a distraction from the main point of the diagram, a case of providing too much information.--Bill Cherowitzo (talk) 20:58, 2 November 2019 (UTC)

Inappropriate Pomposity
Is wikipedia for the masses? Or for the pompous?

re: my recent deletion of “is thus” Scott Cousland (talk) 17:59, 5 January 2021 (UTC)


 * At a minimum, Wikipedia is for people with a basic grasp of English grammar; your edit took a grammatically correct sentence and turned it into an ungrammatical sentence fragment. Also it's not at all clear to me what is supposed to be pompous about a completely standard way of indicating that one thing is a consequence of the thing immediately before it. --JBL (talk) 18:16, 5 January 2021 (UTC)

JBL, "...a basic grasp" is exactly my point.

Your insistence prompted me to take a look at a readability analysis. I was surprised that your version had a slightly higher "Flesch Reading Ease" score of 66.8 (my version was measured at 49.5. Over 60 is considered a good score.). Both of our versions got flagged for adverb count.

I then did a search on Youtube for "thus" and found many videos explaining how to use it properly. If "thus" is complicated enough that people are creating Youtube videos to explain it, it seems to me that using "thus" is beyond a basic grasp of English grammar.

One video I watched suggested "as a result." Using this phrase ("As a result, the sequence begins like this:") results in an Flesch Reading Ease score of 71.8

Another method of measuring readability is the "Gunning Fog Index." (less than 10 is considered good)

Here are the ratings:

Your language: 14.2 My edit: 18 My new version: 8 (no issues found - what I have referred to as "flags," like the adverb count)

In this fun little exercise, I stumbled upon the "Simple English Wikipedia" https://simple.wikipedia.org/wiki/Fibonacci_number

It uses "The list never stops, but it starts this way:" Which scores higher still (Flesch Reading Ease of 113.1 and Gunning Fog Index of 3.6), but was also flagged for adverb count.

[I used the free service at readable.com]Scott Cousland (talk) 00:18, 6 January 2021 (UTC)

Composition example diagram
In revision 2021-01-31T03:05:03, D.Lazard reverted my edit with the note ''Would need a much larger size for being readable, and a much detailed caption for being understandable. Also caption not adapted to the surrounding text and conflict with the (too long) formula that follows)''. I'll try to address each concern, resulting in the thumbnail on the right:
 * 1) I've removed upright so that the thumbnail has the same width as the others. I made it smaller so that it doesn't push other images down too much. Regardeless, the reader can click the thumbnail for an enlarged view.
 * 2) I've rewritten the caption
 * 3) The caption now refers to the composition prose.
 * 4) As it is, $5 = 1+1+1+1+1 = 1+1+1+2 = 1+1+2+1 = 1+2+1+1 = 2+1+1+1 = 2+2+1 = 2+1+2 = 1+2+2$ already extends past the width of my browser window. I can break it up into two rows of four terms each:




 * }
 * }
 * }
 * }
 * }
 * }
 * }
 * }
 * }
 * }
 * }
 * }

do you have further concerns? Thanks, cm&#610;&#671;ee&#9094;&#964;a&#671;&#954; 17:08, 31 January 2021 (UTC)
 * On my screen, the formula fits in the width of the browser window, but not in the width left by the figure. It results a very large white vertical space between the formula and the preceding text. So, spliting the formula is definitively needed.
 * A short explanation of the proof sketched on the figure could be useful in the figure. On the other hand the reference to staircases would probably be more useful in the section text, with a mention of the figure.
 * Otherwise, the inclusion of the figure is OK. D.Lazard (talk) 18:08, 31 January 2021 (UTC)
 * Thanks, I've updated Fibonacci_number as discussed, Hope it's OK now. Cheers, cm&#610;&#671;ee&#9094;&#964;a&#671;&#954; 02:39, 5 February 2021 (UTC)

Benford's Law
An (arguably) interesting fact(oid) is, that the Fibonacci numbers follow Benford's Law. I did a small computation. For the first 100.000 numbers it is, rounded to one decimal place, exactly the values to expect: 1: 30.1% 2: 17.6% 3: 12.5% 4: 9.7% 5: 7.9% 6: 6.7% 7: 5.8% 8: 5.1% 9: 4.6% — Preceding unsigned comment added by Rekisyhp (talk • contribs) 20:06, 14 February 2021 (UTC)
 * Only if it can be referenced to a reliably-published source. —David Eppstein (talk) 21:16, 14 February 2021 (UTC)


 * It is true, but I don't know of a reference either. Anytime you have a sequence where one term is a multiple of the previous one (or close enough to it, like here, where the ratio is phi), you get Benford's law.  Bubba73 You talkin' to me? 21:54, 14 February 2021 (UTC)

Article is Blank?
Is it just me or does most of the article seem blank? There are many gaps between strings of text. Did I come here during a major rewrite of the article? — Preceding unsigned comment added by 208.98.162.228 (talk • contribs) 02:40, 11 May 2021 (UTC)