Talk:Fibonacci sequence/Archive 1

message: I removed the paragraph about miles to kilometers conversion, I thought it of dubious value and potentially misleading. A5 02:05, 1 Sep 2004 (UTC)
thread_title:  Miles to km conversion paragraph removed 

message: Has the sum 1 + 1 + 1/2 + 1/3 + 1/5 + 1/8 + 1/13 + 1/21 + 1/34... (which is equal to 3.35988566624...) known to be irrational as of 2004?? 66.245.105.195 02:11, 9 Oct 2004 (UTC)
replies: text: Yes, according to http://mathworld.wolfram.com/ReciprocalFibonacciConstant.html, this was proved irrational in 1989. Jwwalker 07:02, 13 February 2006 (UTC)
thread_title:  Proven irrational?? 

message: The article has a section describing in details the conformance to Benford's law.  But this conformance isn't surprising, (or, if it is surprising, the article doesn't say why) and since many collections of numbers conform to Benford's law, it's not clear what this is doing here.  The detailed statistics about the distribution of initial digits in Fibonacci numbers does not seem to me to have any intrinsic interest, and smacks of original research.  Am I missing something?  -- Dominus 14:54, 10 Jan 2005 (UTC)
replies: text: I was wondering that myself. I personally don't find Benford's law particularly relevant. And if it's relevant, couldn't the application of Benford's law to the Fibonacci sequence (or any other prominent integer sequence) be discussed in the article on Benford's law instead? --MarkSweep 15:55, 10 Jan 2005 (UTC)
replies: text: My thoughts exactly.  If there is no dissenting opinion in a day or two, I will remove the section. -- Dominus 16:09, 10 Jan 2005 (UTC)
replies: text: I'd say if you want to remove the section and merge it with Benford's law, there's no loss of information and no need to wait. --MarkSweep 17:24, 10 Jan 2005 (UTC)
replies: text: You can do what you want, but I'm going to wait. -- Dominus 18:44, 10 Jan 2005 (UTC)
thread_title:  Benford's law 

message: I would prefer if this page used the latter format. Subscript is most common for integer sequences within Wikipedia and elsewhere, and certainly the most common for denoting the Fibonacci sequence. Fredrik | talk 29 June 2005 18:27 (UTC)
:Both notations should be mentioned as both are common. Convenience and legibillity of formulae should dictate further use. --MarSch 11:12, 30 August 2005 (UTC)
replies: text: I agree with MarSch.  I find it strange that so many people seem to wish to enforce a nonexistent convention. -- Dominus 13:10, 31 August 2005 (UTC)
thread_title:  F(n) or F<sub>n</sub>? 

message: The tiling picture of the Fibonacci series is rather sloppy. To do it right, each next box, should be adjacent to the previous two, to clearly show the construction. As it is now, the construction is not consistent per step. Box for nr 5 adjoins 1, 1 and 3. It should be on the upper side, along boxes 2 and 3. Then 8 can be two the right of 3 and 5 etc.
Or, alternatively, it should be consistently drawn on the opposite side of the previous two. That way the centers of the boxes follow show the Fibonacci spiral.
−Woodstone 16:46, 24 September 2005 (UTC)
thread_title:  Tiling picture sloppy 

message: 1 Black 
1 then 
2 white are 
3 all I see 
5 in my infancy.
8 red and yellow then came to be, 
5 reaching out to me.
3 lets me see.
13 As below, so above and beyond, I imagine
8 drawn beyond the lines of reason.
5 Push the envelope. 
3 Watch it bend.
-Lateralus
-TOOL'''
he sings the sylabols.
http://toolshed.down.net/lyrics/latmaster.html cite
Christa rim 06:30, 22 October 2005 (UTC)
thread_title:  the sequence in music 

message: The statement about the bee generations is incorrect. It assumes that no parentage can be shared. However it is quite likely that two grandmothers of a bee are sisters, so no new parents are added going backwards. −Woodstone 12:59, 24 October 2005 (UTC)
replies: text: Fibonacci is also stated as having described the sequence "encoded in the ancestry of a male bee."
Was it known in 1900, let alone 1250, that an unfertilized bee egg is male?  —Tamfang 07:09, 11 October 2006 (UTC)

text: He didn't. Thanks for pointing this out.  -- Dominus 08:38, 11 October 2006 (UTC)
thread_title:  Bee generations 

message: The roulette page mentions that the fibonacci numbers can be used as a method of gambling. No chance of a mention on this page? (And an extrapolation - including why it is flawed?) --JohnO You found the secret writing! 08:24, 21 February 2006 (UTC)
thread_title:  Roulette 

message: Why is the conch picture here?  Is the ratio in size between successive turns known to be τ?  If not, let's avoid encouraging the popular misconception that all logarithmic spirals have something to do with Fibonacci numbers.  —Tamfang 19:30, 21 February 2006 (UTC)
thread_title:  spirals 

message: I don't understand the last step of the derivation in the relaytion to goldn ratio section. Can someone explain it to me?
How does
::
1+\frac{1}{\displaystyle\lim_{n\to\infty}\frac{F(n)}{F(n-1)}}
equal
::1+\frac{1}{x}
when
::x={\lim_{n\to\infty}\frac{F(n+1)}{F(n)}}
?
Thank you. Loom91 12:26, 28 March 2006 (UTC)
thread_title:  Can you explain the math? 

message: 68.155.181.96 says "a set cannot start with an index of zero".  Must be a Fortran programmer! —Tamfang 06:58, 31 March 2006 (UTC)
thread_title:  indexing 

message: I have removed the following contrbution from an anonymous editor from the main article, as I think it is very unclear, and the final sentence sounds like original research:
:However, since Fib(p) can share no common divisors exceeding one, with F(nWell, I don't think the original contributor means this Carmichael's theorem, which agrees with the definition of Carmichael's Theorem in this mathworld entry. Maybe he means a different Carmichael's Theorem ? Maybe this is where he gets the statement GCD(F(n), F(m)) = F(GCD((m),(n))) from ?? This is exactly why this tangle need more clarity. Gandalf61 10:01, 10 April 2006 (UTC)
replies: text: Fixed this. Carmichael's theorem now describes the theorem that the original contributor was refering to (it was previously a redierct to Carmichael function). Gandalf61 10:44, 11 April 2006 (UTC)

text: Divineprime, I suggest we continue this discussion on your talk page. Gandalf61 08:39, 11 April 2006 (UTC)
thread_title:  Fibonacci primes 

message: I've removed the image to the right from the article, as it makes no claim to have anything to do with Fibonacci numbers. In fact, the whole "Fibonacci numbers in nature" section needs citations. Melchoir 22:31, 23 April 2006 (UTC)
thread_title:  Broccoli? 

message: As of now, this is the progress in verifying the claims made in "Fibonacci numbers in nature" that various things are connected to the Fibonacci numbers, with smoking guns:
*General notability in biology done 
**Douady p.255: "The predominance of Fibonacci order in botany..."
*Flowers done
**Douady p.268: "...the spectacular ordering of sunflower heads... Remarkably high Fibonacci numbers can be reached..."
*Trees done
**Douady p.272: "...even a normal vertical pine tree branch, with a Fibonacci structure..."
*Bushes
*Pine cones done
*Raspberry seeds
*Horns
*Shells
*Lindenmayer grammars done 
**Prusinkiewicz p.??: "???"
*Fractal Fuchsian groups
*Kleinian groups
*Belousov-Zhabotinsky reaction
*Gene regulatory networks
*Sphere packing
Rather than hit every of those with a  tag, it's easier to apply  to the section and list the items here. Please update the above as necessary, crossing off items as they are either verified or removed, or adding items as the article grows. Feel free to remove the tag when every item is crossed out. Melchoir 11:12, 22 May 2006 (UTC)
replies: text: I'll be surprised if someone can show Fibonacci relevance in sphere packing.  —Tamfang 02:29, 21 August 2006 (UTC)
replies: text: Eh, I'll just delete the problems. For the record, the unverified claims can still be found here. Melchoir 02:54, 21 August 2006 (UTC)

text: I removed "segments of snail shells"; I'm guessing someone was confused by the Nautilus, and by the annoyingly common misconception that the golden ratio appears in every exponential spiral.  —Tamfang 07:16, 23 October 2006 (UTC)
replies: text: Hmm, are you saying that some exponential spirals have the golden ratio, and that some don't? Or that None of them do? McKay 19:36, 23 October 2006 (UTC)
replies: text:  The ratio between successive elements of an exponential progression (of which a spiral shell is an example) can be τ, φ, π, e, 2, √2, 3, √3, or any other number >1.  —Tamfang 07:18, 24 October 2006 (UTC)
thread_title:  Elements of "Fibonacci numbers in nature" needing verification 

message: Could some admin please block Bharatveer? This is getting ridiculous. Fredrik Johansson 12:45, 16 September 2006 (UTC)
replies: text: From WP:3RR: "This does not imply that reverting three times or fewer is acceptable." You have repeatedly re-instated the same opinion piece, refusing to listen to the consensus established by other editors. Your appeal to references doesn't help; the opinion is an opinion regardless of whether you put a footnote on it. Fredrik Johansson 13:06, 16 September 2006 (UTC)
replies: text: Your statement about inserting references looks childish.Bharatveer 13:11, 16 September 2006 (UTC)
replies: text:  Who is it that keeps urging others to be "civil"?  —Tamfang 07:19, 17 September 2006 (UTC)
thread_title:  Repeated 3RR violation 

message: How was the number 55 obtained for the sunflower image? I can easily count to 21 and 34 (outwards clockwise and counter-clockwise, respectively), but I'm having trouble identifying a set of spirals adding up to 55. Fredrik Johansson 12:06, 17 September 2006 (UTC)
replies: text: I think I checked it out in Photoshop by drawing curves around the outside. For 55, you really have to work around the edge. Melchoir 18:53, 17 September 2006 (UTC)
thread_title:  Sunflower count 

message: Who decided to start calling this sequence the "Fibonacci" numbers, and when?  The OED has no citation before 1891, and all the early citations concern phyllotaxis.  Isn't that interesting? -- Dominus 10:34, 27 September 2006 (UTC)
replies: text: Although I do not have a primary source, I have seen the name attributed to Edouard Lucas, which would fit the 1891 citation.  Finell (Talk) 21:33, 15 October 2006 (UTC)
thread_title:  "Fibonacci" numbers 

message: In the lead, the first numbers in the Fibonacci sequence are wikilinked (with some links duplicated). In my opinion, this does not contribute to the article and is a distraction. If a reader clicks on any of the links, the reader will not find relevant elucidation. What do others think? Unless there is concesnus to the contrary, I intend to remove the links after allowing time for other editors to respond. Finell (Talk) 21:41, 15 October 2006 (UTC)
thread_title:  Links to first numbers in sequence? 

message: If you have just one number, 1, in a sequence, can that be technically called a Fibonacci sequence? --Waterchan 05:25, 29 October 2006 (UTC)
replies: text: Technically, you could say that {1} is a finite sub-sequence of the Fibonacci sequence which contains only one term, but this is really stretching the definition of sequence. It would be more usual to describe a single term from the Fibonacci sequence as a Fibonacci number. Gandalf61 09:40, 29 October 2006 (UTC)
thread_title:  Is one number a Fibonacci sequence? 

message: I think the article is too long. Wikipedia:Article_size#Science_articles recommends no more than 10 printed pages. I suggest moving the two long sections "Generalizations" and "Popular culture" with their many subsections into two new articles called "Generalizations of Fibonacci numbers" and "Fibonacci numbers in popular culture". They would both be longer than many of the other articles in Category:Fibonacci_numbers. PrimeHunter 00:50, 15 November 2006 (UTC)
replies: text: I personally am almost always in favor of reducing the length of articles by farming out some material to other pages. I would think this is a good idea. The main reason for this in my mind is to make the articles more accessible and more inviting and not so overwhelming and intimidating. --Filll 01:18, 15 November 2006 (UTC)

text: PrimeHunter, I agree with your idea - and especially so if you are volunteering to do the work ;) Gandalf61 11:52, 15 November 2006 (UTC)
replies: text: I can do it after a few days if there is still consensus. PrimeHunter 19:09, 16 November 2006 (UTC)
replies: text: I have now created Generalizations of Fibonacci numbers and Fibonacci numbers in popular culture, and replaced the corresponding article sections with a summary. PrimeHunter 02:55, 19 November 2006 (UTC)
thread_title:  Proposal: Move long sections to new articles 

message: User:PrimeHunter tacitly removed the diacritics on Chhandah-shāstra and Lozanić.  Why?  —Tamfang 23:00, 19 November 2006 (UTC)
replies: text: Oops, my bad. I copied the source to a text editor while editing. Somewhere the software dropped diacritics (and other details). I will fix it now (assuming my software allows it). Thanks for pointing it out. PrimeHunter 01:20, 20 November 2006 (UTC)
replies: text:  I have fixed this, and a similar problem with Ernő in Fibonacci numbers in popular culture. Somebody already corrected that my software had renamed the film π to p when it was moved to that article! I will be careful now, and check other edits. PrimeHunter 02:20, 20 November 2006 (UTC)
thread_title:  diacritics 

message: On http://mathworld.wolfram.com/FibonacciNumber.html under formula 9, which generalizes the fibonacci function for real numbers, they list that the fibonacci function has zeros at each negative number approaching n + 0.5. Should this be included in the article at some point? CodeLabMAster 15:55, 20 November 2006 (UTC)
thread_title:  Fibonacci Zeros 

message: Hi,
I am proposing this link to be added to the article:
http://fibonaccicalc.freehostia.com/fibonacci.cgi
People says that it violates wp policies about Reliable sources. 
First of all Reliable sources policy applies to what is written in the article, and not the links.
Second, many links on the Fibonacci number article are not so authoritative:
http://www.goldenmeangauge.co.uk/fibonacci.htm site of a dentist. So, are dentists Fibonacci experts?
http://www.upl.cs.wisc.edu/~bethenco/fibo/ second year Ph.D. student I'm going to get the degree in computer science, do two years make the differece?
And I do not want to wast more time looking for who are the people writing articles linked here.
So, what's the difference, please?
I didn't get any answere ... why people so fast remove my link, isn't as much fast answering my coment?
PAolo —The preceding unsigned comment was added by 213.156.35.243 (talk) 21:04, 26 January 2007 (UTC)
replies: text: There is a policy that applies to the links, not what is written in the article. It can be found at WP:EL. It is likely that some of the other links in the article violate that policy, so comparing your link to the others is not helpful: instead, you should either justify your link as satisfying the policies in WP:EL, or accept that it is not appropriate. —David Eppstein 21:18, 31 January 2007 (UTC)
thread_title:  Reliable sources 

message: A recent change replaced this:
:Johannes Kepler pointed out that the ratio of consecutive Fibonacci numbers
::\frac{F(n+1)}{F(n)}\,
:converges to the golden ratio \varphi as the limit. 
With this:
:Johannes Kepler pointed out that the ratio of consecutive Fibonacci numbers
::\lim_{n\to\infty}\frac{F(n+1)}{F(n)}=\varphi,
:converges to the golden ratio \varphi as the limit.
The intention in the original text was for the phrase "the ratio of consecutive Fibonacci numbers" to be followed by \frac{F(n+1)}{F(n)}\, the expression for the ratio of consecutive Fibonacci numbers.  This expression is the subject of the sentence.  The following clause then explains that this expression converges to the golden ratio \varphi.
After the change, however, the sentence is at least ungrammatical, and arguably incorrect.   \lim_{n\to\infty}\frac{F(n+1)}{F(n)}=\varphi is not "the ratio of consecutive Fibonacci numbers", as it says; it is an equation.  And the equation does not "converge to the golden ratio" as it says, because equations do not converge; they assert convergence.
It would have been correct to have said something like this:
:Johannes Kepler pointed out that
::\lim_{n\to\infty}\frac{F(n+1)}{F(n)}=\varphi,
because then the formula itself asserts the convergence.  But that is not the change that was made.  The change that was made was redundant, since it say both in symbols and in words that 
\lim_{n\to\infty}\frac{F(n+1)}{F(n)}=\varphi,.  It was also incorrect, as I explained above.
I reverted, but shortly thereafter another editor reverted it again.  I am about to put it back the way it was originally, and point to this explanantion.  -- Dominus 15:32, 15 February 2007 (UTC)
replies: text: This is one of the properties of φ - see golden ratio. Because \phi^2 - \phi - 1 = 0, it follows that \frac{1}{\phi}=\phi-1. Gandalf61 08:59, 16 July 2007 (UTC)
thread_title:  Recent change to limit of consequtive quotients 

message: Hi I'm new to all this so forgive me if I'm doing this all wrong
In the combinatorial proof section, for the "Proof of the third identity" the page says
    
      [F(n + 2) − 1] + [F(n + 1) − 1] + … + [F(2) − 1]
    = [F(n + 2) − 1] + [F(n + 1) − 1] + … + [F(2) − 1] + [F(1) − 1] + F(0)
    = F(n + 2) + [F(n + 1) + … + F(1) + F(0)] − (n + 2)
    = F(n + 2) + F(n + 3) − (n + 2).
Should the last line not be = F(n + 2) + F(n + 3) − (n + 2) − 1  instead?
Also the proof for the fourth identity F(0)2 + F(1)2 + F(2)2 + … + F(n)2 = F(n) F(n + 1) is currently lacking.
Thanks —The preceding unsigned comment was added by Jclistens (talk • contribs) 21:46, 20 February 2007 (UTC)
thread_title:  Combinatorial proof of the identities 

message: Just curious, does anyone know if there are results about the sequences G(n+2)=G(n+1)-G(n)? If G(0)=0 and G(1)=1, G is a periodic trapezoidal wave with a period of 6 and an amplitude equal to 1, for both positive and negative n. Expressed in a matrix form, the transition matrix has complex eigenvalues and complex eigenvectors. The sequence H(n+2)=H(n)-H(n+1) is a backward Fibonacci sequence. As such, it is trivial. 209.167.89.139 15:39, 22 February 2007 (UTC)
replies: text: The G(n) sequence can be viewed as sampled 1.1547[sin(πx/3)] at integers x.Zymogen 16:58, 27 February 2007 (UTC)
thread_title:  Sequence from difference of two preceding terms 

message: What is a Fibonacci spiral? This article features a drawing of such a spiral, but includes no text explaining what it is. I can kind of make the jump from Golden sprial, I think, but the image seems out of place here with no text anchoring it to the article. -- Mikeblas 21:26, 24 February 2007 (UTC)
replies: text: I've expanded the caption on the image and linked to golden spiral. Gandalf61 10:38, 25 February 2007 (UTC)
replies: text: Thanks! I think that helps the piece. -- Mikeblas 15:27, 25 February 2007 (UTC)
thread_title:  Spiral? 

message: Why is there very, very little about calculating the series on a computer in here? It seems like it would be an important area. mrholybrain's talk 03:24, 10 March 2007 (UTC)
replies: text: I added a reference to this (the Dijkstra one). I won't say there's little to say about this topic, because I often use it as the first lecture in my algorithms classes, but I'm not sure what more is appropriate to add here. —David Eppstein 04:01, 10 March 2007 (UTC)

text: The history is mostly found in Wikipedia:Articles for deletion/List of hello world programs, Wikipedia:Articles for deletion/Fibonacci number program (2 nomination), b:Transwiki:Fibonacci number program, b:Fibonacci number program, and this old version of the article. Melchoir 04:33, 10 March 2007 (UTC)
thread_title:  Programming 

message: With the recent move of applications and arts downwards, the structure of the article has not improved. In an earlier discussion, we agreed to have the definition and very simple math at the start, then go into the applications and arts, finally come back to more math details. The problem with bringing all math together at the start is that most readers will never reach the softer part. We should restructure again. −Woodstone 17:19, 15 May 2007 (UTC)
replies: text: Yes I do kind of agree. It did seem a bit odd to go from maths to applications and then maths then popular culture and then a bit more maths. I'm not sure what the ideal structure at the moment is. Plus I think some of the maths could do with a prune, or moving to a sub /Proofs page. --Salix alba (talk) 22:45, 15 May 2007 (UTC)
replies: text: When I split out Generalizations of Fibonacci numbers and Fibonacci numbers in popular culture, I considered doing something similar for proofs and maybe the more advanced math. It is intimidating to some people and proofs may be of interest to few readers. This is a long article and the central in a whole category. (I don't want to do split work again) PrimeHunter 01:13, 16 May 2007 (UTC)
replies: text: Which reminds me that the sub article is on AfD at the moment Wikipedia:Articles for deletion/Fibonacci numbers in popular culture. --Salix alba (talk) 07:34, 16 May 2007 (UTC)
thread_title:  Structure of the article 

message: Fibonacci series can be found amongMesopotamian units, where the cubit or ku was divided into different digits (shusi of about 17 mm  uban of about 20 mm) and hands (qat). Similarly the Greek units also have long, median and short forms reflecting both arithmetric and geometric series.
The proportions continue through the length and width of boards to the diameters of columns and the proportions of rooms such that a room will be twice its height in width and 3 times its height in length.
Column diameters may be related to circumference as 7:22 and their height as 1:8 or with a capital and base 1:13
* The Ionian pous is a typical short pous measuring 296 mm
* The Attic pous measures 309.4 mm
* The Athenian pous measures 316 mm and is considered of median length
* Long pous are actually remen (4 hands) and pygons
* See cubit for the discussion of the choice of division into hands or palms
Generally the sexagesimal (base sixty) or decimal (base-ten) multiples have Mesopotamian origins while the septenary (base-seven) multiples have Egyptian origins. The following table compares several related series based on the module of the Greek daktylos of finger
One example of fibonacci series in architectural proportion would be in found in the board measures used when boards and beams were split, sawed and planed by hand or worked by adze before board measure was modularized for saw mills...its still similar but not exact.
:1 finger,   18.5 mm (1x)
:2 fingers,  37 mm   (2x)
:3 fingers,  55.5 mm strapping
:5 fingers,  92.5 mm (2x4)
:8 fingers, 148 mm   (2x6)
:13 fingers 240.5 mm (2x10)
The proportions continue through the length and width of boards to the diameters of columns and the proportions of rooms such that a room will be twice its height in width and 3 times its height in length. Column diameters may be related to circumference as 7:22 and their height as 1:8 or with a capital and base 1:13
:diameter      0, 3.81", 3.81",   7.64",  11.45"      19" 30.6"
:circumference 0,   1',     1',     2',   3',    5',    8',   
:height        0, 3.14,  3.14,   6.28, 9.42,  15.7,  25.1,
—Preceding unsigned comment added by Rktect (talk • contribs) 
There is nothing about Fibonacci numbers in our current articles on the Rhind Mathematical Papyrus and Egyptian Mathematical Leather Roll. I am skeptical of such claims and would want to see solid scholarly sources before including anything like that here. —David Eppstein 05:45, 24 July 2007 (UTC)
thread_title:  Length