Talk:Fibonacci number

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Contents

[edit] 13 Popular Culture [[1]]

No mention here of the popular culture that exists in the Stock Trading business, Economics, Mysticism and other parts of the culture that are continually on the look out for Fibonacci Numbers in any series - it is because it is a "Natural" Series. Just look at the external links to see just how wide spread and deeply influential in popular culture this series is.

[edit] True or False??

True or false: It has been proven that 149 is the largest prime Tribonacci number.

[edit] Fibonnaci Waltz

http://web.tampabay.rr.com/warhawks/FibonacciWaltz.html A clever use of the sequence that should be incorporated into the article.

[edit] Why two separate "Pythagorean triple" sections?

"Pythagorean triples of Fibonacci numbers" is the subject of two separate sections of this article:

I'm not sure what might be the most parsimonious/harmonious way to do it, but wouldn't it be best to somehow merge these sections?
—Wikiscient— 11:01, 12 March 2008 (UTC)

I merged them. —David Eppstein (talk) 14:46, 12 March 2008 (UTC)

[edit] Bees - Got it backwards I think

Males only come from mated bees (how can a female introduce a male chromosome?) The logic in how it relates to the Fibonacci sequence is still the same, but I think male and female were switched in the logic. I have changed it, and if you find I am wrong (with references of course) feel free to undo my switch. I only found this link as a reference for now, maybe will come back later with more. --Billy Nair (talk) 16:39, 16 March 2008 (UTC)

I am pretty sure the same is with chickens, unfertalized eggs will be female, and only fertalized eggs have the chance to be male, I don't know if it is always male, but need a male to get a male. --Billy Nair (talk) 16:41, 16 March 2008 (UTC)
Sorry, but the article was right - male bees, also known as drones, develop from unfertilised eggs. See our drone (bee) article, which explains how the genetics works. I have changed the article back to how it was. Gandalf61 (talk) 17:35, 16 March 2008 (UTC)
Birds, I believe, have a system analogous to the XY of mammals but the other way around: a bird with matching chromosomes is male, one with differing sex chromosomes is female; but a haploid (unfertilized) egg won't develop at all. —Tamfang (talk) 22:22, 3 April 2008 (UTC)

[edit] Labels in the list of values

I just reverted a change by Virginia-American (talk · contribs) that replaced the list of values near the start of the article,

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, ...

by a list in which each value is labeled,

F0 = 0, F1 = 1, F2 = 1, F3 = 2, F4 = 3, F5 = 5,
F6 = 8, F7 = 13, F8 = 21, F9 = 34, F10 = 55,
F11 = 89, F12 = 144, F13 = 233, F14 = 377, F15 = 610,
F16 = 987, F17 = 1597, F18 = 2584, F19 = 4181, F20 = 6765,
F21 = 10946, F22 = 17711, F23 = 28657, F24 = 46368, F25 = 75025,
F26 = 121393, ...

I think the labels make the list completely unreadable. But since this is a content disagreement rather than something more clear-cut, I thought I'd bring it here for further discussion, if there is any. —David Eppstein (talk) 15:40, 22 March 2008 (UTC)

Obviously I disagree. I got annoyed trying to verify some of the formulas and having to count to see what value of n corresponded to which fibonacci number. Actually, a table of some sort is probably the best way to display the first few values. Virginia-American (talk) 15:50, 22 March 2008 (UTC)

I made a table. I agree that the n is needed.--Patrick (talk) 16:13, 22 March 2008 (UTC)
Sorry, but I reverted the table. If you have TOC switched on the table runs down the left hand side of the TOC and looks just awful. And it makes the TOC appear in the middle of the lead section, for some reason. I wouldn't object to a table if (a) it is multi-column so it takes up less vertical space and (b) it can be arranged so as not to overlap the TOC. Gandalf61 (talk) 18:15, 22 March 2008 (UTC)

I made a table going horizontally instead of vertically. I think it looks better, but in order to work with possibly narrow browser windows I truncated the sequence earlier (21 terms). —David Eppstein (talk) 18:59, 22 March 2008 (UTC)

Yes, that looks better. Good job. Gandalf61 (talk) 21:16, 22 March 2008 (UTC)
Thanks for the table - great reference-ability on that. Bugtank (talk) 04:47, 6 April 2008 (UTC)

The most notable property of the Fibonacci sequence is the ratio converting to \varphi = 1.6180339887... Would it be worth the space to put something like the below table in a section (not the lead)? There have been complaints that the article is complicated. The table is simple and could come before more complicated parts. PrimeHunter (talk) 21:51, 22 March 2008 (UTC)

Fibonacci numbers
n Fn Factorization Fn / Fn-1 abs(Fn / Fn-1 − \varphi)
0 0      
1 1 1    
2 1 1 1 0.6180339887
3 2 2 2 0.3819660113
4 3 3 1.5 0.1180339887
5 5 5 1.6666666667 0.0486326779
6 8 23 1.6 0.0180339887
7 13 13 1.625 0.0069660112
8 21 3·7 1.6153846154 0.0026493733
9 34 2·17 1.6190476190 0.0010136302
10 55 5·11 1.6176470588 0.0003869299
11 89 89 1.6181818182 0.0001478294
12 144 24·32 1.6179775281 0.0000564606
13 233 233 1.6180555556 0.0000215668
14 377 13·29 1.6180257511 0.0000082376
15 610 2·5·61 1.6180371353 0.0000031465
16 987 3·7·47 1.6180327869 0.0000012018
17 1597 1597 1.6180344478 0.0000004590
18 2584 23·17·19 1.6180338134 0.0000001753
19 4181 37·113 1.6180340557 0.0000000669
20 6765 3·5·11·41 1.6180339632 0.0000000255
21 10946 2·13·421 1.6180339985 0.0000000097
22 17711 89·199 1.6180339850 0.0000000037
23 28657 28657 1.6180339902 0.0000000014
24 46368 25·32·7·23 1.6180339882 0.0000000005
25 75025 52·3001 1.6180339890 0.0000000002
PrimeHunter said "The most notable property of the Fibonacci sequence is the ratio converting to \varphi = 1.6180339887... ".
Not really. It doesn't matter what the starting values are, as long as a sequence has the same recurrence Fn+1 = Fn + Fn-1 as the Fibonacci sequence, the ratios converge to phi. I think the fact that the convergents of the continued fraction for phi are the ratios of consecutive Fn s is more notable. Virginia-American (talk) 17:35, 27 March 2008 (UTC)
I meant notable as in Wikipedia:Notability, meaning there are lots of sources about it. I think your property is mentioned relatively rarely. PrimeHunter (talk) 17:42, 27 March 2008 (UTC)

[edit] Plot

There are errors in this:

Patrick (talk) 16:16, 22 March 2008 (UTC)

Errors fixed. Thankyousarindam7 (talk) 15:51, 30 April 2008 (UTC)

[edit] Error in proof

I fixed an error in the proof of the third identity. Paul August ☎ 05:44, 9 April 2008 (UTC)