Talk:Fibonacci sequence/Archive 2: Difference between revisions

Revision as of 01:10, 3 July 2008

Revision as of 01:11, 9 July 2008

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:: 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. —[[User:Tamfang|Tamfang]] ([[User talk:Tamfang|talk]]) 22:22, 3 April 2008 (UTC)

== Labels in the list of values ==

I just reverted a change by {{user|Virginia-American}} 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. —[[User:David Eppstein|David Eppstein]] ([[User talk: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. [[User:Virginia-American|Virginia-American]] ([[User talk:Virginia-American|talk]]) 15:50, 22 March 2008 (UTC)

:I made a table. I agree that the ''n'' is needed.--[[User:Patrick|Patrick]] ([[User talk: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. [[User:Gandalf61|Gandalf61]] ([[User talk: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). —[[User:David Eppstein|David Eppstein]] ([[User talk:David Eppstein|talk]]) 18:59, 22 March 2008 (UTC)

:Yes, that looks better. Good job. [[User:Gandalf61|Gandalf61]] ([[User talk:Gandalf61|talk]]) 21:16, 22 March 2008 (UTC)

:Thanks for the table - great reference-ability on that. [[User:Bugtank|Bugtank]] ([[User talk:Bugtank|talk]]) 04:47, 6 April 2008 (UTC)

The most notable property of the Fibonacci sequence is the ratio converting to <math>\varphi</math> = 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. [[User:PrimeHunter|PrimeHunter]] ([[User talk:PrimeHunter|talk]]) 21:51, 22 March 2008 (UTC)

{| class="wikitable"

|+ Fibonacci numbers

! ''n'' !! ''F_n'' !! Factorization

! ''F_n'' / ''F''_''n''-1

! abs(''F_n'' / ''F''_''n''-1 &minus; <math>\varphi</math>)

|-

!0

| 0||&nbsp; || &nbsp; || &nbsp;

|-

!1

| 1||1 || &nbsp; || &nbsp;

|-

!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 <math>\varphi</math> = 1.6180339887... ".

:: Not really. It doesn't matter what the starting values are, as long as a sequence has the same recurrence F_n+1 = F_n + F_n-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 F_n s is more notable. [[User:Virginia-American|Virginia-American]] ([[User talk: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. [[User:PrimeHunter|PrimeHunter]] ([[User talk:PrimeHunter|talk]]) 17:42, 27 March 2008 (UTC)

== Error in proof ==

I [http://en.wikipedia.org/w/index.php?title=Fibonacci_number&diff=204392272&oldid=204387467 fixed an error] in the proof of the third identity. [[User:Paul August|Paul August]] [[User_talk:Paul August|&#9742;]] 05:44, 9 April 2008 (UTC)