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Nombor Fibonacci
{{Proses/BukanTeamBiasa}}{{pelbagai isu|{{cleanup|reason=memerlukan penterjemahan segera kerana sudah ditinggalkan sejak tahun 2008|date=Ogos 2014}}{{Terjemah|en|fabonacci number|date=Ogos 2014}}}}

[[Image:FibonacciBlocks.svg|thumb|180px|right|Suatu ubinan dengan segi empat yang tepinya adalah nombor Fibonaci berturut-turut pada panjangnya]]
(contracted; show full) untuk ''n''&nbsp;=&nbsp;0,&nbsp;1,&nbsp;2, … ,20 adalah:<ref> Mengikut konvensyen moden, urutannya bermula dengan ''F''<sub>0</sub>=0. ''Liber Abaci'' memulakan urutan dengan ''F''<sub>1</sub> = 1, meninggalkan permulaan 0, dan urutannya masih ditulis secara ini oleh sesetengah.</ref><ref>The website [http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibtable.html]
 {{Webarchive|url=https://web.archive.org/web/20080413003403/http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibtable.html |date=2008-04-13 }} has the first 300 F<sub>''n''</sub> factored into primes and links to more extensive tables.</ref>
:{| class="wikitable"
|-
| ''F''<sub>0</sub>
| ''F''<sub>1</sub>
| ''F''<sub>2</sub>
| ''F''<sub>3</sub>
| ''F''<sub>4</sub>
(contracted; show full)

Dengan pengecualian 1, 8 dan 144 (''F''<sub>0</sub> = ''F''<sub>1</sub>, ''F''<sub>6</sub> dan ''F''<sub>12</sub>) setiap nombor Fibonacci mempunyai faktor utama yang bukan faktor mana-mana nombor Fibonacci yang lebih kecil ([[teorem Carmichael]]).<ref>Ron Knott, [http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibtable.html "The Fibonacci numbers"]
 {{Webarchive|url=https://web.archive.org/web/20080413003403/http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibtable.html |date=2008-04-13 }}.</ref>

Tiada nombor Fibonacci lebih besar daripada ''F''<sub>6</sub> = 8 yang lebih besar atau kurang satu daripada nombor perdana.<ref>Ross Honsberger ''Mathematical Gems III'' (AMS Dolciani Mathematcal Expositions No. 9), 1985, ISBN 0-88385-318-3, p. 133.</ref>

Sebarang tiga nombor Fibonacci berturut-turut, yang diambil dua pada satu masa, adalah [[perdana relatif|secara relatifnya perdana]]: itu adalah,
:[[faktor sepunya terbesar|fstb]](''F''<sub>''n''</sub>, ''F''<sub>''n''+1</sub>) = fstb(''F''<sub>''n''</sub>, ''F''<sub>''n''+2</sub>) = 1.
Lebih umum,
:fstb(''F''<sub>''n''</sub>, ''F''<sub>''m''</sub>) = ''F''<sub>fstb(''n'', ''m'').</sub><ref>[[Paulo Ribenboim]], ''My Numbers, My Friends'', Springer-Verlag 2000</ref><ref>Su, Francis E., et al. [http://www.math.hmc.edu/funfacts/ffiles/20004.5.shtml "Fibonacci GCD's, please."] {{Webarchive|url=https://web.archive.org/web/20091214092739/http://www.math.hmc.edu/funfacts/ffiles/20004.5.shtml |date=2009-12-14 }}, ''Mudd Math Fun Facts''.</ref>

===Pembahagi ganjil===

Jika ''n'' adalah ganjil, semua pembahagi ganjil F<sub>''n''</sub> adalah ≡ 1 (mod 4).<ref>Lemmermeyer, ex. 2.27 p. 73</ref><ref>The website [http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibtable.html] {{Webarchive|url=https://web.archive.org/web/20080413003403/http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibtable.html |date=2008-04-13 }} has the first 300 Fibonacci numbers factored into primes.</ref> <br>
Ini adalah bersamaan dengan mengatakan bahawa untuk ''n'' ganjil semua faktor perdana ganjil F<sub>''n''</sub> adalah ≡ 1 (mod 4).

<blockquote>Contohnya,
(contracted; show full)s into a sum of nombor Fibonacci becomes nearly  kilometer sum apabila nombor Fibonacci are replaced by their successors. This method amounts to a [[radix]] 2 [[Fibonacci coding|number]] [[processor register|register]] in [[asas nisbah keemasan]] φ being shifted. To convert from kilometers to miles, shift  register down  jujukan Fibonacci instead.<ref>[http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibrep.html#kilos An Application of the Fibonacci Number Representation]</ref><ref>
[{{Cite web |url=http://people.bath.ac.uk/pst20/fibonacci.html#Sequence |title=A Practical Use of the Sequence] |access-date=2008-08-21 |archive-date=2008-05-30 |archive-url=https://web.archive.org/web/20080530002543/http://people.bath.ac.uk/pst20/fibonacci.html#Sequence |url-status=dead }}</ref><ref>[http://eom.springer.de/Z/z120020.htm Zeckendorf representation]</ref>

==Nombor Fibonacci dalam persekitaran==
[[Image:Helianthus whorl.jpg|thumb|[[Sunflower]] head displaying florets in lingkaran of 34 and 55 around  outside]]
Jujukan Fibonacci muncul dalam persekitaran biologi,<ref>{{cite journal | author=S. Douady and Y. Couder | title=Phyllotaxis as a Dynamical Self Organizing Process | journal=Journal of Theoretical Biology | year=1996 | issue=178 | pages=  255&ndash;274 | url=http://www.math.ntnu.no/~jarlet/Douady96.pdf   | doi = =10.1006/jtbi.1996.0026 | volume=178| | format=PDF | access-date=2008-08-21 | archive-date=2006-05-26 | archive-url=https://web.archive.org/web/20060526054108/http://www.math.ntnu.no/~jarlet/Douady96.pdf | url-status=dead }}</ref> in two consecutive nombor Fibonacci, such as branching in trees, arrangement of [[leaves]] on a stem,  fruitlets of a [[pineapple]],<ref>{{cite book|first=Judy|last=Jones|coauthors=William Wilson|title=An Incomplete Education|publisher=Ballantine Books|year=2006|id=ISBN 978-0-7394-7582-9|pages=544|chapter=Science}}</ref>  flowering of [[artichoke]], an uncurling fern and  arrangement of  a [[pine cone]].<ref>{{cite journal | author=A. Brousseau | title=Fibonacci Statistics i(contracted; show full)
* Bob Johnson, ''[http://www.dur.ac.uk/bob.johnson/fibonacci/ Fibonacci resources]'', (2004)
* Donald E. Simanek, ''[http://www.lhup.edu/~dsimanek/pseudo/fibonacc.htm Fibonacci Flim-Flam]'', (undated, 2005 or earlier).
* Rachel Hall, ''[http://www.sju.edu/~rhall/Multi/rhythm2.pdf Hemachandra's application to Sanskrit poetry]
 {{Webarchive|url=https://web.archive.org/web/20120716224803/http://www.sju.edu/~rhall/Multi/rhythm2.pdf |date=2012-07-16 }}'', (undated; 2005 or earlier).
* Alex Vinokur, ''[http://semillon.wpi.edu/~aofa/AofA/msg00012.html Computing Fibonacci numbers on a Turing Machine]'', (2003).
* (no author given), ''[http://www.goldenmeangauge.co.uk/fibonacci.htm Fibonacci number Information] {{Webarchive|url=https://web.archive.org/web/20050829093245/http://www.goldenmeangauge.co.uk/fibonacci.htm |date=2005-08-29 }}'', (undated, 2005 or earlier).
* [http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html nombor Fibonacci and  Golden Section] – Ron Knott's Surrey University multimedia web site on the Fibonacci numbers, Golden section and  Golden string.
*[http://www.mscs.dal.ca/Fibonacci/ Fibonacci Association] {{Webarchive|url=https://web.archive.org/web/20051001063730/http://www.mscs.dal.ca/Fibonacci/ |date=2005-10-01 }} incorporated in [[1963]], focuses on nombor Fibonacci and related mathematics, emphasizing new results, research proposals, challenging problems, and new proofs of old ideas.
* Dawson Merrill's [http://www.goldenratio.org/info/ Fib-Phi] link page.
* [http://primes.utm.edu/glossary/page.php?sort=FibonacciPrime Fibonacci primes]
* [http://www.mathpages.com/home/kmath078.htm Periods of Fibonacci Sequences Mod m] at MathPages
* [http://www.upl.cs.wisc.edu/~bethenco/fibo/ The One Millionth Fibonacci Number] {{Webarchive|url=https://web.archive.org/web/20061223104622/http://www.upl.cs.wisc.edu/~bethenco/fibo/ |date=2006-12-23 }}
* [http://www.bigzaphod.org/fibonacci/ The Ten Millionth Fibonacci Number]
* An [http://www.calcresult.com/maths/Sequences/expanded_fibonacci.html Expanded Fibonacci Series Generator]
* Manolis Lourakis, [http://www.ics.forth.gr/~lourakis/fibsrch/ Fibonaccian search in C]
* [http://www.physorg.com/news97227410.html Scientists find clues to the formation of Fibonacci lingkaran in nature]
*[https://web.archive.org/web/2007071503271660212072618/http://mathdl.maa.org/convergence/1/?pa=content&sa=viewDocument&nodeId=630&bodyId=1002 Fibonacci number]  at [http://web.archive.org/web/20060212072618/http://mathdl.maa.org/convergence/1/ Convergence]
* [http://www.tools4noobs.com/online_tools/fibonacci/ Online Fibonacci calculator]
* [https://www.forexchurch.com/fibonacci-calculator Online Fibonacci Calculator with Extension and Retracement Levels]
* [https://giladzuckerman.neocities.org/FIBONACCIOLEHDATETIME2.jpg 94 Bilangan Fibonacci Dari Permulaan Sirinya]

[[Kategori:Fibonacci numbers|*]]
[[Kategori:Articles containing proofs]]

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