## Fibonacci number |

In **Fibonacci numbers**, commonly denoted *F _{n}* form a

and

for *n* > 1.

One has *F*_{2} = 1. In some books, and particularly in old ones, *F*_{0}, the "0" is omitted, and the Fibonacci sequence starts with *F*_{1} = *F*_{2} = 1.^{[2]}^{[3]} The beginning of the sequence is thus:

^{[4]}

Fibonacci numbers are strongly related to the

Fibonacci numbers are named after Italian mathematician Leonardo of Pisa, later known as * Liber Abaci*, Fibonacci introduced the sequence to Western European mathematics,

Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the * Fibonacci Quarterly*. Applications of Fibonacci numbers include computer algorithms such as the

They also appear in biological settings, such as branching in trees,

Fibonacci numbers are also closely related to

The Fibonacci sequence appears in ^{[8]}^{[10]}^{[11]} In the Sanskrit poetic tradition, there was interest in enumerating all patterns of long (L) syllables of 2 units duration, juxtaposed with short (S) syllables of 1 unit duration. Counting the different patterns of successive L and S with a given total duration results in the Fibonacci numbers: the number of patterns of duration *m* units is *F*_{m + 1}.^{[9]}

Knowledge of the Fibonacci sequence was expressed as early as *misrau cha* ("the two are mixed") and scholars who interpret it in context as saying that the number of patterns for *m* beats (*F*_{m+1}) is obtained by adding one [S] to the *F*_{m} cases and one [L] to the *F*_{m−1} cases. ^{[12]}
* Natya Shastra* (c. 100 BC–c. 350 AD).

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

mātrā-vṛttas[prosodic combinations].^{[a]}

^{[7]} writing that "the sum of the last and the one before the last is the number ... of the next mātrā-vṛtta."^{[15]}^{[16]}

Outside India, the Fibonacci sequence first appears in the book * Liber Abaci* (1202) by

- At the end of the first month, they mate, but there is still only 1 pair.
- At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits in the field.
- At the end of the third month, the original female produces a second pair, making 3 pairs in all in the field.
- At the end of the fourth month, the original female has produced yet another new pair, and the female born two months ago also produces her first pair, making 5 pairs.

At the end of the *n*th month, the number of pairs of rabbits is equal to the number of new pairs (that is, the number of pairs in month *n* − 2) plus the number of pairs alive last month (that is, *n* − 1). This is the *n*th Fibonacci number.^{[20]}

The name "Fibonacci sequence" was first used by the 19th-century number theorist ^{[21]}

Other Languages

العربية: عدد فيبوناتشي

azərbaycanca: Fibonaççi ədədləri

বাংলা: ফিবোনাচ্চি রাশিমালা

беларуская: Лікі Фібаначы

български: Числа на Фибоначи

bosanski: Fibonaccijev broj

català: Successió de Fibonacci

čeština: Fibonacciho posloupnost

Cymraeg: Rhif Fibonacci

dansk: Fibonacci-tal

Deutsch: Fibonaccizahlen

eesti: Fibonacci jada

Ελληνικά: Ακολουθία Φιμπονάτσι

español: Sucesión de Fibonacci

Esperanto: Fibonaĉi-nombro

euskara: Fibonacciren zenbakiak

فارسی: اعداد فیبوناچی

français: Nombre de Fibonacci

Gaeilge: Seicheamh Fibonacci

Gaelg: Straih Fibonacci

galego: Sucesión de Fibonacci

ગુજરાતી: ફિબોનાકિ

한국어: 피보나치 수

հայերեն: Ֆիբոնաչիի թվեր

Արեւմտահայերէն: Ֆիպոնաչչիի թիւ

हिन्दी: हेमचन्द्र श्रेणी

hrvatski: Fibonaccijev broj

Bahasa Indonesia: Bilangan Fibonacci

íslenska: Fibonacci-runa

italiano: Successione di Fibonacci

עברית: סדרת פיבונאצ'י

қазақша: Фибоначчи сандары

Latina: Numeri Fibonacciani

latviešu: Fibonači skaitļi

lietuvių: Fibonačio skaičius

magyar: Fibonacci-számok

македонски: Фибоначиева низа

മലയാളം: ഫിബനാച്ചി ശ്രേണി

Bahasa Melayu: Nombor Fibonacci

монгол: Фибоначчийн тоо

Nederlands: Rij van Fibonacci

日本語: フィボナッチ数

norsk: Fibonaccitall

norsk nynorsk: Fibonaccifølgja

oʻzbekcha/ўзбекча: Fibonachchi sonlari

ਪੰਜਾਬੀ: ਫ਼ੀਬੋਨਾਚੀ ਤਰਤੀਬ

پښتو: فیبوناچې اعداد

Piemontèis: Sequensa ëd Fibonacci

polski: Ciąg Fibonacciego

português: Sequência de Fibonacci

Qaraqalpaqsha: Fibonachchi sanları

română: Numerele Fibonacci

русский: Числа Фибоначчи

Scots: Fibonacci nummer

shqip: Numrat e Fibonaccit

sicilianu: Succissioni di Fibonacci

සිංහල: ෆිබොනාච්චි සංඛ්යා

Simple English: Fibonacci number

slovenčina: Fibonacciho postupnosť

slovenščina: Fibonaccijevo število

کوردی: ژمارەی فیبۆناچی

српски / srpski: Фибоначијев низ

srpskohrvatski / српскохрватски: Fibonačijev niz

suomi: Fibonaccin lukujono

svenska: Fibonaccital

Tagalog: Bilang Fibonacci

தமிழ்: ஃபிபனாச்சி எண்கள்

తెలుగు: ఫిబోనాచీ సంఖ్యలు

ไทย: จำนวนฟีโบนัชชี

Türkçe: Fibonacci dizisi

українська: Числа Фібоначчі

Tiếng Việt: Dãy Fibonacci

Võro: Fibonacci arv

West-Vlams: Reke van Fibonacci

Winaray: Ihap Fibonacci

吴语: 斐波那契数列

粵語: 費氏數列

中文: 斐波那契数列