## 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 Fibonacci 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

Fibonacci numbers are also closely related to

- origins
- list of fibonacci numbers
- use in mathematics
- relation to the golden ratio
- matrix form
- recognizing fibonacci numbers
- combinatorial identities
- other identities
- power series
- reciprocal sums
- primes and divisibility
- right triangles
- magnitude
- applications
- in nature
- generalizations
- see also
- references
- external links

The Fibonacci sequence appears in ^{[8]}^{[13]} 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. ^{[14]}
* 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]}

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: Suite de Fibonacci

Gaeilge: Seicheamh Fibonacci

Gaelg: Straih Fibonacci

galego: Sucesión de Fibonacci

ગુજરાતી: ફિબોનાકિ

한국어: 피보나치 수

հայերեն: Ֆիբոնաչիի թվեր

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