Fibonacci number
In mathematics, the Fibonacci numbers, commonly denoted Fn , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes (as did Fibonacci) from 1 and 2.Starting from 0 and 1, the first few values in the sequence are: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.
- Comment
- enIn mathematics, the Fibonacci numbers, commonly denoted Fn , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes (as did Fibonacci) from 1 and 2.Starting from 0 and 1, the first few values in the sequence are: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.
- Depiction
- Formalname
- enFibonacci numbers: F = F + F with F = 0 and F = 1
- Has abstract
- enIn mathematics, the Fibonacci numbers, commonly denoted Fn , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes (as did Fibonacci) from 1 and 2.Starting from 0 and 1, the first few values in the sequence are: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144. The Fibonacci numbers were first described in Indian mathematics, as early as 200 BC in work by Pingala on enumerating possible patterns of Sanskrit poetry formed from syllables of two lengths. They are named after the Italian mathematician Leonardo of Pisa, later known as Fibonacci, who introduced the sequence to Western European mathematics in his 1202 book Liber Abaci. 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 search technique and the Fibonacci heap data structure, and graphs called Fibonacci cubes used for interconnecting parallel and distributed systems. They also appear in biological settings, such as branching in trees, the arrangement of leaves on a stem, the fruit sprouts of a pineapple, the flowering of an artichoke, an uncurling fern, and the arrangement of a pine cone's bracts. Fibonacci numbers are also strongly related to the golden ratio: expresses the nth Fibonacci number in terms of n and the golden ratio, and implies that the ratio of two consecutive Fibonacci numbers tends to the golden ratio as n increases. Fibonacci numbers are also closely related to Lucas numbers, which obey the same recurrence relation and with the Fibonacci numbers form a complementary pair of Lucas sequences.
- Id
- enDRjFV_DETKQ
- enp/f040020
- Is primary topic of
- Fibonacci number
- Label
- enFibonacci number
- Link from a Wikipage to an external page
- books.google.com/books%3Fid=bUARfgWRH14C
- www.mathpages.com/home/kmath078/kmath078.htm
- www.physorg.com/news97227410.html
- www.wiley.com/WileyCDA/WileyTitle/productCd-047131515X.html
- archive.org/details/thoriedesnombr01lucauoft
- Link from a Wikipage to another Wikipage
- 8SVX
- Abraham de Moivre
- Amiga
- Analysis of algorithms
- Arbitrarily large
- Artichoke
- Asymptotic analysis
- AVL tree
- Bharata Muni
- Bijection
- Binary numeral system
- Binary tree
- Binomial coefficient
- Cardinality
- Carmichael's theorem
- Cassini's identity
- Category:Articles containing proofs
- Category:Fibonacci numbers
- Circle packing theorem
- Closed-form expression
- Combinatorial proof
- Companding
- Complete sequence
- Composite number
- Composition (combinatorics)
- Conformal map
- Conjugate (square roots)
- Continued fraction
- Conversion of units
- Coprime integers
- Cycle detection
- Daniel Bernoulli
- Determinant
- Difference equation
- Diophantine equation
- Divisibility sequence
- Domino tiling
- Drone (bee)
- Édouard Lucas
- Eigendecomposition
- Eigenvalue
- Eigenvector
- Euclidean algorithm
- Exponentiation by squaring
- Factorization
- Fermat's spiral
- Fern
- Fibbinary number
- Fibonacci
- Fibonacci coding
- Fibonacci cube
- Fibonacci heap
- Fibonacci number
- Fibonacci polynomials
- Fibonacci Quarterly
- Fibonacci retracement
- Fibonacci search technique
- File:FibonacciChamomile.PNG
- File:Fibonacci climbing stairs.svg
- File:Fibonacci Rabbits.svg
- File:Fibonacci Sanskrit prosody.svg
- File:Fibonacci Spiral.svg
- File:Fibonacci Squares.svg
- File:Fibonacci tiling of the plane and approximation to Golden Ratio.gif
- File:Fibonacci Tree 6.svg
- File:Liber abbaci magliab f124r.jpg
- File:PascalTriangleFibanacci.svg
- File:SunflowerModel.svg
- File:X chromosome ancestral line Fibonacci sequence.svg
- Finite field
- Floor function
- Floret
- Founder effect
- Free group
- Functional equation
- Generalizations of Fibonacci numbers
- Generating function
- Golden angle
- Golden ratio
- Golden ratio base
- Greatest common divisor
- Hemachandra
- Hilbert's tenth problem
- Indian mathematics
- Integer sequence
- Interchange File Format
- Irrational number
- Jacobi symbol
- Jacques Philippe Marie Binet
- Johannes Kepler
- Joseph Schillinger
- Kepler
- Lambert series
- Lattice reduction
- Legendre symbol
- Leucanthemum vulgare
- Liber Abaci
- Linear difference equation
- Linear recurrence with constant coefficients
- Lossy compression
- L-system
- Lucas number
- Lucas sequence
- Mario Merz
- Mathematical induction
- Matiyasevich's theorem
- Matrix diagonalization
- Memoization
- Merge sort
- Modular arithmetic
- Modular exponentiation
- Monotonic
- Mora (linguistics)
- Multiplicative order
- Multiply perfect number
- Natya Shastra
- NegaFibonacci coding
- Network topology
- Optics
- Ordinary generating function
- Padovan sequence
- Parallel computing
- Parastichy
- Partial fraction decomposition
- Partition (number theory)
- Pascal's triangle
- Patterns in nature
- Pell number
- Perfect number
- Periodic sequence
- Perrin number
- Phyllotaxis
- Piecewise
- Pineapple
- Pine cone
- Pingala
- Pisano period
- Planning poker
- Polyphase merge sort
- Power series
- Primefree sequence
- Prime number
- Princeton University Press
- Processor register
- Przemysław Prusinkiewicz
- Pseudorandom number generators
- Pythagorean triple
- Quadratic equation
- Quadratic formula
- Rabbit
- Radix
- Random House
- Reciprocal Fibonacci constant
- Recurrence relation
- Recursion
- Recursion (computer science)
- Refractive index
- Resistor ladder
- Richard André-Jeannin
- Right triangle
- Ring lemma
- Rounding
- Sanskrit prosody
- Scaled agile framework
- Schillinger System
- Special number field sieve
- Specifiable combinatorial class
- Square number
- String (computer science)
- Subset
- Sunflower
- Symbolic method (combinatorics)
- Technical analysis
- The Art of Computer Programming
- Theta function
- Tree height
- Truncation
- Undirected graph
- Unimodular matrix
- Verner Emil Hoggatt Jr.
- Virahanka
- Wall–Sun–Sun prime
- X chromosome
- Y chromosome
- Yuri Matiyasevich
- Zeckendorf's theorem
- Μ-law
- Name
- enFibonacci numbers
- SameAs
- 4QbpM
- Bilangan Fibonacci
- Bilang na Fibonacci
- Dãy Fibonacci
- Fibonacci dizisi
- Fibonaccigetal
- Fibonacci jada
- Fibonaccijev broj
- Fibonaccijev broj
- Fibonaccijevo število
- Fibonacci number
- Fibonacci number
- Fibonacciren zenbakiak
- Fibonacci-runan
- Fibonacci sequence
- Fibonacci sonlari
- Fibonacci-számok
- Fibonaccital
- Fibonacci-tal
- Fibonaccitall
- Fibonaccizahl
- Fibonaççi ədədləri
- Fibonačijev niz
- Fibonaĉi-nombro
- Fibonači skaitļi
- Ihap Fibonacci
- m.02ygw
- Nombre de Fibonacci
- Nombre de Fibonacci
- Număr Fibonacci
- Numeri Fibonacciani
- Numrat e Fibonaccit
- Q47577
- Rhif Fibonacci
- Лікі Фібаначы
- Фибоначиева низа
- Фибоначијев низ
- Фибоначчийн тоо
- Фибоначчи сандары
- Фибоначчи хисепĕ
- Фибоначчи һандары
- Числа Фибоначчи
- Числа Фібоначчі
- Числа на Фибоначи
- Ֆիբոնաչիի թվեր
- סדרת פיבונאצ'י
- اعداد فیبوناچی
- عدد فيبوناتشي
- ژمارەی فیبۆناچی
- फिबोनाची श्रेणी
- हेमचन्द्र श्रेणी
- ফিবোনাচ্চি রাশিমালা
- ਫ਼ੀਬੋਨਾਚੀ ਤਰਤੀਬ
- ફિબોનાકિ
- பிபனாச்சி எண்கள்
- ఫిబోనాచీ సంఖ్యలు
- ഫിബനാച്ചി ശ്രേണി
- ෆිබොනාච්චි සංඛ්යා
- จำนวนฟีโบนัชชี
- フィボナッチ数
- 斐波那契数
- 피보나치 수
- SeeAlso
- Golden ratio
- Sequencenumber
- enA000045
- Subject
- Category:Articles containing proofs
- Category:Fibonacci numbers
- Thumbnail
- Title
- enFibonacci numbers
- enSunflowers and Fibonacci - Numberphile
- WasDerivedFrom
- Fibonacci number?oldid=1124417453&ns=0
- WikiPageLength
- 83807
- Wikipage page ID
- 10918
- Wikipage revision ID
- 1124417453
- WikiPageUsesTemplate
- Template:=
- Template:Anchor
- Template:Annotated link
- Template:Authority control
- Template:Circa
- Template:Citation
- Template:Classes of natural numbers
- Template:Clear
- Template:Efn
- Template:Fibonacci
- Template:Further
- Template:Ill
- Template:In Our Time
- Template:Interwiki extra
- Template:Main
- Template:Math
- Template:Metallic ratios
- Template:Mset
- Template:Mvar
- Template:Notelist
- Template:OEIS el
- Template:Redirect
- Template:Reflist
- Template:See also
- Template:Series (mathematics)
- Template:Sfn
- Template:Short description
- Template:Slink
- Template:Snd
- Template:Space
- Template:Springer
- Template:Wikibooks
- Template:Wikiquote
- Template:YouTube
