Fibonacci sequence

E67350

The Fibonacci sequence is an infinite series of numbers where each term is the sum of the two preceding ones, widely used in mathematics, art, and design due to its connection with the golden ratio and natural growth patterns.

All labels observed (5)

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Statements (53)

Predicate Object
instanceOf integer sequence
mathematical concept
alternativeName Fibonacci sequence
surface form: Fibonacci numbers
appearsIn phyllotaxis patterns
pinecone spirals
rabbit population model
spiral arrangements in plants
sunflower seed patterns
asymptoticForm F(n) ≈ φ^n / √5
belongsTo combinatorics
discrete mathematics
number theory
definedByRecurrence F(n) = F(n−1) + F(n−2)
firstTerms 0
1
13
2
21
3
34
5
55
8
hasCharacteristicPolynomial x^2 − x − 1
hasClosedForm Fibonacci sequence self-linksurface differs
surface form: Binet’s formula
hasFirstTerm 0
hasGeneratingFunction x / (1 − x − x^2)
hasGrowthRate exponential
hasInitialConditions F(0) = 0
F(1) = 1
hasParityPatternPeriod 3
hasSecondTerm 1
isDefinedOn nonnegative integers
isExampleOf linear homogeneous recurrence with constant coefficients
recursively defined sequence
isImplementedIn many programming tutorials
isInfinite true
isLinearRecurrenceOfOrder 2
isStrictlyIncreasingFromIndex 2
isSubsequenceOf Lucas sequences
isUsedInAlgorithm Fibonacci heap
Fibonacci search
dynamic programming examples
limitOfRatioOfConsecutiveTerms golden ratio
moduloPatternName Pisano period
namedAfter Leonardo Fibonacci
relatedTo golden ratio
usedIn architecture
art
computer algorithms
design
mathematical modeling
nature modeling

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Referenced by (22)

Full triples — surface form annotated when it differs from this entity's canonical label.

Le Modulor basedOn Fibonacci sequence
Fibonacci sequence alternativeName Fibonacci sequence
this entity surface form: Fibonacci numbers
Fibonacci sequence hasClosedForm Fibonacci sequence self-linksurface differs
this entity surface form: Binet’s formula
The Book of Numbers coversTopic Fibonacci sequence
this entity surface form: Fibonacci numbers
Penrose tilings relatedTo Fibonacci sequence
Fibonacci heap namedAfter Fibonacci sequence
this entity surface form: Fibonacci numbers
Leonardo Fibonacci knownFor Fibonacci sequence
Leonardo Fibonacci hasConceptNamedAfter Fibonacci sequence
this entity surface form: Fibonacci numbers
Leonardo Fibonacci hasConceptNamedAfter Fibonacci sequence
golden ratio isRelatedTo Fibonacci sequence
this entity surface form: Fibonacci numbers
golden ratio isRelatedTo Fibonacci sequence
this entity surface form: Binet's formula
Lucas sequences includesSequence Fibonacci sequence
this entity surface form: Fibonacci numbers
Lucas sequences generalizes Fibonacci sequence
Lucas sequences specialCaseCondition Fibonacci sequence
this entity surface form: Fibonacci sequence corresponds to P = 1, Q = -1 with suitable initial conditions
Fibonacci search uses Fibonacci sequence
this entity surface form: Fibonacci numbers
Fibonacci search determinesProbePositionsBy Fibonacci sequence
this entity surface form: Fibonacci numbers
Fibonacci search basedOn Fibonacci sequence
Fibonacci search usesMathematicalConcept Fibonacci sequence
this entity surface form: Fibonacci numbers
Pisano period dependsOn Fibonacci sequence
Pisano period relatedTo Fibonacci sequence
this entity surface form: Fibonacci numbers
Jacques Saunière associatedWithSymbol Fibonacci sequence