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