Fibonacci sequence

E67350
integer sequence mathematical concept

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.

Jump to: Surface forms Statements Referenced by

Observed surface forms (2)

Surface form Occurrences
Binet’s formula 1
Fibonacci numbers 1

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 ⓘ

Referenced by (3)

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

Fibonacci sequence → alternativeName → Fibonacci sequence ⓘ
this entity surface form: Fibonacci numbers
Le Modulor → basedOn → Fibonacci sequence ⓘ
Fibonacci sequence → hasClosedForm → Fibonacci sequence self-linksurface differs ⓘ
this entity surface form: Binet’s formula