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.

AI illustration

How this image was made

AI-generated illustration of Fibonacci sequence

This AI-generated illustration was produced by black-forest-labs/FLUX.2-dev (1024x1024) from a prompt written by openai/gpt-oss-120b from the entity's label + description.

Prompt

Generate an image of the Fibonacci sequence (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)

How this entity was disambiguated

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 ⓘ

How these facts were elicited

Referenced by (25)

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 ⓘ
Fibonacci retracement → basedOn → Fibonacci sequence ⓘ
Fermat's spiral → relatedToConcept → Fibonacci numbers ⓘ
linked to: Fibonacci sequence
Liber Abaci → introducedConcept → Fibonacci sequence ⓘ