Fibonacci sequence
Each adds previous two
The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones, typically starting with 0 and 1: 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on.
Named after the medieval Italian mathematician who introduced it to Western mathematics, the sequence appears throughout nature in phenomena like spiral patterns in shells, flower petals, and pinecone scales.
In technical contexts, Fibonacci numbers are used in computer algorithms and financial trading analysis.
The arrangement of seeds in a sunflower follows the Fibonacci sequence.
Process invoking itself
- seriesOrdered set of related items
- summationAdding to find total
- iterationRepeated procedural pass
- algorithmFinite problem-solving procedure
golden ratio · convergence · limit · theorem · proof · numbers · addition · arithmetic
Phi, roughly 1.618
- phiTwenty-first Greek letter
- aestheticsTheory of beauty
- harmonyAgreement or musical blend
- balanceSteadiness or amount owed
beauty · composition · scaling · architecture · Da Vinci · Parthenon · visual design · rectangle
Tall daisy-family plant
- pineconeWoody seed-bearing structure
- spiralCurve winding around center
- branchingSplitting into separate directions
- flower petalsColored leaf-like structures
shells · nautilus · artichoke · pineapple · romanesco · seed heads · honeybees · florets
Act of redoing
- self-similarityIdentical at every magnification
- fractalShape repeating at every scale
- tessellationGapless plane coverage
- rhythmPatterned stress and silence
structure · predictability · motif · regularity · symmetry · growth pattern · tiling · geometric progression
Self-similar expanding curve
- logarithmic spiralCurve maintaining constant tangent angle
- whorlSpiral arrangement of ridges
- voluteArchitectural spiral ornament
- helixSpiraling three-dimensional curve
coiling · chambered nautilus · fiddlehead · snail shell · ram's horn · unfurling · conch
Increasing by constant ratio
- accumulationCollected mass over time
- proliferationRapid increase in quantity
- expansionIncrease in scope
- progressionSequential forward movement
compounding · population growth · doubling · increasing · generational
recursion
Process invoking itself
algorithm · golden ratio · convergence · limit · theorem · proof · numbers · addition · arithmetic · combinatorics
golden ratio
Phi, roughly 1.618
- phiTwenty-first Greek letter
- aestheticsTheory of beauty
- harmonyAgreement or musical blend
balance · beauty · composition · scaling · architecture · Da Vinci · Parthenon · visual design · rectangle · typography
sunflower
Tall daisy-family plant
- pineconeWoody seed-bearing structure
- spiralCurve winding around center
- branchingSplitting into separate directions
flower petals · shells · nautilus · artichoke · pineapple · romanesco · seed heads · honeybees · florets
repetition
Act of redoing
- self-similarityIdentical at every magnification
- fractalShape repeating at every scale
- tessellationGapless plane coverage
rhythm · structure · predictability · motif · regularity · symmetry · growth pattern · tiling · geometric progression
golden spiral
Self-similar expanding curve
- logarithmic spiralCurve maintaining constant tangent angle
- whorlSpiral arrangement of ridges
- voluteArchitectural spiral ornament
helix · coiling · chambered nautilus · fiddlehead · snail shell · ram's horn · unfurling · conch
exponential
Increasing by constant ratio
- accumulationCollected mass over time
- proliferationRapid increase in quantity
- expansionIncrease in scope
progression · compounding · population growth · doubling · increasing · generational
- math conceptsangle, numbers, algebra, circle, equations
- compositionbalance, symmetry, asymmetry, proportion, layout
- EponymsDarwinian, Alzheimer's disease, Freudian slip, cardigan, Parkinson's disease
- math historyEuclid, Pythagoras, Newton, Leibniz, Euler
- ancient mathalgebra, arithmetic, geometry, fractions, addition
- fibonaccigolden ratio, phi, golden spiral, golden rectangle, golden section
sequence, Fibonacci numbers, sequences, sequenced, sequencing, subsequence, Fibonacci