Fibonacci numbers
A Fibonacci number is a member of the sequence where each number is the sum of the two before it, starting 0, 1, 1, 2, 3, 5, 8, 13, 21...
The Fibonacci sequence is one of the best-known sequences in mathematics, with genuine applications in describing certain branching and spiral growth patterns in nature. This hub groups catalogue numbers by that shared mathematical structure — it does not claim every Fibonacci number carries separate cultural significance.
The rule behind the sequence
Fibonacci numbers follow one simple rule: each number is the sum of the two before it, starting from 0 and 1.
F(0) = 0, F(1) = 1, F(n) = F(n − 1) + F(n − 2)
Worked out for the first steps: 0 + 1 = 1, 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8, 5 + 8 = 13 — giving the familiar opening run 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89.
Where the sequence comes from
The sequence appears in Indian mathematics (Pingala, Virahanka, Hemachandra) centuries before it reached Europe, where it became widely known after Leonardo of Pisa ("Fibonacci") used it in his 1202 book Liber Abaci to model a hypothetical rabbit population — hence the name it carries in the West today.
Fibonacci numbers and the golden ratio
Dividing each Fibonacci number by the one before it produces a ratio that settles closer and closer to approximately 1.618 — known as the golden ratio (φ) — as the sequence continues. That convergence is a genuine, provable mathematical result, not folklore.
Common misconception: "The golden ratio is a hidden design rule found throughout art, architecture and the human body"
Many widely shared claims about the golden ratio appearing in specific famous buildings, paintings, or ideal body proportions rely on approximate measurements chosen after the fact, and are not well supported by rigorous evidence. Numberwise treats the sequence-to-φ convergence itself as established mathematics, and treats broader "golden ratio everywhere" claims as disputed rather than repeating them as fact.
Fibonacci numbers in nature
Spiral arrangements approximating Fibonacci numbers are genuinely common in plants — the seed-head spirals of a sunflower and the scales of a pinecone are well-documented examples, arising from an efficient packing pattern during growth. This is a real, widely-observed pattern, but not a universal law: not every flower or plant follows it, and claiming otherwise overstates the evidence.
Fibonacci numbers in the catalogue
Common questions
What is the Fibonacci sequence?
The Fibonacci sequence starts 0, 1, 1, 2, 3, 5, 8, 13, 21... — every number after the first two is the sum of the two before it.
Does every Fibonacci number carry cultural meaning?
No. Being a Fibonacci number is a purely mathematical property. The sequence itself is famous and has genuine applications in describing some natural growth patterns, but Numberwise never claims an individual Fibonacci number is significant beyond its place in the sequence unless a separate, sourced claim exists on its own profile page.