Fibonacci Day — A Tribute to Leonardo of Pisa (Fibonacci)
An illustrated article for mathematicians and curious readers exploring the sequence, its origin, and achievements.
Introduction
The Fibonacci sequence is the integer sequence in which each number is the sum of the two preceding ones. It appears throughout mathematics and nature — in phyllotaxis, branching, and population models. Fibonacci Day is informally celebrated on November 23 (11/23) because the date matches the sequence's first terms: 1, 1, 2, 3.
About the Mathematician
Leonardo of Pisa, commonly known as Fibonacci (c. 1170 – c. 1250), was an Italian mathematician whose 1202 book Liber Abaci introduced Hindu–Arabic numerals to much of Europe and presented a population growth problem of rabbits that popularized the sequence now bearing his name.
Key achievements
Introduced efficient calculation with Hindu–Arabic numerals (0–9) replacing Roman numerals in commercial arithmetic. This text laid the foundation for modern arithmetic in Europe.
Presented a model of idealized rabbit population growth that yields the numeric sequence 1, 1, 2, 3, 5, 8, 13 ... — a sequence later discovered to have deep combinatorial and number-theoretic properties.
His work accelerated adoption of positional base-10 arithmetic for merchants and scholars, enabling the speedy arithmetic that made commerce and science practical.
Beyond the sequence, Fibonacci's writings influenced number theory, modular arithmetic, and inspired centuries of mathematical study and generalizations such as Lucas sequences and Fibonacci polynomials.
Where the sequence shows up
Appearance across mathematics and nature: continued fractions and approximations of φ (the golden ratio), Pascal's triangle diagonals, spirals in shells, phyllotactic patterns in plants, and algorithmic uses (e.g. Fibonacci heaps, search heuristics).
Interactive: compute Fibonacci numbers
A short table
| n | Fn |
|---|
Note for mathematicians: Fibonacci numbers satisfy linear recurrence relations, have closed-form using Binet's formula, and intimate connections to the golden ratio φ = (1+√5)/2. The ratio Fn+1/Fn converges to φ as n → ∞.
