Calculatrice de Fibonacci Gratuite
Calculez les termes de la suite de Fibonacci. Trouvez le n-ième nombre de Fibonacci ou vérifiez si un nombre en fait partie.
Fib N
55
Formule
Fibonacci Sequence
Definition
F(0) = 0, F(1) = 1, F(n) = F(n-1) + F(n-2)
Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
Binet's Formula
F(n) = (phi^n - psi^n) / sqrt(5)
where phi = (1 + sqrt(5))/2 (golden ratio) and psi = (1 - sqrt(5))/2.
For large n, psi^n approaches 0, so F(n) ≈ phi^n / sqrt(5).
Golden Ratio
As n grows, F(n)/F(n-1) approaches the golden ratio phi ≈ 1.6180339887.
Exemple Résolu
Find the 10th Fibonacci number.
- 01F(10) = phi^10 / √5
- 02= 1.61803^10 / 2.23607
- 03≈ 122.992 / 2.236
- 04≈ 55
- 05Sequence up to F(10): 0,1,1,2,3,5,8,13,21,34,55
Questions Fréquentes
What is the Fibonacci sequence?
The Fibonacci sequence starts with 0 and 1, and each subsequent number is the sum of the two preceding ones: 0, 1, 1, 2, 3, 5, 8, 13, 21, ...
What is the golden ratio?
The golden ratio (phi ≈ 1.618) is the limit of the ratio of consecutive Fibonacci numbers. It appears in art, architecture, and nature.
Where do Fibonacci numbers appear in nature?
Fibonacci numbers appear in flower petals, seed spirals in sunflowers, pinecones, pineapples, and branching patterns in trees.
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