Fibonacci Sequence Generator
F(n) = F(n-1) + F(n-2)
Starting with F(0) = 0, F(1) = 1
Range: 1 - 100
About the Fibonacci Sequence
The Fibonacci sequence is one of the most famous sequences in mathematics. Each number after the first two is the sum of the two preceding numbers.
The sequence starts: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...
As the sequence progresses, the ratio of consecutive Fibonacci numbers approaches the golden ratio (φ ≈ 1.618), which appears frequently in art, architecture, and nature.
Frequently Asked Questions
The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, starting from 0 and 1. The sequence goes: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... It's named after Italian mathematician Leonardo Fibonacci.
The Fibonacci sequence appears throughout nature: in the arrangement of leaves on stems, the pattern of seeds in sunflowers, the spiral of shells, the branching of trees, and even in the proportions of the human body. The golden ratio (φ ≈ 1.618) is closely related to Fibonacci numbers.
Fibonacci numbers are used in computer algorithms (dynamic programming, search techniques), financial analysis (Fibonacci retracements in trading), music theory, art composition, and various mathematical proofs and sequences.