Fibonacci Calculator

About Fibonacci Numbers

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones. The sequence starts with 0 and 1, and continues infinitely: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

Formula:

F(n) = F(n-1) + F(n-2)
with F(0) = 0 and F(1) = 1

Properties:

• Each number is the sum of the previous two
• The ratio of consecutive numbers approaches the golden ratio (φ ≈ 1.618033989)
• The sequence grows exponentially
• Many numbers in the sequence are prime

Applications:

• Natural phenomena (spiral patterns in nature)
• Financial market analysis
• Computer algorithms
• Art and architecture

Golden Ratio Connection:

The ratio of consecutive Fibonacci numbers (F(n)/F(n-1)) converges to the golden ratio φ, which is approximately 1.618033989. This number appears frequently in art, architecture, and nature, and is considered aesthetically pleasing.