Fibonacci Calculator
Generate Fibonacci sequences, find nth terms, and explore the fascinating world of Fibonacci numbers.
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Golden Ratio Calculator
About Fibonacci Numbers
What are Fibonacci Numbers?
The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1.
Sequence Definition
F(0) = 0, F(1) = 1
F(n) = F(n-1) + F(n-2) for n ≥ 2
First 20 Terms
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181
Golden Ratio
As n approaches infinity, the ratio F(n+1)/F(n) approaches the golden ratio φ ≈ 1.618033988749895.
Applications
- Nature (spiral shells, flower petals)
- Art and architecture
- Computer algorithms
- Financial markets
- Music composition
Interesting Properties
- Every 3rd number is even
- Every 4th number is divisible by 3
- Every 5th number is divisible by 5
- Sum of any 10 consecutive terms is divisible by 11