Fibonacci Calculator

What is Fibonacci?

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones. It typically starts with 0 and 1, and each subsequent number is the sum of the previous two. This sequence appears in many natural phenomena and has applications in various fields of mathematics and science.

How to Calculate Fibonacci Numbers

To calculate Fibonacci numbers, start with 0 and 1, then generate each subsequent number by adding the two previous numbers in the sequence. This process continues indefinitely, creating an ever-growing sequence of numbers.

Formula

The formula for calculating the nth Fibonacci number is:

\[ F_n = F_{n-1} + F_{n-2} \]

Where F_n is the nth Fibonacci number, with initial conditions F₀ = 0 and F₁ = 1.

Calculation Steps

1. Start with F₀ = 0 and F₁ = 1
2. For each subsequent number n, calculate F_n = F_n-1 + F_n-2
3. Continue this process for as many numbers as needed in the sequence

Example

Let's calculate the first 8 Fibonacci numbers:

1. F₀ = 0
2. F₁ = 1
3. F₂ = F₁ + F₀ = 1 + 0 = 1
4. F₃ = F₂ + F₁ = 1 + 1 = 2
5. F₄ = F₃ + F₂ = 2 + 1 = 3
6. F₅ = F₄ + F₃ = 3 + 2 = 5
7. F₆ = F₅ + F₄ = 5 + 3 = 8
8. F₇ = F₆ + F₅ = 8 + 5 = 13

Therefore, the first 8 Fibonacci numbers are: 0, 1, 1, 2, 3, 5, 8, 13