# The Fibonacci Numbers

In this lesson, we will learn about a flagship application of recursion, the Fibonacci numbers.

## What are the Fibonacci numbers?

Fibonacci numbers are a series of numbers given by the following set of formulas:

$Fib(0) = 0$

$Fib(1) = 1$

$Fib(n) = Fib(n-1) + Fib(n-2)$

This is a classic example of recursion. The first two equations give us the **base cases**, while the third equation is the **recursive step**. Verbally, we can define *n$^{th}$ Fibonacci number as sum of (n-1)$^{th}$ and (n-2)$^{th}$ Fibonacci numbers*.

## Are Fibonacci numbers more than just a formula?

Well, yes! Look at the visualization in Figure 1.

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