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.