Fibonacci's numbers

Definition

How to calculate Fibonacci's numbers?

Mental representation 1 - Fibonacci formula

F_n = F_n-1 + F_n-2
F₀ = 0
F₁ = 1

This formula has a very neat form, which is easy to understand and proves simple to calculate small Fibonacci numbers.

Mental representation 2 - Binet's Fibonacci formula

F_n = ((1 + √5 )ⁿ - (1 - √5 )ⁿ) / (2ⁿ √5)

This formula is good for calculating really big Fibonacci numbers, yet is totally non-intuitive and one has some trouble before he understands what series is being calculated by it.

Result of both equations is the same, but underlying method differs. One is intuitive, the other is fast.