What is the Fibonacci sequence?

I'd love to help you explore this beautiful pattern! Before we dive into the math, could you tell me a little about your background—are you looking for a casual, intuitive overview, or are you interested in a more technical and mathematical deep dive?

I'd prefer a casual, intuitive overview.

At its heart, the is just a game of simple addition. We start with the numbers 0 and 1, and then we follow one golden rule: add the last two numbers together to get the next one. Let's see how this works step-by-step from the very beginning:

We start with 0 and 1.
Add them up ( $0 + 1$ ) to get 1. Now our sequence is: 0, 1, 1.
Add the last two numbers ( $1 + 1$ ) to get 2. Now we have: 0, 1, 1, 2.
Add the last two again ( $1 + 2$ ) to get 3. Our sequence becomes: 0, 1, 1, 2, 3.
Keep it going ( $2 + 3$ ) to get 5.

Following this simple rule, the sequence flows naturally into the distance:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, \dots

While we call this the "Fibonacci" sequence today, the credit actually belongs to ancient Indian mathematicians who documented this beautiful pattern of numbers centuries before it was introduced to Europe by Leonardo of Pisa (who we now know as ).