What is the Fibonacci sequence?

It is great to help you explore the Fibonacci sequence today. Before we jump into how this famous pattern builds itself and where it hides in nature, I would love to learn a little more about what brings you here.

To help me tailor our session, could you tell me a bit about why you're interested in the Fibonacci sequence and if you've studied it or similar patterns before?

I am brand new to this and just curious about how it works.

Welcome! It is wonderful to have you here. Since you are brand new to this, we will start right at the beginning with the core concept: how the sequence builds itself.

Your path

The Fibonacci Sequence in Nature

Applications and Significance

The Adding-Up Pattern

At its heart, the is simply a string of numbers where each new number is found by adding up the two numbers that came right before it.

Let's look at how this sequence actually gets rolling. We always start out with two basic numbers to set the stage:

0

and

1

. To find the next number, we add those first two together:

0 + 1 = 1

Now our list is

0, 1, 1

. To keep going, we take the last two numbers (

1

and

1

) and add them:

1 + 1 = 2

Now we have

0, 1, 1, 2

. Let's do it again with the new last two (

1

and

2

1 + 2 = 3

If we repeat this simple step-by-step game, the sequence naturally grows longer and longer:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

Each step is just a tiny jump, but it quickly builds into a famous progression that appears all over the natural world.