The Fibonacci Sequence can be expressed as F_{n}=F_{n-1} + F_{n-2} . The first two numbers of this sequence are 0 and 1 or 1 and 1, but it’s sorta your choice.

So that means the pattern would be…

0

1

0+1=1

1+1=2

2+1=3

3+2=5

5+3=8

8+5=13

…

On and on forever.

It’s a neat little pattern, if you’re a nerd. You could’ve come up with it if you were really bored at your desk. As a matter of fact, when I’m bored in class, I’ll just add up Fibonacci numbers and fill up pages with it.
The Fibonacci Sequence is cool because as the numbers get bigger and bigger, it approaches infinity (duh), but it’s approaching it at a certain rate that casues a visual phenomenon. The Fibonacci Spiral shows the rate of growth of Fibonacci numbers. The Fibonacci sprial is shown below.

If you draw the squares of the Fibonacci numbers and connect the points, like so, you create an infinite spiral. The Fibonacci Sequence is cool because of the Fibonacci Spiral. But what’s cool about it is that it approaches infinity at a rate that reoccurs in nature. Most people are familiar with the Fibonacci Sequence because it occurs in nature, and there are so many more examples of math occuring in nature (which we’ll talk about more later).

This video shows 3d scultures using the Fibonacci Numbers as inspiration.

Here’s some Fibonacci in the world.

Trees branch off in Fibonacci numbers. The number of petals on a flower are usually found in fibonacci numbers. Plants grow with fibonacci patterns displayed in them. Galaxies spiral in Fibonacci spirals. seashells are grown in Fibonacci Spirals. IT’S SO FLIBBING COOL!

These two plants below have the Fibonacci Spiral going around in both directions.