Introduction

The Fibonacci Sequence is nature's way of expressing the Golden Ratio. As discussed in the previous section phi, the golden ratio, is a number that never ends. Since nothing in our physical universe allows for the perfect expression of the infinite we cannot find a perfect expression of phi. Regardless, life tries it's best to get to this magic number!

Although it is known by the western discoverer of the sequence, Leonardo of Pisa (Fibonacci), it had already been in use in Indian mathematics.

Nick presents a real life example of the Fibonacci Sequence.

Enough of the Crap, What is the Fibonacci Sequence?

It is a series of numbers that have a relationship to the previous two numbers, their mommy and daddy. This sequence needs two numberes to get it started: 0 and 1. The next number is created by adding these two numbers. So 0 + 1 = 1:

Sequence so far: 0, 1, 1

We continue is the same fashion, by adding the last two numbers in the sequence to create the new one, the child of the previous two, i.e. the parents. The parents here are 1 and 1 creating 2.

Sequence so far: 0, 1, 1, 2

Now we add the last two in the sequence again, just as before, 1 + 2 = 3. This is all there is to it, we create the whole series in this way.

Sequence so far: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89....

Looking at the sequence you can pick any number in it, for example 55, and by looking at the two numbers before it you have found its parents, in this case 21 and 34!

That's Cool Guys, But What Does it Mean?

Well this is where it gets interesting. Let's look at one of the numbers in the sequence, 5 for example. We're going to divide 5 by the number just before it, 3.

5 divided by 3 = 1.6666...

Well would look at that, seems pretty close to 1.618! Let's go a bit higher up the sequence and do the same thing. Take 21 and divide it be the number just before it, 13.

21 divided by 13 = 1.61538...

So we notice that the higher we go up in the sequence, the relationship between the pairs of numbers gets closer to phi!

This is how nature does it folks! It uses approximations to phi and the Fibonacci sequence is in common use. As an example have a look at this pine cone.

You'll notice there are 13 spirals going in one direction here, sound familiar? It's one of the numbers in the Fibonacci sequence! There's actually more going on here than just the number 13, there is another Fibonacci number hidden in there but why spoil all the fun :) More on that later.

Now that we know a bit about the Fibonacci sequence lets have a look at the famous golden spiral.