Fibonacci Numbers

The Fibonacci Sequence is the series of numbers:

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

The next number is found by adding up the two numbers before it:

• the 2 is found by adding the two numbers before it (1+1),
• the 3 is found by adding the two numbers before it (1+2),
• the 5 is (2+3),
• and so on!

It is that simple!

Here is a longer list:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,144,233,377,610,987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, ...

Can you figure out the next few numbers?

Makes A Spiral

When we make squares with those widths, we get a nice spiral:

First, the terms are numbered from 0 onwards like this:

So term number 6 is called x₆ (which equals 8).

Example: the 8th term is the 7th term plus the 6th term: x8 = x7 + x6

So we can write the rule:

The Rule is x_n = x_n−1 + x_n−2

where:

• x_n is term number "n"
• x_n−1 is the previous term (n−1)
• x_n−2 is the term before that (n−2)