This is one of the math concepts I often use when designing a new pattern. For an overview, please see Math for Craft Design.
Below is a bit of information about the numbers in the Fibonacci series and a few examples of how to use them.
The Series
The first few numbers are:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233...
How to Get These Numbers
Start with 0 and 1, add them together to get the next number in the series - another 1. You must start with 0 and 1 to produce Fibonacci numbers.
Add the last two numbers - 1 and 1 - to get the next number in the series - 2.
Do this again - adding the last two numbers together - 1 and 2 - to get 3.
Then add 2 and 3 to get 5, 3 and 5 to get 8, and so on.
Practical Uses
The width of your afghan is working out to be 55 inches. Make it 89 inches long - the next number in the series. If you're working it lengthwise and it's 55 inches long, make it 21 inches wide - the previous number in the series.
A stripe is 8 rows deep. Make the next stripe 13 rows deep. For the third, go with 21 rows. Or simply alternate the 8 and 13, or all three depths. Use consecutive numbers in the series.
If you know you'll need approximately 15 balls of yarn for a multi-coloured but randomly patterned article, purchase 8 balls of Colour A, 5 of Colour B and 3 of Colour C. Again, use consecutive numbers in the series to total the amount you need. Add one to each amount, since we should always get an extra ball in each colour just in case!
Knitters who love math may want to try their hand at my Moebius Scarf - a loop with a true half twist, and cozy too! With photo.