The Fibonacci Series

You may think that the pattern of twigs and branches on trees has no order, but just the opposite is true. The pattern of branches of many plants follows an amazing system called the Fibonacci series, named after a thirteenth century investigator by the name of Fibonacci. His number series looks like this:


Now, the way this series works is simple. You begin by adding 1+1 to equal 2, then 1+2 to equal 3, 2+3=5, 3+5=8, 5+8=13, and so on.

So, what does this have to do with trees?! Well, it turns out that the pattern of branches sometimes follows fractions derived from this series. Imagine a series of fractions created by replacing any of the commas in the series with /s. This yields a series of fractions starting as:

1/2, 2/3, 3/5, 5/8, 8/13, etc.

For many plants, one of these fractions describes how far around the plant stem you have to go to see another branch. Say you were to tie a string to the very top branch, then tie it to the next branch down, then the next lower branch, and so forth. Now, count how many times the string touched a branch until it got back to its original starting position (say, on the north side of the tree). This point will, of course, be a few feet below the starting branch, but the alignment of the end point should be directly below the starting branch. This is the number of times the string wound around the tree (until it was directly below the starting point).

Next, notice exactly how many branches it took to get from the top branch to the first branch directly below that starting branch. These are the two numbers you will use to set up a fraction. Place the number of string spirals on top of the fraction and the number of branches on the bottom of the fraction. This fraction will tell you nature's branching pattern for that tree. Bet you that fraction will fit the Fibonacci series!

Now it's time for you to find out more about the trees that surround you! The following is an investigation you can do right in your own backyard. Here are the materials you will need:
1) A long piece of string. That's it.

Take your piece of string to a fairly small tree or large plant outside. Start at the highest branch you can reach. You may need a tall friend or parent to help you. Attach the string to that first branch by tying it around the base of the branch closest to the trunk. Now, spiral the string around the trunk to the next branch. Wrap the string around that branch. Continue this until you end up directly below your starting branch. Count the number of spirals and the number of branches you passed to get to the proper ending place and form the fraction described above. Your fraction should look like this:

Number of Spirals
Number of Branches

Does this fraction fit the Fibonacci series?

Write us at: and tell us what you discovered. Also feel free to tell us anything about your experiment. (Examples: What went wrong? What kind of tree did you test?) We would love to know what you think of this investigation.

Learn more about trees.