Finding Fibonacci numbers in plants

A spiral approach to teaching

Introduction

Plants have parts which create spiral patterns, the seed heads of sunflowers, pine cones,pineapples and artichokes for example. There are usually Fibonacci numbers of spirals.

Material

Pine cones, big ones are easier
Pineapples
optional artichokes or sunflowers or
photos of sunflowers
colored string
scissors
colored pencils
sticky clay to attach the string to the pinecones etc.

To Do and Notice

Look at a pinecone, or pineapple, until you see a spiral of bracts winding away from the stem end.
Stick a colored string onto the pinecone following this spiral. Use the sticky clay.

Move to the right and follow the next spiral.
Mark it with colored string.

Count the number of spirals.

Is it a Fibonacci number?
The Fibonacci series of numbers is 1,1,2,3,5,8,13,21,34,55,... where each number is the sum of the previous two numbers.

Looked at from the tip of the pinecone, the end opposite the stem, the spirals will go around clockwise or counterclockwise. Which way do your spirals turn?

Notice that sometimes a spiral will split into two spirals, mark one branch of these splits with different color string.

Look at the pinecone again.

Find spirals that go around the opposite way from the first set.

Mark these spirals in another color of string.

Count the number of spirals.

Is it a Fibonacci number?

Take a copy of the photo of a sunflower.

Use a colored pencil to mark one set of spirals on the copy. Use a different color to mark the spirals in the opposite direction.

Count the numbers of spirals.

Are the numbers Fibonacci numbers?

What's going on?

Scientists have computed and made models that show that a growth tip that spirals around producing primordia at equal intervals of 137.5 degrees, followed by the primodia growing larger as they age, will produce Fibonacci numbers of spirals in plant parts.

Activity by Paul Doherty.

After an activity by Karen Kalumuck.

 Scientific Explorations with Paul Doherty © 2001 17 April 2001