Math is full of patterns – sequences of numbers. One cool pattern in math is known as the Fibonacci sequence. This pattern shows up everywhere in nature from flowers to galaxies. It’s sometimes called the golden spiral or golden ratio. To make the Fibonacci sequence you have to take the sum of the proceeding numbers starting with 0 and 1.

It looks something like this:

0 + 1 = 1

1 + 1 = 2

1 + 2 = 3

2 + 3 = 5

This pattern goes on forever as long as you continue to add the sum of the two proceeding numbers.

How does this pattern make the spiral we associate with the Fibonacci sequence? We can figure it out now with the project below!

Want to duplicate this experiment at home or in your classroom? Watch the video for an overview, gather the materials listed to the right, and follow the instructions below.

Required Materials

  • paper
  • ruler
  • pen, pencil, or other writing tools

Step-By-Step Instructions

Step 1

Using a ruler, draw two equal squares 1 inch x 1 inch touching each other. This will be the start of our Fibonacci sequence!

Step 2

Remember that the previous two numbers equal our next value. This means we need to draw a 2 inch x 2 inch square right on top.

Step 3

Our next value is 3, because 1 + 2 = 3. This means we need to draw a 3 inch x 3 inch box next to our previous boxes. We’ll be drawing each new box in a counter-clockwise direction.

Step 4

Can you guess the next box? That’s right 3 + 2 = 5, so our next box will be 5 inches x 5 inches.

Step 5

Now on to the last square. We’ll be drawing out 8 inches x 8 inches. Any idea how we got there? You should finish with a giant rectangle of the Fibonacci sequence.