Fibonacci Spiral

Did you know?
In the Fibonacci number sequence each number is the sum of the previous two numbers. So, beginning with 0 and 1, the sequence is as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144… and so forth. We call this the Fibonacci sequence, and the numbers are called Fibonacci numbers.

This pattern was first explained to Western mathematicians by Leonardo Fibonacci in his book written in the middle ages. That’s why we call them Fibonacci numbers. If you divide consecutive Fibonacci numbers, you will always get the Golden ratio. Start with the big numbers. If you divide 89 by 55, you get 1.61. If you divide 55 by 34, you get 1.61. If you divide 34 by 21, you get 1.61. And so on. This is a proportion that is found in nature and in architecture. Many people believe that this proportion creates beauty and balance.

A Fibonacci spiral is something that occurs in nature. The amount of petals on a flower is a representation of a Fibonacci spiral. For example, the next time you look at a flower, look at the petals and their direction. Are they in a spiral? If so, they are in a Fibonacci Spiral.


Fibonacci spiral


  • Graph paper (internet search “free graph paper”)
  • Ruler
  • Compass
  • Colored pencils, optional

First, draw around two squares side by side.

Draw around a 2 × 2 square above the two first squares. Rotate the paper 90 degrees to the right.

Make a 3 × 3 square above the two previous squares. Rotate the paper 90 degrees to the right.

Make a 5 × 5 above the last two squares, rotate the paper 90 degrees to the right and so on.

Keep going until you have made a square that is 21 × 21.

Each square will have an edge that is the sum of the two squares before it, just like in the Fibonacci sequence.

Use a compass to draw quarter circle arcs inside each square, using the length of the side of the square as the radius of the arc. Locate the arcs so that they form a continuous spiral.

Color your spiral if you wish.


Look for Fibonacci spirals in nature. Try pinecones, sunflowers and certain seashells. Do you see other spirals?


This program has been designed for you to share with your child. Read the material together, ask questions and encourage your child to ask questions. Then nurture their curious mind by doing the activities with them. Books included are available via CPL’s digital library (with a library card).