How to Draw a Fibonacci Spiral

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55

Do these numbers mean anything to you? Do you see a pattern? They are called the Fibonacci sequence and they are quite famous. In the Fibonacci sequence, you find the next number by adding together the two numbers that came before:

0 + 1 = 1, 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8, 5 + 8 = 13 and so on.

Fibonacci lived in Italy in the 1100s. He was a very skilled mathematician. We can use his sequence to draw a beautiful spiral that we find in nature.

Equipment

• Grid paper
• A pencil
• A ruler

Instructions

1. Make squares with sides that correspond to the numbers in the Fibonacci sequence. Every new square should be shifted in relationship to the square that came before. You start by making the two 1’s at the beginning of the sequence as two squares on top of each other. Then it s time to make a square that represents 2 on the sequence. This goes to the left of your two 1’s. The square that represents 3 goes on top of your existing squares. Keep working your way outwards in a spiral fashion until you get to 13 (or higher if you have room).
2. Now you can draw the spiral. Trace the squares from corner to corner across the diagonal. Make sure the line as a bend to it, so that you get a beautiful spiral.

The spirals on snail shells, sunflowers and pineapples follow this exact pattern. What’s more, the number of left- and right-leaning spirals on an acorn are always two Fibonacci numbers that follow each other on the sequence.