Exploring Fibonacci and the Golden Ratio Have you

Exploring Fibonacci and the Golden Ratio

Have you ever wondered why flowers have a certain amount of petals or a pineapple has spirals? Well, it is all to do with and a special sequence of numbers!

How many petals are there on each of the flowers?

Photos courtesy of Jill Britton, mathematics instructor, Camosun College in Victoria, British Columbia, Canada.

1 petal white calla lily 8 petals bloodroot 2 Petals euphorbia 13 petals black-eyed Susan 3 Petals trillium 21 petals shasta daisy Do you recognise these numbers? 5 Petals columbine 34 petals field daisies

There is a special number sequence which was discovered over 8000 years ago by an Italian mathematician called Leonardo Fibonacci. It is called the • Can you spot the pattern? 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89…………… .

I wonder what happens if we look at other things in nature!

Pineapples Count the spirals on your pineapple. How many do you have? Try counting them in a different way…

Pine Cones Count the spirals on your pine cone. How many do you have?

Sunflowers Count the spirals on your picture. How many do you have?

Distribution of seed heads in a sunflower 2 1 5 3 8 13 21 34 Click to view

The 1, 1 Ratio √ 5 +1 F= 2 d w o H g e ow ? s i h et t , 2, 3, 5 t a h W , 8, 13, it s e do 21, 3 4, 5 5, 8 9… ? n a me Or F = 1. 618033989…

Nautilus Shell An ear Space Kate Moss Eggs Mona Lisa A rose Parthenon in Greece