MATHEMATICS
2010 - 2011
Golden Ratio and Fibonacci Numbers
Part 1 : The Fibonacci se q ue nce : Storie s and Nature
TASK 4 : Fibonacci numbers in Nature ?
On many plants, the number of petals is a Fibonacci number:
buttercups have 5 petals; lilies and iris have 3 petals; some delphiniums have 8; corn marigolds have 13 petals;
some asters have 21 whereas daisies can be found with 34, 55 or even 89 petals.
 Look at the slideshow
Fibonacci Rectangles and Shell Spirals
We can make a picture showing the Fibonacci numbers 1,1,2,3,5,8,13,21,.. if we start with two
small squares of size 1 next to each other. On top of both of these draw a square of size 2
(=1+1).
We can continue adding squares around the picture, each new square having a side which is
as long as the sum of the latest two square's sides. This set of rectangles are called the
Fibonacci Rectangles. Aren’t they perfect ? Almost one could say… We will see why later…
With this figure, you can create a good approximation of a logarithmic spiral (no matter what it exactly is), that
looks like a shell spiral you have seen on the slideshow.
 Can you do it ? Use a blank sheet.