Petals Most flowers have 5 or 8 petals

Seeds Many plants have 3, 5 or 8 seeds

Pineapples Pineapples have 13 clockwise spirals and 8 anticlockwise spirals

Pine cone spirals

Shell spirals

Rabbits!

What do they all have in common?

Fibonacci Series Leonardo Fibonacci ( )

Fibonacci Series 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89………..

The golden ratio As the fibonacci series gets larger, the ratio of succesive terms gets closer to a number called phi,, the golden ratio 13/8 = 1.625, 21/13 = 1.615, 34/21 = = (√5 + 1)/2 = …..

The golden ratio It can also be calculated from or

The golden section This is a line sectioned into two according to the golden ratio (a + b)/a = a/b =

Apples again! b a a = b

The ancient Greeks loved !

It has been suggested that many of the proportions of the Mona Lisa use the golden ratio

a = b

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