2. Petals Most flowers have 5 or 8 petals

3. Seeds Many plants have 3, 5 or 8 seeds

4. Pineapples Pineapples have 13 clockwise spirals and 8 anticlockwise spirals

5. Pine cone spirals

6. Shell spirals

7. Rabbits!

8. What do they all have in common?

9. Fibonacci Series Leonardo Fibonacci (1170-1240)

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

11. 1 1 2 3 5 8 13

12. 1 1 2 3 5 8

13. 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 = 1.619 = (√5 + 1)/2 = 1.6180339887…..

14. The golden ratio It can also be calculated from or

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

16. Apples again! b a a = b

17. The ancient Greeks loved !

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

19. a = b

20. Let’s listen! http://www.bbc.co.uk/radio4/science/5number s3.shtml