1. What Have These Got in Common?

3. The Fibonacci Sequence & The Golden Ratio
Pine Cones and Snails

4. The Fibonacci Sequence
1, 1,
1, 1, 2,
1, 1, 2, 3,
1, 1, 2, 3, 5,
1, 1, 2, 3, 5, 8,
1, 1, 2, 3, 5, 8, 13,
1, 1, 2, 3, 5, 8, 13, 21,
1, 1, 2, 3, 5, 8, 13, 21, 34, …

5. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 …
1/1 = 1.000
2/1 = 2.000
3/2 = 1.500
5/3 = 1.667
8/5 = 1.600
13/8 = 1.625
21/13 = 1.615
34/21 = 1.619
55/34 = 1.618
… = …

6. A Snail Shell

7. Box
Side 1
1 little square

8. Box
Side 1 2
1 more little square

9. Box
Side 1 2 3
2 x 2 square

10. Box
Side 1 2 3 4
3 x 3 square

11. Box
Side 1 2 3 4 5
5 x 5 square

12. Box
Side 1 2 3 4 5 6 8

13. Box
Side 1 2 3 4 5 6 8 7 13

14. Box
Side 1 2 3 4 5 6 8 7 13 21

15. Box
Side 1 2 3 4 5 6 8 7 13 21

16. A Pine Cone
Where is the Fibonacci Number Here?

17. 15 Spirals
Anti-clockwise
8 Spirals
Clockwise

18. The Fibonacci Sequence in Nature