2. Pure maths:  Axioms  Theorems Applied maths:  What you know  What is used in other disciplines

3.  Reality makes sense  Maths makes sense  Reality is mathematical

4.  Maths in nature  Maths & aesthetics

5. Fibonacci’s sequence: 1, 1, 2, 3, 5, 8, 13, 21... Constructed by the addition of pairs of numbers within the sequence.

7. Calla Lily

8. Euphorbia

9. Trillium

10. Convolvulus

11. Black-eyed Susan

12. Water Lily

13. Succulent Spirals: How many spirals make up the pattern?

15. Anti-clockwise: 34. Clockwise: 55

16. These organic patterns have been explained in terms of ‘packing’, where the greatest number of similar shapes can be fitted into the least space. Nature is an incessant whittler of inefficiency, and the most frugal user of its resources will be the one most likely to survive lean times, reproduce, and succeed.

17. At a molecular level Fibonacci spirals arise spontaneously in mutually repulsive silicon dioxide particles on a silver core. Differing amounts of stress placed on the microstructures lead to different Fibonacci spirals.

18. This forms a very special shape – the Golden Section. The Golden Section or Golden ratio is said to be a natural shape that appears in nature, and art & architecture from around the world.

21. Snail shells form a spiral of growth in the same ratio As do some climbing plants

23. Nature: Measuring shells Counting leaves Art:Perspective calculation (Alberti’s Algebra) The Brunelleschi method