1. The Golden Curve Maths, art and nature

2. It’s surprising who uses maths Many of the writers for The Simpsons have maths degrees.

3. Maths helps us… Design

4. DesignPlan

5. DesignPlanUnderstand

6. Where’s the maths?

7. Where’s the maths? (1)

8. Where’s the maths? (2)

9. Where’s the maths? (3)

10. Where’s the maths? (4)

11. The “Golden Curve”

12. The Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, …. What comes next? 21 + 34 = 5534 + 55 = 89 55 + 89 = 14489 + 144 = 233

13. The ratios of the sequence 1 ÷ 1 = 11 ÷ 1 = 1 2 ÷ 1 = 22 ÷ 1 = 2 3 ÷ 2 = 1.53 ÷ 2 = 1.5 5 ÷ 3 = 1.6666666666…5 ÷ 3 = 1.6666666666… 8 ÷ 5 = 1.68 ÷ 5 = 1.6 13 ÷ 8 = 1.62513 ÷ 8 = 1.625 21 ÷ 13 = 1.615384615384615384615…21 ÷ 13 = 1.615384615384615384615…

14. The ratios of the sequence… 8 ÷ 5 = 1.68 ÷ 5 = 1.6 13 ÷ 8 = 1.62513 ÷ 8 = 1.625 21 ÷ 13 = 1.615384615384615384615…21 ÷ 13 = 1.615384615384615384615… 34 ÷ 21 = 1.619047619047619047619…34 ÷ 21 = 1.619047619047619047619… 55 ÷ 34 = 1.6176470588235294117647…55 ÷ 34 = 1.6176470588235294117647… 89 ÷ 55 = 1.6181818181818181818…89 ÷ 55 = 1.6181818181818181818…

15. The ratios tend to a number!

16. The golden ratio The number that these ratios tend towards is called the golden ratio:The number that these ratios tend towards is called the golden ratio:1.618033988749…

17. Why golden? It has lots of special propertiesIt has lots of special properties People have studied it for over 2000 yearsPeople have studied it for over 2000 years It occurs in art, architecture and natureIt occurs in art, architecture and nature

18. Golden rectangles A golden rectangle has one side which is 1.618033… times the length of the otherA golden rectangle has one side which is 1.618033… times the length of the other The United Nations building in New York has this shapeThe United Nations building in New York has this shape

19. People like golden rectangles Too long? Too short? Just right!Too long? Too short? Just right!

20. Nature and the golden ratio Sunflowers use the Fibonacci sequenceSunflowers use the Fibonacci sequence

21. Shells and the golden curve The shell of a nautilus (sea creature)The shell of a nautilus (sea creature)