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The Golden Curve

The Golden Curve. Maths, art and nature. It’s surprising who uses maths. Many of the writers for The Simpsons have maths degrees. Maths helps us…. Design. Maths helps us…. Design Plan. Maths helps us…. Design Plan Understand. Where’s the maths?. Where’s the maths? (1).

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The Golden Curve

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  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. Maths helps us… Design Plan

  5. Maths helps us… Design Plan Understand

  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” Golden Curve

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

  13. The ratios of the sequence • 1 ÷ 1 = 1 • 2 ÷ 1 = 2 • 3 ÷ 2 = 1.5 • 5 ÷ 3 = 1.6666666666… • 8 ÷ 5 = 1.6 • 13 ÷ 8 = 1.625 • 21 ÷ 13 = 1.615384615384615384615…

  14. The ratios of the sequence… • 8 ÷ 5 = 1.6 • 13 ÷ 8 = 1.625 • 21 ÷ 13 = 1.615384615384615384615… • 34 ÷ 21 = 1.619047619047619047619… • 55 ÷ 34 = 1.6176470588235294117647… • 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: 1.618033988749…

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

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

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

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

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

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