Principals

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Principals

  1. 2. BSc Design Management for Fashion Retail Nick Clarke
  2. 48. The Fibonacci Sequence & The Golden Ratio
  3. 49. The Fibonacci Sequence & The Golden Ratio Leonardo Fibonacci (c. 1170 – c. 1250), also known as Leonardo of Pisa
  4. 50. The Fibonacci Sequence & The Golden Ratio His book ‘Liber Abaci’ posed, and solved, a problem involving the growth of a hypothetical population of rabbits based on idealized assumptions. The solution, generation by generation, was a sequence of numbers later known as Fibonacci numbers. The number sequence was known to Indian mathematicians as early as the 6th century.
  5. 51. 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, … The Fibonacci Sequence & The Golden Ratio
  6. 52. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 … The Fibonacci Sequence & The Golden Ratio
  7. 53. <ul><li>1/1 = 1.000 </li></ul><ul><li>2/1 = 2.000 </li></ul><ul><li>3/2 = 1.500 </li></ul><ul><li>5/3 = 1.667 </li></ul><ul><li>8/5 = 1.600 </li></ul><ul><li>13/8 = 1.625 </li></ul><ul><li>21/13 = 1.615 </li></ul><ul><li>34/21 = 1.619 </li></ul><ul><li>55/34 = 1.618 </li></ul>The Fibonacci Sequence & The Golden Ratio
  8. 54. 1.618034 The Fibonacci Sequence & The Golden Ratio
  9. 55. 1 1 Side Box
  10. 56. 1 2 1 1 Side Box
  11. 57. The Fibonacci Sequence & The Golden Ratio 2 3 1 2 1 1 Side Box
  12. 58. 3 4 2 3 1 2 1 1 Side Box
  13. 59. The Fibonacci Sequence & The Golden Ratio 5 5 3 4 2 3 1 2 1 1 Side Box
  14. 60. The Fibonacci Sequence & The Golden Ratio 8 6 5 5 3 4 2 3 1 2 1 1 Side Box
  15. 61. The Fibonacci Sequence & The Golden Ratio 13 7 8 6 5 5 3 4 2 3 1 2 1 1 Side Box
  16. 62. The Fibonacci Sequence & The Golden Ratio 21 8 13 7 8 6 5 5 3 4 2 3 1 2 1 1 Side Box
  17. 63. The Fibonacci Sequence & The Golden Ratio 21 8 13 7 8 6 5 5 3 4 2 3 1 2 1 1 Side Box
  18. 64. The Fibonacci Sequence & The Golden Ratio
  19. 70. The Birth of Venus by Sandro Botticelli (1483)
  20. 71. The Birth of Venus by Sandro Botticelli (1483)
  21. 72. According to one art expert, Seurat &quot;attacked every canvas by the golden section&quot;. His Bathers ...has obvious golden subdivisions. Three golden figures have been added here. Can you find more?
  22. 77. Draw a jug
  23. 78. <ul><li>For an experiment a number of people were asked to draw a jug on a piece of paper. </li></ul><ul><li>All the pieces of paper were of the same size and shape </li></ul><ul><li>After the drawings had been collected the same people were asked to draw the same jug again, with the sheet of paper turned by 90 degrees. </li></ul><ul><li>Note: None of these people were professional artists. </li></ul><ul><li>When the two sets of drawings were compared it was found that the average drawing of the jug tended to follow the shape of the paper. </li></ul><ul><li>It was taller when the paper was used upright and squatter when the paper was used horizontally. </li></ul><ul><li>Each draughtsman unconsciously tried to bring about a harmonious relationship between the ratio of the paper & that of the jug. </li></ul>
  24. 79. It is natural for human beings to try and find harmonious relationships between ratios in this way.
  25. 80. part 2

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