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# Principals

## on Sep 08, 2011

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## PrincipalsPresentation Transcript

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• BSc Design Management for Fashion Retail Nick Clarke
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• The Fibonacci Sequence & The Golden Ratio
• The Fibonacci Sequence & The Golden Ratio Leonardo Fibonacci (c. 1170 – c. 1250), also known as Leonardo of Pisa
• 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.
• 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
• 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 … The Fibonacci Sequence & The Golden Ratio
• 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
The Fibonacci Sequence & The Golden Ratio
• 1.618034 The Fibonacci Sequence & The Golden Ratio
• 1 1 Side Box
• 1 2 1 1 Side Box
• The Fibonacci Sequence & The Golden Ratio 2 3 1 2 1 1 Side Box
• 3 4 2 3 1 2 1 1 Side Box
• The Fibonacci Sequence & The Golden Ratio 5 5 3 4 2 3 1 2 1 1 Side Box
• The Fibonacci Sequence & The Golden Ratio 8 6 5 5 3 4 2 3 1 2 1 1 Side Box
• The Fibonacci Sequence & The Golden Ratio 13 7 8 6 5 5 3 4 2 3 1 2 1 1 Side Box
• The Fibonacci Sequence & The Golden Ratio 21 8 13 7 8 6 5 5 3 4 2 3 1 2 1 1 Side Box
• The Fibonacci Sequence & The Golden Ratio 21 8 13 7 8 6 5 5 3 4 2 3 1 2 1 1 Side Box
• The Fibonacci Sequence & The Golden Ratio
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• The Birth of Venus by Sandro Botticelli (1483)
• The Birth of Venus by Sandro Botticelli (1483)
• 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?
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• Draw a jug
• For an experiment a number of people were asked to draw a jug on a piece of paper.
• All the pieces of paper were of the same size and shape
• 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.
• Note: None of these people were professional artists.
• 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.
• It was taller when the paper was used upright and squatter when the paper was used horizontally.
• Each draughtsman unconsciously tried to bring about a harmonious relationship between the ratio of the paper & that of the jug.
• It is natural for human beings to try and find harmonious relationships between ratios in this way.
• part 2
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