The Mathematics of Nature
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Transcript of The Mathematics of Nature
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The Mathematics of Nature
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Fibonacci Took an interest in breeding
rabbits
If you assume that a pair of rabbits takes one month to become sexually mature, can produce a new pair of rabbits each month and none ever dies, then count the pairs of rabbits you get:
•1, 1, 2, 3, 5, 8, 13, 21, 34, 55……
•TASK: Continue the sequence until the first number greater than 1000
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Fibonacci’s Spiral Draw:
1 x 1 square to the left of the centre of the page 1 x 1 square above this 2 x 2 square to the right of this 3 x 3 square below this 5 x 5 square to the left …keep working round in a spiral adding squares in
line with the Fibonacci sequence Starting at the middle draw an arc through each
square to create the spiral
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The Romanesco (a cousin of broccoli)
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The Golden Ratio, φ (pronounced ‘phi’) φ = (1 + 5)/2 = 1.61803…….
The mathematical key to beauty
Appears everywhere.
Calculate the ratio of: Width of A4 paper: length of A4 paper First-second knuckle: first knuckle-finger tip Second-third knuckle: second knuckle-finger tip Elbow-wrist: elbow-finger tip
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Who it more beautiful: Pitt, Rooney or The Bieber? Use the sheet ‘Measuring Beauty’ to help For each face, draw on the solid and dotted
lines, and calculate the ratio of solid : dotted in each case.
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Who it more beautiful: Pitt, Rooney or The Bieber? Use the sheet ‘Measuring Beauty’ to help For each face, draw on the solid and dotted
lines, and calculate the ratio of solid : dotted in each case.
1.4
1.8
1.3
1.9
1.9
1.66
1.1
1.3
1.1
2.2
1.7
1.48
1.5
1.8
1.5
1.7
1.5
1.60
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Where does φ come from? Remember the Fibonacci sequence?
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…..
Divide each number by its predecessor
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What does it all mean?
What does this say, if anything, about the origin and nature of maths?