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The Mathematics of Nature
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  1. The Mathematics of Nature

  2. 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

  3. 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

  4. The Romanesco (a cousin of broccoli)

  5. 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

  6. 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.

  7. 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. 1.1 1.5 1.4 1.66 1.60 1.48 1.8 1.3 1.8 1.7 1.9 1.3 1.1 1.5 1.5 1.9 2.2 1.7

  8. 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

  9. What does it all mean? • What does this say, if anything, about the origin and nature of maths?