The Mathematics of Nature

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

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

The Romanesco (a cousin of broccoli)

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

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.

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

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

What does it all mean?

What does this say, if anything, about the origin and nature of maths?