Phi and Nature
a) the pine cone
Pine cones scales form gold spirales : 13 clokwise (in red) and 8 counter-clockwise (in green)
These two numbers (8 and 13) are consecutive numbers of the Fibonacci series
The numbers of points on each spirale are part of the Fibonacci series
If you join all these points in just one spirale, the angle you get between two points is the gold angle :360/phi+1=137.5°
b) the fibonacci series
Suppose a newly-born pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose that our rabbits never die and that the female always produces one new pair (one male, one female) every month from the second month on. The puzzle that Fibonacci posed was :
How many pairs will there be in one year?
| Each season a new couple of rabbits is born | Babies |
| The couple grows up during a season | Youngs |
| The two rabbits give birth to a new couple | Adults |
| Seasons | Babies | Youngs | Adults | Total |
| 1 | 0 | 1 | 0 | 1 |
| 2 | 0 | 0 | 1 | 1 |
| 3 | 1 | 0 | 1 | 2 |
| 4 | 1 | 1 | 1 | 3 |
| 5 | 2 | 1 | 2 | 5 |
| 6 | 3 | 2 | 3 | 8 |
| 7 | 5 | 3 | 5 | 13 |
| 8 | 8 | 5 | 8 | 21 |
| 9 | 13 | 8 | 13 | 34 |
| 10 | 21 | 13 | 21 | 55 |
represents
females and 
males
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