The problem from which Fibonacci (year 1202) started as a family of rabbits could develop under ideal circumstances.
Suppose we have a pair of rabbits (male and female). Rabbits are able to reproduce at the age of one month so at the end of her second month a female can produce another pair of rabbits. Suppose our rabbits never die and the female always produces a new pair (one male and one female) every month from the second month onwards. The problem posed by Fibonacci was: how many pairs will there be after a year?
The number of pairs of rabbits at the beginning of each month will be 1, 1, 2, 3, 5, 8, 13, 21, 34, ...
It is evident that each term of the series can be obtained by adding the two immediately preceding terms, so that the next term in the series indicated above will be given by 21 + 34 = 55.
Nell'albero riportato di sopra si mostra come si perviene a questo risultato.
It is possible to verify that proceeding in the development of the series we obtain a numerical succession that approximates more and more a geometric progression of reason Ø fi (golden section ratio corresponding to about 1.618
All this could seem a pure mathematical curiosity linked to the particularity of this problem and to purely random factors. However, the recurring presence of these numbers in multiple natural situations (animals and plants) is of considerable interest, such as to induce many artists to recognize in this numerical sequence a sort of natural order that is well in accord with the harmony induced by the golden ratio.
The whole part on the Fibonacci problem and related images were elaborated by: © Dr Ron Knott R.Knott@surrey.ac.uk. The Italian version was edited by Franco Di Cataldo for educational use only