In the twelfth century, it is said, Leonardo of Pisa, in Italy, also known as Fibonacci, had to solve the following problem concerning rabbit breeding:

A new born pair of rabbits takes one month to mature and then produces offspring in pairs after two months, and each month after that.

If we start with one new-born pair of rabbits, how many new-born rabbits are there at the end of the year?

Suggestions

Fibonacci discovered that the number of pairs of rabbits alive (n) at the end of each month (x) followed a pattern

Complete the table and continue if for values of x up to 12.

This sequence became known as the Fibonacci sequence 1, 1, 2, 3,...

Further Investigations

• Calculate the ratio t _n+1/ t_n

i.e. Divide each term by the one before it.

• Investigate the statement: "All Fibonacci numbers can be written as the sum of two or more non-consecutive Fibonacci numbers."
• Find out what you can about the Golden Ratio.
• Find out what you can about the Fibonacci sequence, plants and music.