Math 409/409G History of Mathematics The Fibonacci Sequence Part 1

The Fibonacci Problem “A man put one pair of rabbits in a certain place entirely surrounded by a wall. How many rabbits can be produced from that pair in a year if the nature of these rabbits is such that every month each pair bears a new pair which from the second month on becomes productive.”

Assumptions Rabbits don’t have baby rabbits until they are two months old. From the age of two months on, a pair of rabbits produces one pair of rabbits each month. A “pair” means one male and one female rabbit. The first pair of rabbits is at least two months old. None of the rabbits ever die.

The problem posed by Fibonacci asked how many rabbits can be produced in one year.

From the chart we see that there are a total of F n+2 pairs of rabbits in the n th month. So there are F 14 pairs of rabbits in the 12 th month.

F 14  377  total pairs of rabbits in one year. But the problem asked how many rabbits can be produced in one year. Since the original pair of rabbits wasn’t produced in the enclosure, the answer to the problem is 376 pairs of rabbits, giving a total of 752 rabbits produced in a year.

In the next lesson we will look at some of the properties of the Fibonacci sequence, but until then I’d like you to think about the following puzzle which is based on the Fibonacci numbers F 4  3, F 5  5, F 6  8, and F 7  13.

This ends the lesson on Part 1 of The Fibonacci Sequence