The Fibonacci sequence

The Fibonacci sequence

Fibonacci, also known as Leonardo of Pisa, was an Italian mathematician and merchant who lived around the year 1200. He is one of the most famous European mathematicians of the Middle Ages. Fibonacci pondered the following problem:

At the beginning of the year, there is a newborn pair of rabbits in the paddock. From the age of two months, rabbits give birth to one female and one male every month, all of whom continue to reproduce in the same way. How many pairs of rabbits will there be in a year?

There is one pair of rabbits at the beginning of the first month, and also one pair of rabbits at the beginning of the second month. At the beginning of the third month, a pair of rabbits gives birth to a new pair of rabbits, so there are now two pairs of rabbits. The first pair of rabbits give birth again at the beginning of the fourth month, so there are now three pairs of rabbits. At the beginning of the fifth month, both the first and second pairs of rabbits give birth to a new pair, so there are five pairs of rabbits, etc. Continuing in this way, there are [[$144 $]] pairs of rabbits at the beginning of the 12th month.
The number of rabbit pairs forms a Fibonacci sequence, where the first two numbers are ones, and the other numbers are obtained by adding the previous two numbers together. So the first twelve numbers in the Fibonacci sequence are [[$ 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 $]] and [[$144 $]].

The Fibonacci number sequence can be found in many contexts. Even Fibonacci himself discovered in his time that the number of petals of flowers is usually one of the numbers in the sequence. For example, daisies can have [[$ 34 $]], [[$ 55 $]] or even [[$ 89 $]] petals. In addition, in the leaf vortices of many plants, the difference between the directions of two consecutive leaves is [[$\displaystyle\frac{3} {5} $]] from a full round.