The Fibonacci series

The Fibonacci series.

The spiral, Fibonacci series and golden sequence is well known in the mathematical scene. At the end of s. XII, the Italian mathematician Leonardo of Pisa (1170-1240), who was better known as Fibonacci, described this formula as a solution to a problem of raising rabbits. The formula had been described earlier by Hindu mathematicians Gopala and Hemachandra, who investigated the rhythmic patterns that formed syllables with one or two pulses. The number of such rhythms (keeping together a number n of pulses) was F (n +1), which is like sed n +1 represents the term of the Fibonacci sequence. Kepler also wrote of such succession.

In 1202, Fibonacci published his book Liber Abaci, which included several problems and algebraic methods. The famous spiral, called "Fibonacci sequence" appears constantly in nature. The can see for example:

- Counting the scales of a pineapple. After watching her, you'd be surprised that appear spirally around the corner in equal numbers to the terms specified in the Fibonacci sequence.

- Also in pineapples sunflower. In them, a network of spirals are formed, some that go in the direction of clockwise and others to the contrary, but in any case always, quantities of ones and others are consecutive terms of the Fibonacci sequence.

This sequence so beloved by fans of mathematics, is formed by adding the previous two series elements, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 Apparently ... it could be either a mathematical series, with no relevance, but no. Besides being very important in the application of various theories (computer science, mathematics, biological settings and game theory), is very curious and does not fail to call attention, as this series appears in nature in an optical way.

The sequence of this series starts with 0 and 1 and thereafter every element is the sum of the previous two. 

Each element forming this sequence is called the Fibonacci number.

And it all started with a problem of raising rabbits. It was the following:

A certain man had one pair of rabbits together in a closed room and one wishes to know how many are created from this pair in a year when nature bear another pair in a single month, and in the second month also born calve.

So  we see that:

 

As you can see in the picture, the number of partners over the months coincide with the terms set out in succession. Simplified: the sequence is used to determine the number of couples who have rabbits in twelve months and also to know if these are played continuously, and if each pair of rabbits produces a new pair of rabbits (one male and one female). Each rabbit you can cross to the age of one month, and its gestation period one month.