Fibonacci writes in his
famous book Liber abaci (1202):
When my father, who had been appointed by his country as
public notary in the customs at Bugia acting for the Pisan merchants going
there, was in charge, he summoned me to him while I was still a child, and
having an eye to usefulness and future convenience, desired me to stay there
and receive instruction in the school of accounting. There, when I had been
introduced to the art of the Indians' nine symbols through remarkable
teaching, knowledge of the art very soon pleased me above all else and I came
to understand it, for whatever was studied by the art in Egypt, Syria, Greece,
Sicily and Provence, in all its various forms Around 1200, Fibonacci returned to Pisa. Leonardo Fibonacci was the gratest European mathematician of the Middle Ages. He was the first to introduce the Hindu - Arabic number system into Europe. Leonardo wrote a book on how to do arithmetic in the decimal system, called "Liber abaci", completed in 1202. It describes the rules we are all now learn at elementary school for adding numbers, subtracting, multiplying and dividing.
In his book Leonardo wrote the numerals in descending order and his fractions came
before the numeral like 1/2 4 instead of 4 1/2.
One result of his book attested to his mastery not only of the Hindy-Arabic techniques of practical calculation but also of the theory of quadratic equations. In his work, Fibonacci put forth not so much an original exposition as a compilation of the techniques of Arabic arithmetic and algebra. Leonardo`s mathematical environment encompassed more than this Arabic theory of algebra however. Within his sphere of commercial activities, there also a need for comprehensive catalogues of techniques for solving day-to-day problems.
A problem in the third section of Liber abaci led to the
introduction of the Fibonacci numbers :
A certain man put a pair of rabbits in a place surrounded
on all sides by a wall. How many pairs of rabbits can be produced from that
pair in a year if it is supposed that every month each pair begets a new pair
which from the second month on becomes productive?
By charting the populations of rabbits Fibonacci discovered a number series from which one can derive the Golden Section. Here`s the beginning of the sequence :
| 1, |
1, |
2, |
3, |
5, |
8, |
13, |
21, |
34, |
55, |
..... |
Each number is the sum of the two preceeding numbers as follows :
1 |
= |
1 |
+ |
0 |
2 |
= |
1 |
+ |
1 |
3 |
= |
2 |
+ |
1 |
5 |
= |
3 |
+ |
2 |
8 |
= |
5 |
+ |
3 |
13 |
= |
8 |
+ |
5 |
21 |
= |
13 |
+ |
8 |
34 |
= |
21 |
+ |
13 |
55 |
= |
34 |
+ |
21 |
| ..... |
...... |
..... |
..... |
..... |
French
mathematician Edouard Lucas (1842 - 1891) gave the name Fibonacci numbers to this series and found many other important applications of them.It also caused some of the people many years after Fibonacci made the discovery to
create a society in his name. The Fibonacci Society was founded in 1962, and a
journal, The Fibonacci Quarterly, first appeared in 1963, and was
dedicated to unraveling its secrets. There were a lot of secrets to be found.
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