Fibonacci

The universe is written in the language of numbers.

To understand numbers is to understand the world.

The Indian figures are the most universal of all figures.

These are the nine figures of the Indians: 9 8 7 6 5 4 3 2 1. With these nine figures, and with the sign 0 which the Arabs call zephir, any number whatsoever is written.

I joined my father after his assignment by his homeland Pisa, at the Bugia customshouse established there for the Pisan merchants; there I was introduced to the art of the Indians' nine symbols through remarkable teaching.

Knowledge of the art of the Indians' nine symbols is most necessary for anyone who wishes to study the art of calculation.

The method of the Indians surpasses any known method to compute. It's a marvelous method. They do not use multiplication or division, but they use the nine figures and the symbol zero.

If by chance I have omitted anything more or less proper or necessary, I beg indulgence, since there is no one who is without fault and circumspect in all matters.

In fact, I have published this book in a clearer style and have shown the method with proof, so that people in the future shall learn from it.

There is also a method of finding the root of any number, which is very necessary for many problems.

Geometry is the science of measurement.

I have striven to compose this work as clearly as I could, dividing it into fifteen chapters.

Almost everything that has been introduced to geometry concerning the measurement of figures is contained in this book.

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?

The solution to this problem is the sequence we now call the Fibonacci numbers.

The numbers of the sequence are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, and so on.

I have found this sequence to appear in many natural forms.

The root of a number is a number which, multiplied by itself, produces the proposed number.

There is no number that cannot be expressed by these nine figures and the sign zero.

The merchants of Pisa and elsewhere who have learned this art from me have found it most useful in their business.