Fibonacci

Joke: Numbers are odd, except for zero, which is even-tempered.

Key insight: Fractions unite the whole and the part.

If anyone should find a method of solving these problems with greater elegance and brevity than I have, let him not grudge to communicate it to me.

I have been led to this by the desire to show how the numbers of the Indians can be used in all calculations.

These are the nine Indian figures: 9 8 7 6 5 4 3 2 1. With these nine figures, and with the sign 0 which the Arabs call zephyr, any number can be written.

The more I studied, the more I understood the errors of the Egyptians, the Greeks, and the Arabs, and the more I admired the Indian method.

After my father's appointment by his country as a public notary in the customs house of Bugia, as a young boy still in my tunic, he had me brought to him, and there he wanted me to devote myself to and be instructed in the study of accounting.

I learned the art of the nine Indian figures through being taught by a master.

I have composed this book, which I have called Liber Abaci, for the benefit of those who wish to learn the art of calculation.

For the sake of brevity, I have omitted many things which are not necessary for those who have a good understanding of the art of calculation.

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 another pair, and that rabbits begin to beget in the second month after their birth?

The sum of the squares of the numbers from 1 to n is n(n+1)(2n+1)/6.

The sum of the cubes of the numbers from 1 to n is (n(n+1)/2)^2.

I have also added some problems which are not found in other books, and which are very useful for those who wish to learn the art of calculation.

I have also shown how to extract square roots and cube roots, and how to solve many other problems which are found in the books of the Arabs.

I have also shown how to solve problems of proportion, and how to find the value of a quantity when it is divided into parts.

I have also shown how to solve problems of partnership, and how to divide profits and losses among partners.

I have also shown how to solve problems of exchange, and how to convert money from one currency to another.

I have also shown how to solve problems of interest, and how to calculate the interest on a loan.

I have also shown how to solve problems of alloying, and how to mix different metals together.