Saturday, August 3, 2019

Fibonacci: Revolution by 10 Numerals

Statue of Fibonacci (1863)
What Leonardo Pisano, who is better known as Fibonacci, did in the thirteenth century with the publication of Liber Abbaci (Book of Calculation) was every bit as revolutionary for the field of mathematics as the revolution that Copernicus brought in the field of astronomy. Pisano’s book introduced the system of 10 numerals to the masses— it took computing from a small group of mathematicians, and made it available to and usable by almost everyone.

When Pisano’s father moved from Pisa to the North African port of Bugia (now in Algeria), in around 1185, to serve as a trade representative and customs official, he took his son with him. It was in Bugia that Pisano mastered the Hindu system of 10 numerals and realized that it was far superior to the system of Roman numerals. Much of what we know about Pisano comes from a small biographical paragraph that he wrote for the 1228 edition of the Liber Abbaci (the book’s first edition was published in 1202).

In his 1973 essay, “The Autobiography of Leonardo Pisano,” Richard E. Grimm provides a literal translation of the autobiographical paragraph:
After my father's appointment by his homeland as state official in the customs house of Bugia for the Pisan merchants who thronged to it, he took charge; and, in view of its future usefulness and convenience, had me in my boyhood come to him and there wanted me to devote myself to and be instructed in the study of calculation for some days. There, following my introduction, as a consequence of marvelous instruction in the art, to the nine digits of the Hindus, the knowledge of the art very much appealed to me before all others, and for it I realized that all its aspects were studied in Egypt, Syria, Greece, Sicily, and Provence, with their varying methods; and at these places thereafter, while on business, I pursued my study in depth and learned the give-and-take of disputation. But all this even, and the algorism, as well as the art of Pythagoras I considered as almost a mistake in respect to the method of the Hindus. Therefore, embracing more stringently that method of the Hindus, and taking stricter pains in its study, while adding certain things from my own understanding and inserting also certain things from the niceties of Euclid’s geometric art, I have striven to compose this book in its entirety as understandably as I could, dividing it into fifteen chapters. Almost everything which I have introduced I have displayed with exact proof, in order that those further seeking this knowledge, with its pre-eminent method, might be instructed, and further, in order that the Latin people might not be discovered to be without it, as they have been up to now. If I have perchance omitted anything more or less proper or necessary, I beg indulgence, since there is no one who is blameless and utterly provident in all things.
Before the thirteenth century, some mathematicians in Europe were aware of the system of 10 numerals; they were using it for their personal calculations. But the population in Europe was dependent on the Roman numerals which were difficult to use. Pisano’s Liber Abbaci made the masses aware that, with the 10 numerals, they could conduct their calculations with ease. The traders of Europe became the first supporters of the system of 10 numerals—they adopted these numerals to keep record of their commercial activity.

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