Leonardo Fibonacci, born around 1175
in the present-day Pisa, Italy, is known by various names. Being of Pisa, he is called
Leonardo of Pisa, which in Italian is Leonardo Pisano. His full name was Leonardo Pisano
Bigollo. Historians are not sure what "bigollo" means. It could mean "traveller" or
"good-for-nothing" (see "Did his countrymen..."). Fibonacci's father's name was
Guglielmo Bonaccio. As such, in 1828, centuries after Fibonacci's time, Guillaume Libri
invented the name "Fibonacci" from "filius Bonacci," latin for "the son of Bonacci."
Fibonacci, as he is called by most today, is therefore, just a short version of "filius
Statue of Leonardo Fibonacci (Fortezza Camp Santo - Pisa, Italy)
His father, Guglielmo Bonaccio, was a
customs officer for Pisa in the North African port town of Bugia (present-day Bejaia, Algeria).
Fibonacci, who joined his father there as a teenager, recieved an education from the Moors, an
Arabic people. Through his experiences in North Africa, which no doubt included meeting merchants
and learning their systems of applied arithmetic, he was introduced to the "Hindu-Arabic" system
of numerals, the same one we all use today.
Did his countrymen wish to
express by this epithet [bigollo] their disdain for a man who concerned himself
with questions of no practical value, or does the word in the Tuscan dialect mean
a much-travelled man, which he was?
- Dictionary of Scientific Biography
These "Hindu-Arabic" numerals consisted of the
symbols one through nine, zero, and a decimal. To understand the advantages of such a system
one has only to look at what most of Europe was using for numbers at that time; Roman numerals.
Roman numerals were extremely awkward to begin with. For one, each of the symbols had numerical
equivalents (see left: Roman Numerals) that had to be memorized. To write a number, one
had to use a combination of the numerals. For example, the number 1999 would be written: MDCCCCLXXXXVIIII
(just add them up to find that it is equal to 1999).
Adding the numerals also worked to make IV 6 as well
as VI. Later it became even more complex when the system was modified to give significance to what order
the numerals are in. Now, if a smaller numeral was before a larger one, it would be subtracted from the
larger one. If a smaller one was after a larger one, it would be added like before. Now, IV is 4 and VI is 6.
The only advantage to this ordered system is that larger numbers can be written with less numerals. 1999 is now
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.
- Leonardo Fibonacci in Liber abbaci
It is awkward enough finding what
numbers written in Roman numerals are, let alone performing basic arithmetic
with them like adding and subtracting. Let's say you had to add 1999 and 1998:
MCMXCIX + MCMXCVIII
The one on the left is easy.
Any 5th-grader could do it. But the one on the right requires a lot of effort and it
makes clear the shortcomings of the system of Roman numerals.
It's no wonder that such a system caught on
so quickly with merchants and other people in professions where day-to-day use of
mathematics was essential. With the new system, people could compute sums and differences
more quickly, giving them a competitive edge. Fibonacci realized the advantages
of this new system, as did most who were exposed to it, so when he returned to Pisa,
he wrote a book about it that he finished in 1202. Titled Liber abbaci,
meaning "Book of Calculating," the work dealt with the methods of arithmetic in the decimal
system (now taught to all elementary school children) and it eventually persuaded European
mathematicians to drop the old way in favor of the new.
The Leaning Tower of Pisa (Pisa, Italy)
Random Fibonacci number from the 1st through the 200th: