Leonardo Fibonacci (1175 - 1250)

The greatest European mathematician of the middle ages, his full name was Leonardo of Pisa, or Leonardo Pisano in Italian since he was born in Pisa (Italy), the city with the famous Leaning Tower, about 1175 AD.

Pisa was an important commercial town in its day and had links with many Mediterranean ports. Leonardo's father (Guglielmo Bonaccio) was a kind of customs officer in the North African town of Bugia now called Bougie where wax candles were exported to France.

So Leonardo grew up with a North African education under the Moors and later travelled extensively around the Mediterranean coast. He would have met with many merchants and learned of their systems of doing arithmetic. He soon realised the many advantages of the "Hindu-Arabic" system over all the others.

He called himself Fibonacci [pronounced fib-on-arch-ee or fee-bur-narch-ee] short for filius Bonacci which means son of Bonacci. Since Fibonacci in Latin is "filius Bonacci" and means "the son of Bonacci", two early writers on Fibonacci (Boncompagni and Milanesi) regard Bonacci as the family name so that Fib-Bonacci is like the English names of Robin-son or John-son. Fibonacci himself wrote both "Bonacci" and "Bonaccii" as well as "Bonacij"! Others think Bonacci may be a kind of nick-name meaning "lucky son" (literally, "son of good fortune").
He is perhaps more correctly called Leonardo of Pisa or, using a latinisation of his name, Leonardo Pisano. Occasionally he also wrote Leonardo Bigollo since, in Tuscany, bigollo means a traveller.

He was one of the first people to introduce the Hindu-Arabic number system into Europe - the positional system we use today - based on ten digits with its decimal point and a symbol for zero: 1 2 3 4 5 6 7 8 9 and 0

His book on how to do arithmetic in the decimal system, called Liber abbaci (meaning Book of the Abacus or Book of Calculating) completed in 1202 persuaded many European mathematicians of his day to use this "new" system.

The book describes (in Latin) the rules we all now learn at elementary school for adding numbers, subtracting, multiplying and dividing, together with many problems to illustrate the methods.

The method in use in Europe until then used the Roman numerals:

I = 1,   V = 5,  X = 10,  L = 50,  C = 100,  D = 500  and  M = 1000

You can still see them used on foundation stones of old buildings and on some clocks. For instance, 13 would be written as XIII or perhaps IIIX. 2003 would be MMIII or IIIMM. 99 would be LXXXXVIIII and 1998 is MDCCCCLXXXXVIII.

Later, an abbreviation became popular where the order of letters did matter and, if a single smaller value came before the next larger one, it was subtracted and if it came after, it was added as usual.
For example, XI means 10+1=1 but IX means 1 less than 10 or 9. 8 is still written as VIII (not IIX). [Note that in the UK we use a similar system for time when 6:50 is often said as "ten to 7" rather than "6 fifty", similarly for "a quarter to 4" meaning 3:45. In the USA, 6:50 is sometimes referred to as "10 of 7".]
Using this method, 1998 would be written much more compactly as MCMXCVIII but this takes a little more time to interpret: 1000 + (100 less than 1000) + (10 less than 100) + 5 + 1 + 1 + 1.

The Decimal Positional System

The system that Fibonacci introduced into Europe came from India and Arabia and used the Arabic symbols 1, 2, 3, 4, 5, 6, 7, 8, 9 with, most importantly, a symbol for zero 0.
With Roman numbers, 2003 could be written as MMIII or, just as clearly, it could be written as IIIMM - the order does not matter since the values of the letters are added to make the number in the original (unabbreviated) system. With the abbreviated system of IX meaning 9, then the order did matter but it seems this sytem was not often used in Roman times.
In the "new system", the order does matter always since 23 is quite a different number to 32. Also, since the position of each digit is important, then we may need a zero to get the digits into their correct places (columns) eg 2003 which has no tens and no hundreds. (The Roman system would have just omitted the values not used so had no need of "zero".)

This decimal positional system, as we call it, uses the ten symbols of Arabic origin and the "methods" used by Indian Hindu mathematicians many years before they were imported into Europe. It has been commented that in India, the concept of nothing is important in its early religion and philosophy and so it was much more natural to have a symbol for it than for the Latin (Roman) and Greek systems.

The Fibonacci Series

In Fibonacci's book he introduces a problem for his readers to use to practice their arithmetic:-

a pair of rabbits are put in a field and, if rabbits take a month to become mature and then produce a new pair every month after that, how many pairs will there be in twelve months time?

He assumes the rabbits do not escape and none die. The answer involves the series of numbers:

1, 1, 2, 3, 5, 8, 13, 21, ...

But it was the French mathematician Edouard Lucas (1842-1891) who gave the name Fibonacci numbers to this series and found many other important applications of them.

He died in the 1240's and there is now a statue commemorating him located at the Leaning Tower end of the cemetery next to the Cathedral in Pisa.