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FUZZY GALORE |
Leonardo Pisano Bonacci, better known as Fibonacci (standardized in
the 19th century from Fillius Bonacci), played a major role
in the advancement of mathematics in the daily lives of Europeans,
particularly with the publication of his Liber Abaci 800 years
ago in 1202. He explained the practicality of using a 10-base notation
rather than Roman numerals, which effectively ended their use.
He also contributed his own mathematical gems, particularly in
Euclidian geometry and number theory.
His engaging use of examples such as the reproduction of rabbits
made everyone notice the use of his sequence
in many natural phenomena,
something which we are still discovering, and we're still using it in many designs.
The only biographical details we know about him are that he was born
in Pisa and that his father
was a customs official in North Africa. It's this later fact
that led young Leonardo to be educated in Arabic mathematics
and accounting methods,
and to be able to popularize these concepts among Northern Europeans.
The Roman numerals in use in medieval Europe
were a clumsy affair at best, barely allowing
one to add and substract. A torturous method had been devised
for multiplication and division, and the tool of choice was
an abacus for practical use, after which results were translated and
recorded in Roman numerals.
The ealiest known example of this device is dated
from about 3000 BC and originated in Babylonia, where no doubt
it contributed to its inventors' domination of their neighbors
by giving them better
architectural, astronomical (and therefore navigational) and financial
tools.
Meanwhile, Indian mathematicians had long before started their long tradition of fine mathematical thought. In the early parts of the first millenium, they had invented a whole new system of numerical notation, which allowed effortless expansion into what we now think of as basic arithmetic :-). The introduction of zero (zifr in Arabic) can be considered to be the foundation of the whole of modern algebra, and a notation where position denoted the power of 10 was of incalculable significance for practical applications. Indian mathematicians' achievements had done much to help the ancient Egyptians who studied with them, and in turn the Greeks who studied in Egypt and which are now generally credited with all this. Unfortunately, the collapse of the Roman empire and the rise of a repressive branch of Christianity had pretty much wiped out all mathematical thought from medieval Northern Europe.
But the Arabic empire that was first centered in Damascus had been very active in trading with India, and besides exotic spices and new cuts of fitted clothes had brought back a lively interest in new mathematical concepts, and put the Indian notation into general use (it's still called 'Hindi numerals' in Arabic now). When a change in regime led to a move to Baghdad as the new capital, library development and translations on a vast scale were part of an amazing, unique investment in incorporating different intellectual traditions. This in part led to the preservation of nearly all the works of Greek philosophy and sciences that we know of today, and many Indian and mathematical treatises were included in this effort, popularized and expanded on.
One of the people working there in the 9th century was Persian mathematician Al-Khwarizmi (whose name is preserved in 'algorithm'). He was born during the reign of famous caliph Harun al-Rashid of 1001 nights fame, if that can put it in context for you :-). He wrote several major works, including "Kitab al jabr w'al-muqabala", the first written work on algebra, which it named. Another major contribution was 'Al-Khwarizmi on the Hindu Art of Reckoning', about the Indian numeric notation.
By the time Fibonacci came around in the late 12th century, the political situation was in a state of flux but many mathematical concepts were in common use in the Arabic world. The successor to Baghdad in translations had been established in Toledo, and they were busy in turn translating many of the previous texts into Latin. A major translation was what was rendered as 'Algoritmi de numero Indorum', but unfortunately it was mostly noticed by scholars at the time.
It was Fibonacci's Liber Abaci which finally popularized the use of what we now call Arabic numerals in the rest of Europe. He was primarily a trader, so this was the group that first took up the new notation. It was only after a couple centuries that the scientific push of the 15th and 16th centuries could take full advantage of it to develop much of the technology that allowed Europe's expansion in the rest of the world.
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First published: 01/21/03
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