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Math
The Dreamer
by Margaret Etherton
Do you like to daydream? In the twelfth century a boy was born in Pisa who liked to dream at school. His name was Leonardo Fibonacci. Even when he grew up he stayed a dreamer. He was nicknamed 'bigollo" which means "someone who studies something useless" or "traveller". What did he dream about? And what was the useless thing he studied?
Sitting crossed-legged on the floor at school, Leonardo learned Latin, Music, Astronomy and public speaking. But his favorite lessons were Geometry and Numbers. All the sums had to be calculated using Roman Numerals, which looked like this: MCCXXVII. Students used a wooden frame with beads sliding on wires, called an abacus, to work out their sums. Adding and subtracting were not too hard, but imagine multiplying IX by VIII !
At the river port he daydreamed as he watched the sailing ships, the galleys and the river flatboats. Men on the shore unloaded precious cargo, like sacks of salt from Sardinia and bales of squirrel skins from Sicily. The merchants used the abacus to count their bales just like he did at school. Leonardo dreamt of sailing to faraway places.
When Leonardo was 18, his father moved to Bougia, a port on the African coast. Something very different was happening in the market place where olives, carpets and special candles were sold. The merchants did not use Roman numerals--- instead they used only nine Indian symbols - 9 8 7 6 5 4 3 2 1 - and a dot called sifr. Straight away Leonardo spotted they were much easier to use than the old Roman numerals because the new numbers could be added or subtracted in columns. Leonardo named them the Hindu numbers. Based on the tens, like the number of fingers we have, this is the Hindu-Arabic system we use today with a zero instead of a dot.
When he grew up Leonardo did not want to be a merchant like his father. He dreamed of being a mathematician. So he toured the famous libraries of the Mediterranean, where he read many ancient books. These helped him to work out his own way of bookkeeping, using geometry and solving problems.
After returning to Pisa at the age of 25, he showed the people the new number system, but they laughed at him and called him 'bigollo'. Leonardo wrote down the many things he had learned in his travels and called his book Liber Abaci---meaning Book of the Abacus. It was not about the abacus at all! Besides describing how to write the new numbers used in Arab lands and India, he demonstrated clever solutions to many of the ancient problems.
At first the new numbers were banned by the city of Pisa, partly because people thought it was too easy to change a 0 into a 6 or a 9. But when he was an old man, the city elders paid Leonardo to teach the secrets of the numbers 0 to 9 to the merchants of the city.
Hindu-Arabic numbers are used in classrooms all over the world. So when you are learning your times-tables, you can blame Leonardo Fibonacci! If you visit Italy, you can view a statue of Leonardo built in his honor, close to the famous Leaning Tower of Pisa.
Leonardo is more often remembered for a sequence of numbers, the Fibonacci sequence, in which each number is the sum of the two previous numbers. This sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on …. Leonardo came up with these numbers by counting the number of members in a rabbit's family at the end of each month, starting with two rabbits. They are sometimes called the magic numbers because they appear so often in nature---two eyes, five fingers, eight petals on a flower, the number of spirals in a pine cone, etc. They also have implications for things like architecture, art, astronomy and computers.
As he grew into old age, Leonardo signed his name at the end of his solved problems: Leonardo Bigollo. So he did not mind his funny name. The 'useless things' he studied proved to be useful after all. He was saying maybe it is a good thing to be a dreamer.
Bibliography:
Burton, David. Burton's History of Mathematics: An Introduction. Dubuque, IA: Wm. C. Brown Publishers, 1991.
Fauve, John and Gray, Jeremy. The History of Mathematics - A Reader. London: The Open University, 1987.
Gies, Joseph and Frances. Leonard of Pisa and the New Mathematics of the Middle Ages. New York: Thomas Y Crowell Company, 1969.
Hogben, Lancelot. Mathematics for the Million. Suffolk: The Merlin Press, 1989.
Internet:
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibBio.html
http://fibonacci.biography.ms
http://www.andrews.edu/~calkins/math/biograph/199899/biofibo.htm
Photos: © P. O'brien 2003
Margaret Etherton is a teacher, tutor and freelance writer. She has taught a range of subjects, such as reading, writing, mathematics and computers to people of all ages--- from small kids to seniors! Margaret lives close to the beach in Sydney with her husband, two of her four children and her cat, Mushka.
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