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Primary Magazine - Issue 20: A little bit of history


This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 26 January 2010 by ncetm_administrator
Updated on 09 February 2010 by ncetm_administrator

Primary Magazine Issue 20
 

A little bit of history
Famous Mathematicians - Fibonacci

Fibonacci is said to have been the greatest European mathematician of the middle ages. His full name was Leonardo Pisano Bogollo, he was also known as Leonardo of Pisa, Leonardo Pisano, Leonardo Bonacci, Leonardo Fibonacci or, most commonly, Fibonacci! He was born in Pisa in Italy (hence Pisa as his surname) in around 1170AD.

map of Italy

His father was Guglielmo Bonacci, which is where his nickname Fibonacci came from. It was shortened from the term filius Bonacci, which means ‘the son of Bonaccio’. His father was a wealthy Italian merchant who was a kind of customs officer in charge of a trading post in Bugia. Bugia is now known as Bejaia, a port east of Algiers in North Africa. As a young boy, Fibonacci travelled with his father to help him with his work. It was in Bugia that he learned about the Hindu-Arabic numeral system which was to become one of his most significant contributions to the European world of mathematics.
 

roman numerals

The Europeans were using Roman numerals at the time and he saw that calculating with Hindu-Arabic numerals was much simpler and more efficient. This inspired him to travel throughout the Mediterranean to study under the leading Arab mathematicians of the time in order to learn more about their way of doing things. After he returned in around 1200, he wrote a book Liber Abaci (Book of Abacus or Book of Calculation) published in 1202, when he was 32. In it he wrote about all he had learned and it was in this way that he introduced Hindu-Arabic numerals to Europe. See A little bit of history in Issue 8 of the Primary Magazine for a more detailed look at the history of our number system.

His book also posed and solved a problem involving the growth of a hypothetical population of rabbits. The problem was based on several assumptions:

  • you start with one male and one female rabbit who have just been born
  • each will reach sexual maturity after one month
  • the gestation of a rabbit is one month
  • a female rabbit will always give birth to one male and one female
  • rabbits never die!

rabbitThe question he asked was: how many rabbits will there be in one year? The solution to this forms a sequence of numbers that was to become known as the Fibonacci sequence. This sequence was known to Indian mathematicians as early as the sixth century, so he didn’t invent it, but he did introduce it to the West.

Why not explore the rabbit problem with your class? You can find the solution on the ThinkQuest website. There is a great picture book The Rabbit Problem by Emily Gravett which explores Fibonacci’s problem – and lots more, in a really delightful way.

In the Fibonacci sequence, each number is the sum of the previous two numbers, starting with 0 and 1. It begins 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610 etc.

How far can your children take this sequence in up to five minutes?

The higher up in the sequence, the closer two consecutive Fibonacci numbers, when divided by each other, will approach the golden ratio. You could give the children calculators to see how close to the golden ratio they can get with the consecutive Fibonacci numbers in their sequences.

Fibonacci numbers appear all around us in nature. It is worth exploring this website with your children – some cross-curricular maths!

Fibonacci is also famous for his rectangle and spiral. Visit the Nrich website for more about this and also some very challenging Fibonacci problems.

Fibonnaci rectangles and spiral

You might like to explore some of these number puzzles either by yourself or with your class.

Fibonacci died in 1240s and there is a statue commemorating him in the cemetery of the cathedral in Pisa near the famous leaning tower.
 

statue of Fibonacci in Pisa

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