Leonardo Fibonacci

Leonardo Fibonacci also known as Leonardo Pisano, Leonardo of Pisa,  was the greatest European mathematician of the Middle ages. He was born in Pisa in Italy circa 1170 and died some time after 1240.

Leonardo’s father, Gugliemo, was a customs official and engaged in commerce representing Pisa at Bougie on the north coast of Africa. Young Leonardo consequently received a Moorish education as well as the traditional European education and was introduced to Hindu-Arabic numbers. Later on he traveled about the Mediterranean visiting Egypt, Syria, Greece, Sicily and Provence, meeting with scholars and becoming acquainted with the various arithmetical system used by the merchants.

The influence of Christians and Moslem cultures greatly stimulated Fibonacci resulting in a flow of mathematical writings. ‘Liber Abaci (The Book of Calculations) was published in 1202 AD.

Europe was still using the Roman and Greek alphabet for numbers consequently the abacus had to be used for calculations. By helping to introduce Hindu-Arabic numbers, Fibonacci freed arithmetic from this need for the abacus.

Though not the first to write about the Hindu-Arabic number system- 1, 2, 3, 4, 5, 6, 7, 9, 0 – he showed by examples the superiority of this system over the Roman system. To Fibonacci also goes the credit for first using the bar in a fraction i.e. 5/6 separating the numerator and denominator.

In the "Liber Abaci", Fibonacci also examined the theoretical aspects of arithmetic such as series and their properrties, extractions of square roots and cube roots. The Fibonacci Sequence was first named as such by the French mthematician Eduard Lucas in the 1870's. This sequence had been demonstrated by Fibonacci in a problem solving the breeding of rabbits.

“A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair which from the second month on becomes productive?”

This problem gave rise to the Fibonacci sequence 1.1.2.3.5.8.13.21.34 55 and so on, in which each number is the sum of the two preceding numbers, was the first recursive number sequence developed in Europe.  It was also the first in which the relation between two or more successive terms can be expressed by a formula.

Other works by Fibonacci are:

• Practica Geometriae  (The Practice of Geometry: 1220)
• Liber Quadratorium  (The Book of Square Numbers: 1225)
• Flos  (The Flower: 1225)
  

The term Fibonacci Sequence was coined by the French mathematician Edward Lucas in the 19^th century when scientist began to discover the numbers in nature.

The numbers include those found in:

• the spirals of sunflower heads and pine cones;
  
• the genealogy of the male bee;
• the related logarithmic spiral in snail shells;
• the arrangement of leaf buds on a stem and animal horns.

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