Leonardo Pisano was the first great mathematician of medieval Christian Europe. He played an important role in reviving ancient mathematics and made great contributions of his own. After his death in 1240, Leonardo Pisano became known as Leonardo Fibonacci. Leonardo Fibonacci was born in Pisa in about 1180, the son of a member of the government of the Republic of Pisa. When he was 12 years old, his father was made administer of Pisa’s trading colony in Algeria.
It was in Algeria that he was taught the art of calculating. His teacher, who remains completely unknown seemed to have imparted to him not only an excellently ractical and well-rounded foundation in mathematics, but also a true scientific curiosity. In 1202, two years after finally settling in Pisa, Fibonacci produced his most famous book, Liber abaci (the book of the Calculator). The book consisted of four parts, and was revised by him a quarter of a century later (in 1228).
It was a thorough treatise on algebraic methods and problems which strongly emphasized and advocated the introduction of the Indo-Arabic numeral system, comprising the figures one to nine, and the innovation of the “zephirum” the figure zero. Dealing with operations in whole numbers systematically, he also proposed the dea of the bar (solidus) for fractions, and went on to develop rules for converting fraction factors into the sum of unit factors. At the end of the first part of the book, he presented tables for multiplication, prime numbers and factor numbers.
In the second part he demonstrated mathematical applications to commercial transactions. In part three he gave many examples of recreational mathematical problems, much like the type which are enjoyed today. Next he prepared a thesis on series from which was derived what is now called the “Fibonnaci series. ” The “Fibonacci Sequence” is also named after Fibonacci. The Fibonacci sequence s a sequence in which each term is the sum of two terms immediately preceding it. The Fibonacci Sequence that has one as its first term is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55. . . The numbers may also be referred to as Fibonacci numbers. Fibonacci sequences have proven useful in number theory, geometry, the theory of continued fractions, and genetics.
They also arise in many unrelated phenomena, for example, the Golden Section, (whose value is 1. 6180) a shape valued in art and architecture because of its pleasing proportions, and spiral arrangement of petals and branches on certain types of flowers and plants. In the final part of the book Fibonnaci, a student of Euclid, applied the algebraic method. Fibonacci’s book, the Liber abaci remained a standard text for the next two centuries.
In 1220 he published Practica geometriae, a book on geometry that was very significant to future studies of the subject. In it he uses algebraic methods to solve many arithmetical and geometrical problems. He also published Flos (flowers) in 1224. In this work he combined Euclidean methodology with techniques of Chinese and Arabic origin in solving determinate problems. Liber quadratorum was published in 1225(“Book of Square Numbers”) was dedicated to the Holy Roman emperor, Frederick II. This book was devoted entirely to Diophantine equations of the second degree (i. e. , containing squares).
The Liber quadratorum may be considered Fibonacci’s masterpiece. It is a systematically arranged collection of theorems, many invented by the author, who used his own proofs to work out general solutions. Probably his most creative work was in congruent numbers- numbers that give the same remainder when divided by a given number. He worked out an original solution for finding a number that, when added to or subtracted from a square number, leaves a square number. Leonardo’s statement that X + Y and X – Y could not both be squares was of great importance to the detemination of the area of rational right triangles.
Although the Liber abaci was more influential and broader in scope, the Liber quadratorum alone ranks its author as the major contributor to number theory between Diophantus and Pierre de Fermat, the 17th-century French mathematician. Except for his roll of spreading the use of the Hindu-Arabic numerals, Fibonacci’s contribution to mathematics has been largely overlooked. His name is known to modern mathematicians mainly because of the Fibonacci Sequence dervived from a problem n the Liber abaci: A certain man puts 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? The resulting number sequence, 1,1,2,3,5,8,13,21,35,55 (Leonardo himself omitted the first term), in which each number is the sum of the two preceding numbers, is the first recursive number sequence (in which the relation between two or more succesive terms can be expressed by a formula) known in Europe.
Fibonacci died in around 1240 and despite Fibonacci’s importance as the most orginal and capable mathematician of the medieval world, none of his work has been translated into English. In the 19th century, the term Fibonacci Sequence was coined by the French mathematician, Edouard Lucas, and since then scientists began to discover the numbers in nature which brought about a new interest in the topic. Although still relatively unknown in the United States, there is a “Fibonacci Association” in California. The purpose of that association is to encourage research in the topics that this great man once mastered.
