Life and Contributions of Leonardo Fibonacci

Leonardo Pisano which translates to Leonardo of Pisa in English is the original name of Leonardo Fibonacci who was born around 1170 and died after 1240 (perhaps in 1250). Fibonacci was Leonardo Pisano’s nickname. He is also known as Leonardo Pisano Bigollo. Bigollo means a traveler or good for nothing. Little is known about his life beyond the few facts disclosed in his mathematical writings. It is rumored that he was born in Pisa and died there although no one is sure about the exact details. Fibonacci was born in the Bonacci family as the son of Guilielmo. Although Fibonacci was born in Italy, he was educated in North Africa where his father held a diplomatic post. His father’s task was to represent the merchants from the Republic of Pisa who conducted trade in Bugia. Bugia would later be called Bougie and is now known as Bejaia, which is a Mediterranean port situated in the northeastern part of Algeria. This town lies at the mouth of Wadi Soummam near Cape Carbon and Mount Gouraya. It’s here that Fibonacci was taught mathematics while traveling with his father only to discover the significant advantages of the mathematical systems of countries they toured (Connor & Robertson, 1998)

Besides being sent to study calculation with an Arab master, Fibonacci went to Syria, Sicily, Egypt, Greece and provence to study various numerical systems and methods of calculation (Carney, 1998).Fibonacci would later be popularly known as the most talented medieval Italian mathematician. Very few people know that it was Fibonacci who gave us our decimal number system that replaced the Roman numeral system. The decimal number system was actually conceived from the Hindu-Arabic numbering system. When Fibonacci was studying mathematics, he mostly used the Hindu-Arabic symbols 0-9 instead of using the traditional Roman symbols that lacked place value and did not have 0’s. In fact, when using the Roman numeral system, an abacus was a common requirement (Russell, 2016).

Apart from popularizing the Hindu-Arabic numeral system to the Western world, Fibonacci is famously known for composing the Liber Abaci (1202; “Book of the Abacis” or Book of Calculation).This book was the first European work to be created on Arabian and Indian mathematics. He also introduced Europeans to the sequence of Fibonacci numbers. He used these sequences as an example in Liber Abaci. Other books he wrote include the following (Knott, 2009):

•         Practica Geometriae (The Practice of Geometry) in 1220

•         Liber Quadratorum (The Book of Square Numbers) in 1225

•         Flos (The Flower) in 1225 and

•         Letter to Master Theodore

  Contributions

Fibonacci’s contributions in the world of mathematics (especially to number theory) cannot go unmentioned. In a nutshell, mathematicians recognize his prudence in the following areas:

•                                He introduced to the world the bar used in fractions. Before this, the numerator had quotations around it.

•                                The square root notation is also his method

•                                He introduced the use of Arabic numerals and Hindu-Arabic place-valued decimal system into Europe through his book Liber Abaci

Some people argue that the Fibonacci numbers are also the numbering system of nature and thus even apply to how living things grow including petals on a flower, cells, honeycomb, wheat, pine cones and much more.

Contribution to Number Theory

Fibonacci corresponded with Fredrick II alongside his scholars for several years as he exchanged problems with them. In fact, he dedicated his 1225 book named quadratorum  ( “Book of Square Numbers”) to Fredrick. This book is considered Fibonacci’s masterpiece and was committed wholly to Diophantine equations of the second degree. It’s a collection of theorems that are systematically arranged, many of which were invented by Fibonacci who used proofs of his own to figure out general solutions. His most creative work was probably incongruent numbers (numbers that produce the same number when divided by a given number. Fibonacci worked out the original solution to finding a number that, when subtracted from or added to a square number, it leaves a square number. His statement that the following x2 + y2 and x2 - y2 could not result to both squares was of significant importance to determining the area of rational right triangles. Even though the Liber Abaci was broader in scope and more influential, the Liber quadratorum also ranks Fibonacci as a significant contributor to number theory between Pierre de Fermat, the 17th-century French mathematician, and Diophantus.

Liber Abaci (1202)

In the book Liber Abaci, Fibonacci introduced modus Indorum (method of the Indians) that is today called Hindu-Arabic numerals.  This book advocated for numeration with the digits 0 – 9 and place value. It also showed the value of the new Arabic numeral system and its practical use by applying the numerals to the calculation of interest, converting weights and measures, money-changing, and commercial bookkeeping among other applications. The book had a profound impact on European thought apart from being well received throughout Europe. However, no copies of the original book (the 1202 version) are known to exist. The first section of the 1228 edition introduces the Arabic numeral system and tries to compare it with other systems including the Roman numerals, and techniques of converting the other numeral systems into Arabic numerals. Using abacus for calculations with an Arabic numeral system instead of the Roman numeral system and its ancient Egyptian multiplication method was a development in making business calculations much easier and faster. This change led to the growth of banking and accounting in Europe. The second section explains the use of Arabic numerals in business, for instance converting different currencies and calculating profits as well as interests. These calculations were paramount to the growing banking industry. Liber Abaci also discusses prime numbers and irrational numbers (Sigler, 2003).

Fibonacci sequence

Fibonacci posed a problem in Liber Abaci that involves the growth of a population of rabbits based on idealized assumptions then solved it. The solution, generation after another, was a sequence of numbers that later came to be known as Fibonacci numbers (Hom, 2013). Although Liber Abaci by Fibonacci contains the earliest description (known by anyone) of the sequence outside of India, Indian mathematicians had noted the sequence even as early as the sixth century. Each number in the Fibonacci sequence of numbers is the sum of the two previous numbers. Fibonacci did not begin his sequence with 0, 1, 1, 2 as modern mathematicians do but with 1, 1, 2 as he continued. He then carried the calculation up to the thirteenth place (which is fourteenth in modern counting) which is 233. However, another manuscript carries it to the next place. Here is an example: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377. Fibonacci did not mention anything to do with the golden ratio being the limit of the ratio of consecutive numbers in the sequence.

Fibonacci’s Legacy

A statue to commemorate Fibonacci was constructed and raised in Pisa in the 19th century. Today, the statue is located in the western gallery of the Camposanto which is a historical cemetery on the Piazza Dei Miracoli. Due to their connection to the Fibonacci numbers, many mathematical concepts have been named after Fibonacci. Examples include the Pisano period, Fibonacci search technique, and the Brahmagupta. Beyond mathematics, Fibonacci’s namesakes include the art rock band The Fibonnacis and the asteroid 6765 Fibonacci.