Leonardo Pisano which
translates to Leonardo of P...
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
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
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 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.
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.