A Mathematician Who Still Teaches Us Lessons Today

Have you ever stopped to consider the numerical system that we use each day in our lives? When we learned to count – to add, subtract, multiply and divide, we have Leonardo Bonacci, better known as Fibonacci to thank for it. He is generally considered to be the most talented Western mathematician of the Middle Ages. Fibonacci’s father was Guglielmo Bonacci, a wealthy Italian merchant and by some accounts, the consul for Pisa. Guglielmo directed a trading post in Bugia, a port in the Almohad dynasty’s sultanate in North Africa. Born around the year 1170, as a young boy, Fibonacci traveled extensively around the Mediterranean coast with his father. Always inquisitive about numbers, he would bother merchants with questions about how they kept track of their goods and their money and learned about the different systems of performing arithmetic. It was in Bugia (now Béjaïa, Algeria) that he learned about the Hindu–Arabic numeral system. He soon realized the many advantages of the system.

In 1202, he wrote a composition called “Liber Abaci” (Book of Calculation). The book advocated numeration with the digits 0–9 and place value. The book showed the practical use and value of the new system by applying the numerals to commercial bookkeeping, converting weights and measures, money-changing and other applications. Unfortunately, no copies of the 1202 edition are known to exist; however, the copies of the 1228 edition have survived the ages. The first section of the book introduced the numeral system that we use today and compares it with other systems, such as Roman numerals, as well as methods to convert the other numeric systems into the Arabic numerals. The second section of the book explained the uses of the numerals in business, for example converting different currencies, calculating profit and the computation of interest. Replacing the Roman numeral system and its ancient Egyptian multiplication method, Fibonacci integrated the use of an abacus for calculations and combined with the numeral system, business calculations became faster and easier. This resulted in the growth of banking and accounting in Europe.

Scholars and mathematicians in Europe were astounded by the book. It is cited as being responsible for popularizing the numeral system in the Western World that we use today. He also introduced Europe to the sequence of numbers that have become known as Fibonacci numbers and the Fibonacci Sequence.

Based on his writings, Fibonacci became a guest of Emperor Frederick II, who enjoyed mathematics and science. In 1240, the Republic of Pisa honored Fibonacci (referred to as Leonardo Bigollo) by granting him a salary in a decree that recognized him for the services that he had given to the city as an advisor on matters of accounting and instruction to citizens. He is believed to have died around 1250.

Fibonacci’s Liber Abaci contains the earliest known description of the Fibonacci sequence in the Western world, where each number is the sum of the previous two numbers. Fibonacci began the sequence with 1,1, 2, etc. He carried the calculation up to the thirteenth place, that is 233.

Fibonacci numbers appear unexpectedly, but frequently in mathematics, so much so that there is an entire journal dedicated to their study, the Fibonacci Quarterly. Fibonacci numbers and sequence applications are extensive, from computer algorithms to the branching of tress. Most applications would give the typical person a headache simply looking at the formulas, but every time you write a check, or even count to ten, you can thank Fibonacci for it.

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