Leonardo Pisano, The Mathematician Who Westernized the Hindu-Arabic Numerals

By Ashley Langham

Leonardo Pisano, also known as Fibonacci, or son of Bonacci in Latin, was an Italian mathematician who brought the Hindu-Arabic numeral system to Europe, and more broadly, to the Western world. In his famous book Liber Abaci, the Book of Calculations, he started using the numbers 0–9 instead of the clumsy Roman numerals system. (0, or zephyr, was from the Arabic numeral system; and 1–9 was from the Indian ‘Hindu’ numeral system).‍

He grew up traveling around merchant ports because he was born into a rich merchant family. One of the problems he set out to solve was to make it easier for merchants to calculate the exchange of currency, since every republic along the Mediterranean sea (including Northern Africa and other European republics) had their own form.‍

He wrote several books in his time that made revelations in algebra, numbers theory, geometry, and trigonometry. He was so well known for his work that he even caught the attention and favor of the Holy Roman Emperor Frederick II.‍

The loose collections of his other algebraic works, published in a 1963 Journal by the Fibonacci Association, still stumps mathematicians today.‍

Read on to learn more about his work and life!

Fibonacci (1170–1250) Son of a Merchant

Monument of Leonardo da Pisa, done by artist Giovanni Paganucci in 1863, via Wikimedia

Fibonacci was born into a wealthy family in Pisa, Italy in 1170. His father, Guglielmo Bonacci, was an Italian merchant who was eventually stationed in Bugia, modern day Algeria, as the public clerk in the customs house for the Republic of Pisa. Bugia was a Pisan colony. He sent for his son who eventually accompanied him there.

Fibonacci grew up in a tumultuous time in Europe. The Crusades were in full swing and there were violent conflicts in the Holy Roman Empire. The Pisa, Genoa, Venice, and Amalfi territories were constantly at war with one another. His father, being a merchant, was relatively unencumbered by the conflict of the day and traveled with his son across the Mediterranean sea and neighboring merchant ports freely.‍

While accompanying his father at his Algerian post and traveling with him across the Mediterranean, Fibonacci got a lot of interaction with foreign merchants from India, The Middle East, and the North African regions. He was constantly exposed to the problems of calculating currency when every single republic had their own units of money. He became very acquainted with the Hindu-Arabic numeral system, for which he considered a better form of calculating value than the Roman number system.‍

His father, wanting him to get up to speed with calculating currencies so he could assist with the family business, got Fibonacci a private Muslin tutor. His tutor first introduced him to algebra through a book called al-Kitāb al-mukhtaṣar fī ḥisāb aljabr wal-muqābala (The Compendious Book on Calculation by Completion and Balancing) by Persian mathematician Muhammad ibn Mūsā al-Khwārizmī. It was this book where the word “algebra” first was derived.‍

With the introduction of algebra; Fibonacci decided to learn more about the subject and calculations more generally; so he decided to extend his travels to major merchant ports: Egypt, Syria, Greece, Sicily, and Provence. He continued to conduct business for his father and learn from the mathematicians he met there.

Fibonacci’s Liber Abaci

A page taken from Fibonacci’s Liber Abaci, via Wikimedia

Fibonacci returned to Pisa in 1200. He had gathered an enormous amount of knowledge about calculation and algebra. In 1202, he compiled his knowledge in his most famous work Liber Abaci. He had to write this by hand because the printing press had not yet been invented.

It was this book that was the first ever introduction to the Hindu-Arabic numeral system and its usefulness in calculations, in Europe. And, it is primarily the reason why today, the world has adopted this system instead of Roman numerals.‍

In the book, he widely plagiarized a lot of what he learned on his travels from other mathematicians. Yet, he did make several of his own contributions. Primarily, he was the first to define “factors of multiplication”, “numerator and denominator”. He also helped merchants find a way to calculate interest on loans legally, as it was a banned practice by the Holy Roman Empire. Basically, he provided a solution to hide the interest by calculating a higher initial sum for goods. He also created solutions to convert currency, calculate profit on transactions, and a way to solve linear equations. He also was the first person to introduce the horizontal fractions bar in his book.

Fibonacci Meets The Emperor

Leonardo Pisano was gaining in fame during the early 13th century. He wrote several more books that caught the attention of mathematicians and scientists that were members of the Holy Roman court.‍

Michael Scotus, the Court’s astrologer, particularly had his eye on Pisano and told Frederick II, the Emperor, to invite him to the Court. Frederick II was actually a patron of science and mathematics so he was eager to invite Pisano. Pisano obliged and was asked to solve three problems to see if he could impress the emperor.‍

  1. Answer x3 + 2x2 + 10x = 20
  2. Find the perfect square that remains a perfect square when increased or decreased by 5.
  3. If three men share an amount of money in ½, ⅓, ⅙ and each person takes some money from this total amount until there is nothing left. In other words, the first man returns ½ of what he took, the second, ⅓, and the third, ⅙. When the total of what was returned is divided equally among the three, each has his correct share. What is the original amount of money and how much did each person get from the original sum?‍

Pisano was able to solve all three problems to the satisfaction of the Court and he became one of the most famous mathematicians of his time. He went on to write Flos (Flower or Blossom) which provided solutions to all three of the problems and dedicated it to Michael Scotus.‍

Around the same time he wrote several other books; though some of them were lost because all had to be written by hand. Liber Quadratorum (The Book of Squares) survived and distinguished him as a talented mathematician, particularly in numbers theory. He also wrote a book on geometry, commenting on Euclid’s Elements Book 10, called Commentary on Book X. Instead of solving geometric problems using geometrical solutions, he used irrational numbers. He often solved geometry problems using algebraic methods and vice versa.‍

Fibonacci died sometime between 1240–1250. It still remains a mystery because everything was hand written; it is hard to get an accurate picture of the times. In 1240, he received the honor of a lifetime salary by the Republic of Pisa for offering accounting services to the people of Pisa for free. The assumption, however, is that he had to be alive at some point during this year to accept this gift.‍

Fibonacci’s knowledge of arithmetic, algebra, geometry, trigonometry, and numbers theory is quite impressive for his time. His work continues to present modern mathematicians with challenges today in his collection of works compiled by the Fibonacci Association in a 1963 Journal.

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Dr. Aditya Nagrath

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