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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!
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.
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.
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.
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.
Elephant Learning's teacher dashboard is now released. Here is a blog walkthrough of the dashboard.
Many math apps are parent-free zones or, at best, parents are an afterthought within the app. Elephant Learning knows that the best results come when the parent is involved in the child’s education. Every study shows outcomes for students are better when parents are involved. The truth is, when I started this company, my first child was on his way. I created this system as a tool to ensure that he receives the benefits of mathematics education and avoids the American educational pitfall. We live in a time when, increasingly, if you are not the person creating the automation, you are the person being replaced by it. Our reports detail exactly how we intend to teach each topic down to the milestone level with advice on how you can further learning with fun games outside of the system. This turns your child’s playtime in the system into a tool to succeed in playtime with you. We provide advice on how to work with the students on mistakes so that the pressure is always off. At any point in time, if your student is struggling, we are always happy to look at the data and advise. That is why Elephant Learning can guarantee results. The math app you choose for your child’s learning matters. Apps that focus on games and graphics with math sprinkled throughout may end up turning those math problems into perceived work for your child (and can become addictive). Elephant Learning begins with a proven curriculum and scientific understanding of how children learn math. We then build games and puzzles around the curriculum, empowering students to truly grasp math concepts. Knowing that parental involvement is key to student success, we also ensure that you, the parent, are involved every step of the way.
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