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Leonardo Fibonacci

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Leonardo Fibonacci Fibonacci Michael Stanfield The Life of Fibonacci The Italian mathematician Fibonacci was born as Leonard Pisano in 1170 A.D. His mathematical name, Fibonacci, is short for the Latin expression son of Bonacci. He was born in the city of Pisa and later passed away there about 80 years later. Even though Fibonacci is Italian, he received his education in North Africa after his father received a superior profession and moved the both of them there. The North African education he received is what led him to his primary contributions to the modern day mathematical subject. Guilielmo Bonacci, the father of Fibonacci, was a Holy Roman Empirical diplomat. In Pisa, Guilielmo was the representative of the merchants that resided and transacted there. This was an important profession during the time because this was a time period that the Italy was experiencing increasingly important and persistent sea trade. Although Pisa is not a sea port, a massive amount of traded goods still went through the town as it was close to the coast. When Fibonacci was young, his father became a consul to a North African port of Bugia, in present day Algeria, due to his work as a representative. He protected the Roman interest in the port of Bugia. After Fibonacci and his father moved to North Africa, Fibonacci received his education there. This is when and where he learned from Arab masters of mathematics. After learning from the Arab mathematicians, Fibonacci traveled around Northern Africa and Europe to Egypt, Syria, Greece, and other countries to study more about different systems and calculations. Fibonacci enjoyed doing so as he was given the opportunity to learn about how different mathematic systems around the region worked. After Fibonacci learned a subject, he would teach it to other people. It was not until after his travels that his greatest works were released. After his travels, Fibonacci finally settled in Pisa at about the age of 30. This was the time frame that a majority of his work of accomplished. During his lifetime, Fibonacci wrote four books. His most popular and well known is Liber abaci. Liber abaci, or the book of calculations, was the first book written by Fibonacci. He wrote it in 1202, only a few years after he settled back in Pisa. He also later revised Liber abaci in 1228 after he wrote the rest of his books. Practica geometriae, or Practice of Geometry, was written is 1220 when Fibonacci was 50. At the age of 55, he wrote two books. One was called Flos, or the Flower, while the other one was Liber quadratorum, or The Book of Squares. The Book of Squares contained many questions involving squares including some work with Pythagorean triples. Fibonacci was greatly influenced by trading. His entire life had revolved around it even though it was not his profession. He spent his life around merchants. His father was a representative of the merchants after all. A majority of what he introduced greatly helped commerce and trading around the world at that time. He knew it would so that is why he taught it. Even though Fibonacci is considered one of the best mathematicians during the Middle Ages, we know very little about him. Fortunately, we are still able to received a detailed description due to the autobiographical notes that Fibonacci left in his books. If it were not for those notes, we may not know anything about him. Along with the notes he left, the books are where his mathematical computations come from. The most well known book he wrote was Liber abaci. Liber abaci is what effectively introduced Europe to the Arabic numeral system. His absolute understanding of Arabic numerals allowed him to easily and simply explain how they work to the rest of the Europeans. Although Liber abaci was more influential, it is Fibonacci's work in Liber quadratorum that places him as the largest contributor to number theory between Diophantus and Fermat. Fibonacci´s Mathematical Works Fibonacci's greatest contributions to mathematics were not through his computational work, but the notations he provided. Fibonacci standardized multiple notions and the numerical system that we still use today. He greatly influenced the mathematicians of his day and the future. His work is not very well known, but the notations that he left behind, and the Fibonacci sequence, are his greatest legacy. Fibonacci wrote four mathematical books. The first, and by far the most well known, is Liber abaci. Liber abaci is the book that caused Europe to use the Arabic numeral system. The writing Fibonacci does in this book produces his most well known contributions to mathematics. First and foremost, the introduction of the Arabic numeral system in Europe. In Liber abaci, Fibonacci shows the superiority of the Arabic numeral system. He first shows how to use the system, then explains how it will benefit everyone from mathematicians to merchants, who he had grown up around. Liber abaci shows the flaws of the Roman numeral system including its lack of 0 and a decimal system. Liber abaci also introduced the fraction bar to mathematical notation. Before the fraction bar, people mainly used quotation marks to set off the numerator. The use of the fraction bar allows to a much more comprehendible notation. Although Liber abaci was not the first time Arabic numerals were used, it is what subsequently standardized the notation in Europe. The excellent portrayal that Fibonacci uses to explain these numbers allow it to have been easily understood by the Europeans. Along with his excellent explanations, the superiority of the system is what eventually led to its widespread use. Soon after the release of Liber abaci, Europeans realized that using LXXXVIII to write 88 was not the best notation, therefore; they switched over to the Arabic numeral system that will still use today. This notation has made mathematics substantially simpler to use. It made mathematics an easier to understand concept. The use of 10 characters to quantify any value versus the use of 7 characters whose largest difference in value is 500 made the use of Arabic numerals a much preferred choice. Roman numerals ranged in value, and the largest Roman numeral only stood for 1000, the second largest being 500, third largest being 100, so on. After Fibonacci release Liber abaci, the Arabic numerals were not taken up immediately as you would imagine. Instead, it took a while for Arabic numerals to be adopted. Fibonacci did not only introduce Arab mathematics to Europe, but he also taught it to some Arabs as well. Even though Fibonacci learned mathematics from Arab, it was only the scientists and mathematicians that used those characters. Fibonacci taught this kind of mathematics to Arab businessmen. Fibonacci did not introduce Arabic numerals to everyone for no reason. He felt they were more effective at displaying information as well as better to use computationally. This is why Fibonacci taught everyone these numerals. He believed these numerals would help commerce and business become easier. This is the case since after Fibonacci introduced Arabic numerals, banking and business became very common. It was due to Fibonacci's introduction of Arabic numerals that led Italy to start making banks. Arabic numerals made things easier. Fibonacci understood this and that is why he introduced them to everyone. In Liber abaci, the use of the fraction bar presented by Fibonacci is substantial. The fraction bar allows the ability to easily write and comprehend fractions. However in Liber abaci, Fibonacci wrote his fractions a little bit differently. One major difference is the way in which Fibonacci wrote mixed numbers. 3 3 Our mixed numbers:2 4 versus Fibonacci's mixed numbers: 4 2. 2 As shown above, Fibonacci wrote his whole units on the right rather than the left how we do now. Fibonacci was also a major user of unit fractions described as: 1=n Fibonacci liked to use unit fractions to show other fractions such as: 5=8 = 1=2 + 1=8 17=18 = 1=2 + 1=3 + 1=9 Although this seems messing, this is how Fibonacci wrote his fractions often. He enjoyed using unit fractions so that is what he did. After Fibonacci wrote Liber abaci, he then wrote a brief book called Practica geometriae, or Practice of Geometry. This book was only eight chapters long. Even though it was short, all eight chapters were filled with theorems designed around Euclid's Elements and On Divisions. He did not release another book until 5 years later. It was after the release of Practica geometriae that the Holy Roman empire noticed the works that Fibonacci had produced. The Holy Roman emperor wanted to challenge Fibonacci so he sent a member of his court to present Fibonacci with a multitude of mathematical problems. Out of these problems sent, three of them appeared in his next book, Flos. Flos was written in 1225. One of the problems Fibonacci was challenged to solve was as follows: 10x + 2x2 + x3 = 20 Fibonacci successfully answered this problem. Fibonacci accurately solved the problem to nine decimal places. In the same year, Fibonacci wrote another book, this one being his last. Liber quadratorum was the last book that Fibonacci wrote before his death in 1250. It is this book that makes modern mathematicians consider Fibonacci as a great number theorist. In Liber quadratorum, Fibonacci searches for new and various ways to find Pythagorean triples. Along with working with Pythagorean triples, Fibonacci also worked with Diophantine equations. One of the first occurrences he notes it this book is that squares can be constructed as sums of odd numbers as in the formula below.
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