Mathematics Essay, Research Paper
Fibonacci born in 1175 AD, one of the greatest European mathematicians was born. His birth name was Leonardo Pisano. Pisano is Italian for the city of Pisa, which is where Leonardo was born. Leonardo wanted to carry his family name so he called himself Fibonacci, which is pronounced fib-on-arch-ee. Guglielmo Bonnacio was Leonardo’s father. Fibonacci is a nickname, which comes from filius Bonacci, meaning son of Bonacci. However, occasionally Leonardo would us Bigollo as his last name. Bigollo means traveler. I will call him Leonardo Fibonacci, but if anyone who does any research work on him may find the other names listed in older books. Guglielmo Bonaccio, Leonardo’s father, was a customs officer in Bugia, which is a Mediterranean trading port in North Africa. He represented the merchants from Pisa that would trade their products in Bugia. Leonardo grew up in Bugia and was educated by the Moors of North Africa. As Leonardo became older, he traveled quite extensively with his father around the Mediterranean coast. They would meet with many merchants. While doing this Leonardo learned many different systems of mathematics. Leonardo recognized the advantages of the different mathematical systems of the different countries they visited. But he realized that the ??Hindu-Arabic?? system of mathematics had many more advantages than all of the other systems combined. Leonardo stopped travelling with his father in the year 1200. He returned to Pisa and began writing. Books by Fibonacci Leonardo wrote numerous books regarding mathematics. The books include his own contributions, which have become very significant, along with ancient mathematical skills that needed to be revived. Only four of his books remain today. His books were all handwritten so the only way for a person to obtain one in the year 1200 was to have another handwritten copy made. The four books that still exist are Liber abbaci, Practica geometriae, Flos, and Liber quadratorum. Leonardo had written several other books, which unfortunately were lost. These books included Di minor guisa and Elements. Di minor guisa contained information on commercial mathematics. His book Elements was a commentary to Euclid??s Book X. In Book X, Euclid had approached irrational numbers from a geometric perspective. In Elements, Leonardo utilized a numerical treatment for the irrational numbers. Practical applications such as this made Leonardo famous among his contemporaries. Leonardo??s book Liber abbaci was published in 1202. He dedicated this book to Michael Scotus. Scotus was the court astrologer to the Holy Roman Emperor Fredrick II. Leonardo based this book on the mathematics and algebra that he had learned through his travels. The name of the book Liber abbaci means book of the abacus or book of calculating. This was the first book to introduce the Hindu-Arabic place value decimal system and the use of Arabic numerals in Europe. Liber abbaci is predominately about how to use the Arabic numeral system, but Leonardo also covered linear equations in this book. Many of the problems Leonardo used in Liber abacci were similar to problems that appeared in Arab sources. Liber abbaci was divided into four sections. In the second section of this book, Leonardo focused on problems that were practical for merchants. The problems in this section relate to the price of goods, how to calculate profit on transactions, how to convert between the various currencies in Mediterranean countries and other problems that had originated in China. In the third section of Liber abbaci, there are problems that involve perfect numbers, the Chinese remainder theorem, geometric series and summing arithmetic. But Leonardo is best remembered today for this one problem in the third section: ??A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair which from the second month on becomes productive??? This problem led to the introduction of the Fibonacci numbers and the Fibonacci sequence, which will be discussed in further detail in section II. Today almost 800 years later there is a journal called the ??Fibonacci Quarterly?? which is devoted to studying mathematics related to the Fibonacci sequence. In the fourth section of Liber abbaci Leonardo discusses square roots. He utilized rational approximations and geometric constructions. Leonardo produced a second edition of Liber abbaci in 1228 in which he added new information and removed unusable information. Leonardo wrote his second book, Practica geometriae, in 1220. He dedicated this book to Dominicus Hispanus who was among the Holy Roman Emperor Fredrick II??s court. Dominicus had suggested that Fredrick meet Leonardo and challenge him to solve numerous mathematical problems. Leonardo accepted the challenge and solved the problems. He then listed the problems and solutions to the problems in his third book Flos. Practica geometriae consists largely of geometry problems and theorems. The theorems in this book were based on the combination of Euclid??s Book X and Leonard??s commentary, Elements, to Book X. Practica geometriae also included a wealth of information for surveyors such as how to calculate the height of tall objects using similar triangles. Leonardo called the last chapter of Practica geometriae, geometrical subtleties; he described this chapter as follows: ??Among those included is the calculation of the sides of the pentagon and the decagon from the diameter of circumscribed and inscribed circles; the inverse calculation is also given, as well as that of the sides from the surfaces?Kto complete the section on equilateral triangles, a rectangle and a square are inscribed in such a triangle and their sides are algebraically calculated?K?? In 1225 Leonardo completed his third book, Flos. In this book Leonardo included the challenge he had accepted from the Holy Roman Emperor Fredrick II. He listed the problems involved in the challenge along with the solutions. After completing this book he mailed it to the Emperor. Also in 1225, Leonardo wrote his fourth book titled Liber quadratorum. Many mathematicians believe that this book is Leonardo’s most impressive piece of work. Liber quadratorum means the book of squares. In this book he utilizes different methods to find Pythagorean triples. He discovered that square numbers could be constructed as sums of odd numbers. An example of square numbers will be discussed in section II regarding root finding. In this book Leonardo writes: ??I thought about the origin of all square numbers and discovered that they arose from the regular ascent of odd numbers. For unity is a square and from it is p
Dr. Ron Knott ??Fibonacci??s Mathematical Contributions?? March 6, 1998 www.ee.surrey.ac.uk/personal/R.Knott/Fibonacci/fibBio.html (Feb. 10, 1999) ??Mathematics Encyclopedia?? www.mathacademy.com/platonic_realms/encyclop/articles/fibonac.html