Fibbonacci Essay Example For Students

Fibbonacci Essay 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 Leonardos father. Fibonacci is a nickname, which comes from filius Bonacci, meaning son of Bonacci. However, occasionally Leonardo would use 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, Leonardos 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 â€Å"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, al ong 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 remembe red today for this one problem in the third section: â€Å"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 â€Å"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 Euclidâ€℠¢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. CORPORAL PUNISHMENT EssayRoot Finding Leonardo amazingly calculated the answer to the following challenge posed by Holy Roman Emperor Fredrick II: What causes this to be an amazing accomplishment is that Leonardo calculated the answer to this mathematical problem utilizing the Babylonian system of mathematics, which uses base 60. His answer to the problem above was: 1, 22, 7, 42, 33, 4, 40 is equivalent to: Three hundred years passed before anyone else was able to obtain the same accurate results. Fibonacci Sequence As discussed earlier, the Fibonacci sequence is what Leonardo is famous for today. In the Fibonacci sequence each number is equal to the sum of the two previous numbers. For example: (1,1,2,3,5,8,13†¦) Or 1+1=2 1+2=3 2+3=5 3+5=8 5+8=13 Leonardo used his sequence method to answer the previously mentioned rabbit problem. I will restate the rabbit problem: â€Å"A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbit s 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?† I will now give the answer to the problem, which I discovered in the â€Å"Mathematics Encyclopedia†. â€Å"It is easy to see that 1 pair will be produced the first month, and 1 pair also in the second month (since the new pair produced in the first month is not yet mature), and in the third month 2 pairs will be produced, one by the original pair and one by the pair which was produced in the first month. In the fourth month 3 pairs will be produced, and in the fifth month 5 pairs. After this things expand rapidly, and we get the following sequence of numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 235, †¦ This is an example of recursive sequence, obeying the simple rule that two calculate the next term one simply sums the preceding two. Thus 1 and 1 are 2, 1 and 2 are 3, 2 and 3 are 5, and so on.† (page 1) III Conclusion Conclusion Leonardo Fibonacci was a mathematical genius of his time. His findings have contributed to the methods of mathematics that are still in use today. His mathematical influence continues to be evident by such mediums as the Fibonacci Quarterly and the numerous internet sites discussing his contributions. Many colleges offer classes that are devoted to the Fibonacci methods. Leonardo’s dedication to his love of mathematics rightfully earned him a respectable place in world history. A statue of him stands today in Pisa, Italy near the famous Leaning Tower. It is a commemorative symbol that signifies the respect and gratitude that Italy endures toward him. Many of Leonardo’s methods will continue to be taught for generations to come. Works Cited Dr. Ron Knott â€Å"Fibonacci’s Mathematical Contributions† March 6, 1998 www.ee.surrey.ac.uk/personal/R.Knott/Fibonacci/fibBio.html (Feb. 10, 1999) â€Å"Mathematics Encyclopedia† www.mathacademy.com/platonic_realms/encyclop/articles/fibonac.html (March 23, 1999)Bibliography: