Mathematicss 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 metropolis of Pisa, which is where Leonardo was born. Leonardo wanted to transport his household name so he called himself Fibonacci, which is marked fib-on-arch-ee. Guglielmo Bonnacio was Leonardo & # 8217 ; s male parent. Fibonacci is a moniker, which comes from filius Bonacci, intending boy of Bonacci. However, on occasion Leonardo would us Bigollo as his last name. Bigollo means traveller. I will name him Leonardo Fibonacci, but if anyone who does any research work on him may happen the other names listed in older books. Guglielmo Bonaccio, Leonardo & # 8217 ; s male parent, was a customs officer in Bugia, which is a Mediterranean trading port in North Africa. He represented the merchandisers from Pisa that would merchandise their merchandises in Bugia. Leonardo grew up in Bugia and was educated by the Moors of North Africa. As Leonardo became older, he traveled rather extensively with his male parent around the Mediterranean seashore. They would run into with many merchandisers. While making this Leonardo learned many different systems of mathematics. Leonardo recognized the advantages of the different mathematical systems of the different states 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 going with his male parent in the twelvemonth 1200. He returned to Pisa and began composing. Books by Fibonacci Leonardo wrote legion books sing mathematics. The books include his ain parts, which have become really important, along with ancient mathematical accomplishments that needed to be revived. Merely four of his books remain today. His books were all handwritten so the lone manner for a individual to obtain one in the twelvemonth 1200 was to hold another handwritten transcript made. The four books that still exist are Liber abbaci, Practica geometriae, Flos, and Liber quadratorum. Leonardo had written several other books, which unluckily were lost. These books included Di minor guisa and Elementss. 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 Numberss from a geometric position. In Elementss, Leonardo utilized a numerical intervention for the irrational Numberss. Practical applications such as this made Leonardo celebrated among his coevalss. Leonardo? ? s book Liber abbaci was published in 1202. He dedicated this book to Michael Scotus. Scotus was the tribunal astrologist 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 ciphering. This was the first book to present the Hindu-Arabic topographic point value decimal system and the usage of Arabic numbers in Europe. Liber abbaci is predominately about how to utilize the Arabic numerical system, but Leonardo besides covered additive equations in this book. Many of the jobs Leonardo used in Liber abacci were similar to jobs that appeared in Arab beginnings. Liber abbaci was divided into four subdivisions. In the 2nd subdivision of this book, Leonardo focused on jobs that were practical for merchandisers. The jobs in this subdivision relate to the monetary value of goods, how to cipher net income on minutess, how to change over between the assorted currencies in Mediterranean states and other jobs that had originated in China. In the 3rd subdivision of Liber abbaci, there are jobs that involve perfect Numberss, the Chinese balance theorem, geometric series and summing arithmetic. But Leonardo is best remembered today for this one job in the 3rd subdivision: ? ? A certain adult male put a brace of coneies in a topographic point surrounded on all sides by a wall. How many braces of coneies can be produced from that brace in a twelvemonth if it is supposed that every month each brace begets a new brace which from the 2nd month on becomes productive? ? ? This job led to the debut of the Fibonacci Numberss and the Fibonacci sequence, which will be discussed in farther item in subdivision II. Today about 800 old ages subsequently there is a diary called the? ? Fibonacci Quarterly? ? which is devoted to analyzing mathematics related to the Fibonacci sequence. In the 4th subdivision of Liber abbaci Leonardo discusses square roots. He utilized rational estimates and geometric buildings. Leonardo produced a 2nd edition of Liber abbaci in 1228 in which he added new information and removed unserviceable information. Leonardo wrote his 2nd book, Practica geometriae, in 1220. He dedicated this book to Dominicus Hispanus who was among the Holy Roman Emperor Fredrick II? ? s tribunal. Dominicus had suggested that Fredrick run into Leonardo and dispute him to work out legion mathematical jobs. Leonardo accepted the challenge and solved the jobs. He so listed the jobs and solutions to the jobs in his 3rd book Flos. Practica geometriae consists mostly of geometry jobs and theorems. The theorems in this book were based on the combination of Euclid? ? s Book X and Leonard? ? s commentary, Elementss, to Book X. Practica geometriae besides included a wealth of information for surveyors such as how to cipher the tallness of tall objects utilizing similar trigons. Leonardo called the last chapter of Practica geometriae, geometrical nuances ; he described this chapter as follows: ? ? Among those included is the computation of the sides of the Pentagon and the decagon from the diameter of circumscribed and inscribed circles ; the reverse computation is besides given, every bit good as that of the sides from the surfaces? Kto complete the subdivision on equilateral trigons, a rectangle and a square are inscribed in such a trigon and their sides are algebraically calculated? K? ? In 1225 Leonardo completed his 3rd book, Flos. In this book Leonardo included the challenge he had accepted from the Holy Roman Emperor Fredrick II. He listed the jobs involved in the challenge along with the solutions. After finishing this book he mailed it to the Emperor. Besides in 1225, Leonardo wrote his 4th book titled Liber quadratorum. Many mathematicians believe that this book is Leonardo & # 8217 ; s most impressive piece of work. Liber quadratorum means the book of squares. In this book he utilizes different methods to happen Pythagorean three-base hits. He discovered that square Numberss could be constructed as amounts of uneven Numberss. An illustration of square Numberss will be discussed in subdivision II sing root determination. In this book Leonardo writes: ? ? I thought about the beginning of all square Numberss and discovered that they arose from the regular acclivity of uneven Numberss. For integrity is a square and from it is p

roduced the first square, viz. 1 ; adding 3 to this makes the 2nd square, viz. 4, whose root is 2 ; if to this amount is added a 3rd uneven figure, viz. 5, the 3rd square will be produced, viz. 9, whose root is 3 ; and so the sequence and series of square Numberss ever rise through the regular add-on of uneven numbers. ? ? Leonardo died sometime during the 1240? ? s, but his parts to mathematics are still in usage today. Now I would wish to take a closer expression at some of Leonardo? ? s parts along with some illustrations. II Fibonacci? ? s Contributions to Math Decimal Number System vs. Roman Numeral System Algorithm Root Finding Fibonacci Sequence Decimal Number System vs. Roman Numeral System As antecedently mentioned Leonardo was the first individual to present the denary figure system or besides known as the Hindu-Arabic figure system into Europe. This is the same system that we use today, we call it the positional system and we use basal 10. This merely means we use 10 figures, 0,1,2,3,4,5,6,7,8,9, and a denary point. In his book, Liber abbaci, Leonardo described and illustrated how to utilize this system. Following are some illustrations of the methods Leonardo used to exemplify how to utilize this new system: 174 174 174 174? i28 = 6 balance 6 + 28 – 28 x28 202 146 3480 + 1392 4872 It is of import to retrieve that until Leonardo introduced this system the Europeans were utilizing the Roman Numeral system for mathematics, which was non easy to make. To understand the trouble of the Roman Numeral System I would wish to take a closer expression at it. In Roman Numerals the undermentioned letters are tantamount to the corresponding Numberss: I = 1 V = 5 X = 10 L = 50 C = 100 D = 500 M = 1000 In utilizing Roman Numerals the order of the letters was of import. If a smaller value came before the following larger value it was subtracted, if it came after the larger value it was added. For illustration: Eleven = 11 but IX = 9 This system as you can conceive of was rather cumbrous and could be confounding when trying to make arithmetic. Here are some illustrations utilizing Roman numbers in arithmetic: CLXXIM + XXVIII = CCII ( 174 ) ( 28 ) ( 202 ) Or CLXXIV – XXVIII = CXLVI ( 174 ) ( 28 ) ( 146 ) The order of the Numberss in the denary system is really of import, like in the Roman Numeral System. For illustration 23 is really different from 32. One of the most of import factors of the denary system was the debut of the figure nothing. This is important to the denary system because each figure holds a topographic point value. The nothing is necessary to acquire the figures into their right topographic points in Numberss such as 2003, which has no 10s and no 100s. The Roman Numeral System had no demand for nothing. They would compose 2003 as MMIII, excluding the values non used. Algorithm Leonardo? ? s Elementss, commentary to Euclid? ? s Book X, is full of algorithms for geometry. The undermentioned information sing Algorithm was obtained from a study by Dr. Ron Knott titled? ? Fibonacci? ? s Mathematical Contributions? ? : An algorithm is defined as any precise set of instructions for executing a calculation. An algorithm can be every bit simple as a cookery formula, a knitwork form, or travel instructions on the other manus an algorithm can be every bit complicated as a medical process or a computation by computing machines. An algorithm can be represented automatically by machines, such as puting french friess and constituents at right topographic points on a circuit board. Algorithms can be represented automatically by electronic computing machines, which store the instructions every bit good as informations to work on. ( page 4 ) An illustration of using algorithm rules would be to cipher the value of pi to 205 denary topographic points. Root Finding Leonardo surprisingly calculated the reply to the undermentioned challenge posed by Holy Roman Emperor Fredrick II: What causes this to be an astonishing achievement is that Leonardo calculated the reply to this mathematical job using the Babylonian system of mathematics, which uses base 60. His reply to the job above was: 1, 22, 7, 42, 33, 4, 40 is tantamount to: Three hundred old ages passed before anyone else was able to obtain the same accurate consequences. Fibonacci Sequence As discussed earlier, the Fibonacci sequence is what Leonardo is celebrated for today. In the Fibonacci sequence each figure is equal to the amount of the two old Numberss. For illustration: ( 1,1,2,3,5,8,13? K ) Or 1+1=2 1+2=3 2+3=5 3+5=8 5+8=13 Leonardo used his sequence method to reply the antecedently mentioned coney job. I will repeat the coney job: ? ? A certain adult male put a brace of coneies in a topographic point surrounded on all sides by a wall. How many braces of coneies can be produced from that brace in a twelvemonth if it is supposed that every month each brace begets a new brace which from the 2nd month on becomes productive? ? ? I will now give the reply to the job, which I discovered in the? ? Mathematics Encyclopedia? ? . ? ? It is easy to see that 1 brace will be produced the first month, and 1 brace besides in the 2nd month ( since the new brace produced in the first month is non yet mature ) , and in the 3rd month 2 braces will be produced, one by the original brace and one by the brace which was produced in the first month. In the 4th month 3 braces will be produced, and in the 5th month 5 braces. After this things expand quickly, and we get the undermentioned sequence of Numberss: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 235, ? K This is an illustration of recursive sequence, obeying the simple regulation that two calculate the following term one merely sums the predating two. Therefore 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 mastermind of his clip. His findings have contributed to the methods of mathematics that are still in usage today. His mathematical influence continues to be apparent by such mediums as the Fibonacci Quarterly and the legion cyberspace sites discoursing his parts. Many colleges offer categories that are devoted to the Fibonacci methods. Leonardo? ? s dedication to his love of mathematics truly earned him a respectable topographic point in universe history. A statue of him stands today in Pisa, Italy near the celebrated Leaning Tower. It is a commemorating symbol that signifies the regard and gratitude that Italy endures toward him. Many of Leonardo? ? s methods will go on to be taught for coevalss to come. Works Cited 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

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