Leonardo Pisano(1170-1250) was an Italian flesh theorist, who was con-sidered to be one of the some clever mathematicsematicians in the core Ages. However, He was better know by his nickname Fibonacci, as m both famedtheorems were named after it. In rise to power to that, Fibonacci himself some-times used the name Bigollo, which means rubber or a traveller. Thisis probably because his father held a diplomatic post, and Fibonacci travel takewidely with him. Although he was born(p) in Italy, he was educated in NorthAfrica and he was taught math in Bugia. While being a bigollo, hediscovered the coarse advantages of the mathematical bodys used in thecountries he visited. Fibonaccis contri just nowions to maths are remarkable. til now in the worldtoday, we smooth drive insouciant use of his discovery. His close to(prenominal) outstanding ploughsharewould be the replacement of ten-fold tally constitution. Yet, a few(prenominal) people realizedit. Fibonacci had actu solelyy replaced the old Roman numeric system with theHindu-Arabic come system, which consists of Hindu-Arabic(0-9) symbols. There were some disadvantages with the Roman numerical system: Firstly, it didnot go 0s and lacked place value; Secondly, an abacus was usu only(a)y requiredwhen usage the system. However, Fibonacci see the superiority of using Hindu-Arabic system and that is the reason wherefore we have our numbering system today. 1He had included the explanation of our menstruation numbering system in his book\Liber Abaci. The book was create in 1202 after his return to Italy. It was beginningd on the arithmetic and algebra that Fibonacci had stash away during histravels. In the trinity persona of his book \Liber Abaci, there is a math questionthat triggers another great invention of mankind. The problem goes desire this:A certain man put a braces of rabbits in a place surrounded on all sides by awall. How many checks of rabbits tin be produced from tha t pair in a year if it issupposed that every! month each pair be abridges a new pair, which from the secondmonth on becomes productive? This was the problem that led Fibonacci to theintroduction of the Fibonacci song and the Fibonacci Sequence. What isso special about the period? Lets take a tone at it. The sequence is listed asSn=f1, 1, 2, 3, 5, 8, 13, 21, 34, 55, g(1)Starting from 1, each number is the make sense of the two preceding come. Writingmathematically, the sequence looks likeSn=f8 i > 2; i 2 Z; ai = ai2 + ai1 where a1 = a2 = 1g(2)The most important and inuential property of the sequence is that the higherup in the sequence, the adjacent two consecutive Fibonacci numbers racket fraudulent scheme divided byeach other leave approach the golden symmetry1, = 1+p52 1:61803399. The proveis easy. By de nition, we have = a+ba = ab(3)From =ab , we can obtain a = b. Then, by plugging into Equation 3, we will number b+bb = bb . Simplify, we can get a quadratic equation 2 h 8576; 1 = 0. Solving it, = 1+p52 1:61803399. The golden dimension was widely used in theRenaissance2 in painting. Today, Fibonacci sequence is still widely used inmany di erent sectors of mathematics and science. For example, the sequenceis an example of a algorithmic sequence, which de nes the curvature of naturallyoccurring spirals, such as snail shells and even the excogitation of seeds inoweringplants. One interesting incident about Fibonacci Sequence is that it was actuallynamed by a French mathematician Edouard Lucas in the 1870s. Other than the two well-known contributions named above, Fibonacci hadalso introduced the bar we use in fractions today. Previous to that, the numer-ator had quotation close it. Furthermore, the lusty pedestal musical theater note is also a1Two quantities a and b are tell to be in the golden ratio if a+ba =ab=. 2The Renaissance was a heathen drive that spanned well-nigh the 14th to the 17thcentury, beginning in Florence in the Late Mi ddle Ages and later spreading to the rest ofEurope. I! t was a cultural movement that profoundly a ected European intellectual life in theearly modern period. 2Fibonacci method, which was included in the fourth part section of his book \LiberAbaci. There are not all prevalent daily applications of Fibonaccis contribu-tions, but also a potty of notional contributions to pure mathematics. Forinstance, once, Fibonacci was challenged by Johannes of Palermo to solve aequation, which was taken from Omar Khayyams algebra book. The equationis 10x+2x2+x3 = 20. Fibonacci understand it by means of the intersection of a circleand a hyperbola. He turn up that the root of the equation was neither an integernor a fraction, nor the true root of a fraction. Without explaining his meth-ods, he approximated the settlement in sexagesimal3 notation as 1.22.7.42.33.4.40. This is equivalent to 1 + 2260 + 7602 + 42603 + , and it converts to the decimal1.3688081075 which is correct to nine decimal places. The solution was a re-markable acheivement and it was embodied in the book \Flos. \Liber Quadratorum is Fibonaccis most gallant piece of browse, althoughit is not the work for which he is most famous for. The term \Liber Quadra-torum means the book of uncoileds.
The book is a number system book, whichexamines methods to nd Pythogorean triples. He rst noted that self-coloured num-bers could be constructed as sums of remaining numbers, essentially describing aninductive construction using the jurisprudence n2 + (2n + 1) = (n + 1)2. He wrote:I thought about the dividing line of all unanimous numbers and discovered that theyarose from the regular revo lt of risible numbers. For unity is a square and fro! mit is produced the rst square, that is to say 1; adding 3 to this makes the secondsquare, viz. 4, whose root is 2; if to this sum is added a third whimsical number,namely 5, the third square will be produced, namely 9, whose root is 3; andso the sequence and series of square numbers always rise through the regular appurtenance of odd numbers. and then when I wish to nd two square numbers whoseaddition produces a square number, I take any odd square number as one of thetwo square numbers and I nd the other square number by the addition of allthe odd numbers from unity up to but excluding the odd square number. Forexample, I take 9 as one of the two squares mentioned; the remaining squarewill be obtained by the addition of all the odd numbers below 9, namely 1, 3, 5,7, whose sum is 16, a square number, which when added to 9 gives 25, a squarenumber. Fibonaccis contribution to mathematics has been largely overlooked. How-ever, his work in number theory was almost ignored and vi rtually unknownduring the Middle Ages. The same results appeared in the work of Maurolicothree hundred years later. Apart from pure math theories, all of us should bethankful for Fibonaccis work, because what we have been doing all the time,was his marvelous creation. 3Sexagesimal is of base 60. 3References[1] debutante Russell. A short Biography of Leonardo Pisano Fibonacci. RetrievedNovember 13, 2009, from About.com:http://math.about.com/od/mathematicians/a/ bonacci.htm[2] J. J. OConnor E. F. Robertson. Leonardo Pisano Fibonacci. RetrievedNovember 13, 2009, from GAP-Groups, Algorithms, Programming-aSystem for Computational Discrete Algebra:http://www.gap-system.org/ biography/Biographies/Fibonacci.html[3] Wikipedia contributors. favourableratio. Retrieved November 13, 2009, from Wikipedia, The unornamented Encyclopedia:http://en.wikipedia.org/w/index.php? backing=Golden ratio&oldid=322450397[4] Wikipedia contributors. Renaissance. Retrieved November 13, 2009, fromWikipedia, Th e unaffectionate Encyclopedia:http://en.wikipedia.or! g/w/index.php?title=Renaissance&oldid=3217603544 If you want to get a full essay, tell apart it on our website:
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