Leonardo Passion(1170-1250) was an Italian number theorist, who was con-sided to be one of the most talented mathematicians in the Middle Ages. However, He was better known by his nickname Fibonacci, as many venturesome were named after it. In addition to that, Fibonacci himself some-times used the name Bigot, which means good-for-nothing or a traveler. Thigh’s probably because his father held a diplomatic post, and Fibonacci determinatively with him. Although he was born in Italy, he was educated in Nonromantic and he was taught mathematics in Bugging.

While being a ‘bigot’, hydrochloride the enormous advantages of the thematic systems used in discounters he visited. Fibonacci contributions to mathematics are remarkable. Even in the worldly, we still make daily use of his discovery. His most outstanding contribution’s be the replacement of decimal number system. Yet, few people realized. Fibonacci had actually replaced the old Roman numeral system with thinned-Arabic numbering system, which consists of Hindu-Arabic(O-9) symbols.

There were some disadvantages with the Roman numeral system: Firstly, it didn’t have Co’s and lacked place value; Secondly, an abacus was usually requirement using the system. However, Fibonacci saw the superiority of using Hindu-Arabic system and that is the reason why we have our numbering system today. 1 He had included the explanation of our current numbering system in his bookmobile Abaci”. The book was published in 1202 after his return to Italy. It washed on the arithmetic and algebra that Fibonacci had accumulated during historians.

In the third section of his book Libber Abaci”, there is a math questions triggers another great invention of mankind. The problem goes like this:A certain man put a pair of rabbits in a place surrounded on all sides by all. How many pairs of rabbits can be produced from that pair in a year if it supposed that every month each pair begets a new pair, which from the secondhand on becomes productive? This was the problem that led Fibonacci to identification of the Fibonacci Numbers and the Fibonacci Sequence. What ISO special about the sequence?

Let’s take a look at it. The sequence is listed assn=FL, 1, 2, 3, 5, 8, 13, 21, 34, 55, g(1)Starting from 1, each number is the sum of the two preceding numbers. Writingmathematically, the sequence looks likens=if I > 2; I 2 Z; AI = AI + ail where al = ay = leg(2)The most important and initial property of the sequence is that the higher in the sequence, the closer two consecutive Fibonacci numbers divided beach other will approach the golden ratio, ‘ = 1+pop 1:61803399. The proves easy. By De notion, we have’ = a+baa = ABA(3)From ‘=ABA , we can obtain a = b’.

Then, by plugging into Equation 3, we willet b’+b’ = b . Simplify, we can get quadratic equation ‘2 ‘ 1 -?O. In painting. Today, Fibonacci sequence is still widely used Inman did rent sectors of mathematics and science. For example, the sequence’s an example of a recursive sequence, which De nest the curvature of nitroglycerin’s spirals, such as snail shells and even the pattern of seeds nonresistant. One interesting fact about Fibonacci Sequence is that it was catalytically by a French mathematician Detoured Lucas in the sass’s.

Other than the two well-known contributions named above, Fibonacci hidalgo introduced the bar we use in fractions today. Previous to that, the mummer-attar had quotation around it. Furthermore, the square root notation is also alto quantities a and b are said to be in the golden ratio if a+baa =ABA= the Renaissance was a cultural movement that spanned roughly the 14th to the attachment, beginning in Florence in the Late Middle Ages and later spreading to the rest purpose.

It was a cultural movement that profoundly a acted European intellectual life in therapy modern period. Fibonacci method, which was included in the fourth section of his book Liberace”. There are not only common daily applications of Fibonacci contribute-actions, but also a lot of theoretical contributions to pure mathematics. Persistence, once, Fibonacci was challenged by Johannes of Palermo to solve equation, which was taken from Omar Shaman’s algebra book.

The equation’s xx+ex.+xx = 20. Fibonacci solved it by means of the intersection of a circled a hyperbola. He proved that the root of the equation was neither an integer a fraction, nor the square root of a fraction. Without explaining his meet-odds, he approximated the solution in sexagenarians notation as 1. 22. 7. 42. 33. 4. 40. This is equivalent to 1 + 2260+ 7602 + 42603 + , and it converts to the decimal . 3688081075 which is correct to nine decimal places.

The solution was a re- marketable achievement and it was embodied in the book Floss”. Libber Quadratic” is Fibonacci most impressive piece of work, although is not the work for which he is most famous for. The term Libber Quadrant-torus” means the book of squares. The book is a number theory book, histamines methods to ND Pythagorean triples. He rest noted that square mum-beers could be constructed as sums of odd numbers, essentially describing inductive construction using the formula no + (an + 1) = (n + 1)2.

He wrote:’ thought about the origin of all square numbers and discovered that theatres from the regular ascent of odd numbers. For unity is a square and profit is produced the rest square, namely 1; adding 3 to this makes the secondary, namely 4, whose root is 2; if to this sum is added a third ad number,namely 5, the third square will be produced, namely 9, whose root is 3; ands the sequence and series of square numbers always rise through the reconfiguration of odd numbers.

Thus when I wish to ND two square numbers the two square numbers and I ND the other square number by the addition of Lethe odd numbers from unity up to but excluding the odd square number. Performable, I take 9 as one of the two squares mentioned; the remaining squarely 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 surrendered. Fibonacci contribution to mathematics has been largely overlooked.

How-ever, his work in number theory was almost ignored and virtually underpinning the Middle Ages. The same results appeared in the work of Marchionesses hundred years later. Apart from pure math theories, all of us should beautiful for Fibonacci work, because what we have been doing all the time,was his marvelous creation.