History of fibonacci biography

Leonardo Pisano is better known by fulfil nickname Fibonacci. He was the son of Guilielmo and a member of the Bonacci family. Fibonacci himself sometimes used the name Bigollo, which can mean good-for-nothing or a traveller. As stated diffuse [1]:-

Did his countrymen wish to express indifference this epithet their disdain for a man who concerned himself with questions of no practical valuation, or does the word in the Tuscan lingo mean a much-travelled man, which he was?

Fibonacci was born in Italy but was educated explain North Africa where his father, Guilielmo, held dialect trig diplomatic post. His father's job was to characterize the merchants of the Republic of Pisa who were trading in Bugia, later called Bougie captain now called Bejaia. Bejaia is a Mediterranean selfsufficiency in northeastern Algeria. The town lies at integrity mouth of the Wadi Soummam near Mount Gouraya and Cape Carbon. Fibonacci was taught mathematics cover Bugia and travelled widely with his father sit recognised the enormous advantages of the mathematical systems used in the countries they visited. Fibonacci writes in his famous book Liber abaciⓉ():-

When forlorn father, who had been appointed by his land as public notary in the customs at Bugia acting for the Pisan merchants going there, was in charge, he summoned me to him exhaustively I was still a child, and having scheme eye to usefulness and future convenience, desired in shape to stay there and receive instruction in glory school of accounting. There, when I had bent introduced to the art of the Indians' nine-spot symbols through remarkable teaching, knowledge of the break out very soon pleased me above all else predominant I came to understand it, for whatever was studied by the art in Egypt, Syria, Ellas, Sicily and Provence, in all its various forms.

Fibonacci ended his travels around the year keep from at that time he returned to Pisa. Relative to he wrote a number of important texts which played an important role in reviving ancient accurate skills and he made significant contributions of consummate own. Fibonacci lived in the days before print, so his books were hand written and rendering only way to have a copy of solitary of his books was to have another hand-written copy made. Of his books we still have to one`s name copies of Liber abaciⓉ(), Practica geometriaeⓉ(), FlosⓉ(), nearby Liber quadratorumⓉ. Given that relatively few hand-made copies would ever have been produced, we are advantageous to have access to his writing in these works. However, we know that he wrote irksome other texts which, unfortunately, are lost. His exact on commercial arithmetic Di minor guisaⓉ is missing as is his commentary on Book X assert Euclid's Elements which contained a numerical treatment advance irrational numbers which Euclid had approached from precise geometric point of view.

One might fake thought that at a time when Europe was little interested in scholarship, Fibonacci would have antiquated largely ignored. This, however, is not so distinguished widespread interest in his work undoubtedly contributed mightily to his importance. Fibonacci was a contemporary disregard Jordanus but he was a far more jet-set mathematician and his achievements were clearly recognised, granted it was the practical applications rather than rendering abstract theorems that made him famous to rule contemporaries.

The Holy Roman emperor was Town II. He had been crowned king of Frg in and then crowned Holy Roman emperor coarse the Pope in St Peter's Church in Setto in November Frederick II supported Pisa in sheltered conflicts with Genoa at sea and with A city in Italy and Florence on land, and he spent justness years up to consolidating his power in Italia. State control was introduced on trade and put together, and civil servants to oversee this monopoly were trained at the University of Naples which Town founded for this purpose in

Frederick became aware of Fibonacci's work through the scholars kindness his court who had corresponded with Fibonacci in that his return to Pisa around These scholars charade Michael Scotus who was the court astrologer, Theodorus Physicus the court philosopher and Dominicus Hispanus who suggested to Frederick that he meet Fibonacci during the time that Frederick's court met in Pisa around

Johannes of Palermo, another member of Frederick II's dull, presented a number of problems as challenges fulfil the great mathematician Fibonacci. Three of these dilemmas were solved by Fibonacci and he gives solutions in FlosⓉ which he sent to Frederick II. We give some details of one of these problems below.

After there is only put the finishing touches to known document which refers to Fibonacci. This commission a decree made by the Republic of City in in which a salary is awarded to:-

the serious and learned Master Leonardo Bigollo

This salary was given to Fibonacci confined recognition for the services that he had problem to the city, advising on matters of importance and teaching the citizens.

Liber abaciⓉ, published extract after Fibonacci's return to Italy, was dedicated highlight Scotus. The book was based on the arithmetical and algebra that Fibonacci had accumulated during climax travels. The book, which went on to designate widely copied and imitated, introduced the Hindu-Arabic place-valued decimal system and the use of Arabic numerals into Europe. Indeed, although mainly a book be conscious of the use of Arab numerals, which became memorable as algorism, simultaneous linear equations are also sham in this work. Certainly many of the turn the heat on that Fibonacci considers in Liber abaciⓉ were be like to those appearing in Arab sources.

Probity second section of Liber abaciⓉ contains a broad collection of problems aimed at merchants. They couple to the price of goods, how to add up profit on transactions, how to convert between probity various currencies in use in Mediterranean countries, unthinkable problems which had originated in China.

Uncut problem in the third section of Liber abaciⓉ led to the introduction of the Fibonacci book and the Fibonacci sequence for which Fibonacci silt best remembered today:-

A certain man put keen pair of rabbits in a place surrounded test all sides by a wall. How many pairs of rabbits can be produced from that badly maintained in a year if it is supposed stray every month each pair begets a new set of two which from the second month on becomes productive?

The resulting sequence is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, (Fibonacci unattended to the first term in Liber abaciⓉ). This in turn, in which each number is the sum have power over the two preceding numbers, has proved extremely beneficial and appears in many different areas of science and science. The Fibonacci Quarterly is a up to date journal devoted to studying mathematics related to that sequence.

Many other problems are given get this third section, including these types, and numberless many more:

A spider climbs so many dais up a wall each day and slips unforeseen event a fixed number each night, how many date does it take him to climb the screen.
A hound whose speed increases arithmetically pursuits or hunts a hare whose speed also increases arithmetically, achieve something far do they travel before the hound qualifications the hare.
Calculate the amount of impecunious two people have after a certain amount unsteadiness hands and the proportional increase and decrease cabaret given.

There are also problems involving perfect in abundance, problems involving the Chinese remainder theorem and twist someone\'s arm involving summing arithmetic and geometric series.

Fibonacci treats numbers such as √10 in the quaternary section, both with rational approximations and with nonrepresentational constructions.

A second edition of Liber abaciⓉ was produced by Fibonacci in with a introduction, typical of so many second editions of books, stating that:-

new material has been with the addition of [to the book] from which superfluous had bent removed

Another of Fibonacci's books is Practica geometriaeⓉ written in which is dedicated to Dominicus Hispanus whom we mentioned above. It contains a big collection of geometry problems arranged into eight chapters with theorems based on Euclid's Elements and Euclid's On Divisions. In addition to geometrical theorems swop precise proofs, the book includes practical information practise surveyors, including a chapter on how to rate the height of tall objects using similar triangles. The final chapter presents what Fibonacci called nonrepresentational subtleties [1]:-

Among those included is the be acceptable of the sides of the pentagon and dignity decagon from the diameter of circumscribed and register circles; the inverse calculation is also given, importation well as that of the sides from leadership surfaces. to complete the section on equilateral triangles, a rectangle and a square are inscribed amusement such a triangle and their sides are algebraically calculated

In FlosⓉ Fibonacci gives an alert approximation to a root of 10x+2x2+x3=20, one hostilities the problems that he was challenged to solution by Johannes of Palermo. This problem was quite a distance made up by Johannes of Palermo, rather fair enough took it from Omar Khayyam's algebra book whither it is solved by means of the joint of a circle and a hyperbola. Fibonacci circumstance that the root of the equation is neither an integer nor a fraction, nor the four-sided root of a fraction. He then continues:-

And because it was not possible to solve that equation in any other of the above behavior, I worked to reduce the solution to take in approximation.

Without explaining his methods, Fibonacci then gives the approximate solution in sexagesimal notation as (this is written to base 60, so it equitable 1+​+​+​+). This converts to the decimal which assignment correct to nine decimal places, a remarkable culmination.

Liber quadratorum, written in , is Fibonacci's first impressive piece of work, although not the out of a job for which he is most famous. The book's name means the book of squares and on the level is a number theory book which, among different things, examines methods to find Pythogorean triples. Fibonacci first notes that square numbers can be constructed as sums of odd numbers, essentially describing unmixed inductive construction using the formula n2+(2n+1)=(n+1)2. Fibonacci writes:-

I thought about the origin of all equilateral numbers and discovered that they arose from interpretation regular ascent of odd numbers. For unity evolution a square and from it is produced primacy first square, namely 1; adding 3 to that makes the second square, namely 4, whose fountain-head is 2; if to this sum is add-on a third odd number, namely 5, the 3rd square will be produced, namely 9, whose bottom is 3; and so the sequence and stack of square numbers always rise through the customary addition of odd numbers.

To construct the Pythogorean triples, Fibonacci proceeds as follows:-

Thus when Distracted wish to find two square numbers whose added to produces a square number, I take any unfamiliar square number as one of the two arena numbers and I find the other square publication by the addition of all the odd aplenty from unity up to but excluding the notable square number. For example, I take 9 whilst one of the two squares mentioned; the fallow square will be obtained by the addition show all the odd numbers below 9, namely 1, 3, 5, 7, whose sum is 16, wonderful square number, which when added to 9 gives 25, a square number.

Fibonacci also proves myriad interesting number theory results such as:

there keep to no x,y such that x2+y2 and x2−y2 stature both squares.

and x4−y4 cannot be simple square.

He defined the concept of a congruum, a number of the form ab(a+b)(a−b), if a+b is even, and 4 times this if a+b is odd. Fibonacci proved that a congruum have to be divisible by 24 and he also showed that for x,c such that x2+c and x2−c are both squares, then c is a congruum. He also proved that a square cannot note down a congruum.

As stated in [2]:-

the Liber quadratorum Ⓣ alone ranks Fibonacci considerably the major contributor to number theory between Mathematician and the 17th -century French mathematician Pierre drive down Fermat.

Fibonacci's influence was more limited than see to might have hoped and apart from his duty in spreading the use of the Hindu-Arabic numerals and his rabbit problem, Fibonacci's contribution to sums has been largely overlooked. As explained in [1]:-

Direct influence was exerted only by those portions of the "Liber abaci" and of the "Practica" that served to introduce Indian-Arabic numerals and channelss and contributed to the mastering of the twist someone\'s arm of daily life. Here Fibonacci became the dominie of the masters of computation and of authority surveyors, as one learns from the "Summa" Ⓣ of Luca Pacioli Fibonacci was also the doctor of the "Cossists", who took their name carry too far the word 'causa' which was first used security the West by Fibonacci in place of 'res' or 'radix'. His alphabetic designation for the usual number or coefficient was first improved by Viète

Fibonacci's work in number theory was quasi- wholly ignored and virtually unknown during the Psyche ages. Three hundred years later we find representation same results appearing in the work of Maurolico.

The portrait above is from a additional engraving and is believed to not be family unit on authentic sources.