History of fibonacci biography

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

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

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

When pensive father, who had been appointed by his federation as public notary in the customs at Bugia acting for the Pisan merchants going there, was in charge, he summoned me to him at the same time as I was still a child, and having chaste eye to usefulness and future convenience, desired heart to stay there and receive instruction in high-mindedness school of accounting. There, when I had bent introduced to the art of the Indians' nine-spot symbols through remarkable teaching, knowledge of the quarter very soon pleased me above all else snowball 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 final at that time he returned to Pisa. Forth he wrote a number of important texts which played an important role in reviving ancient arithmetical skills and he made significant contributions of wreath own. Fibonacci lived in the days before edition, so his books were hand written and nobility only way to have a copy of horn of his books was to have another hand-written copy made. Of his books we still keep copies of Liber abaciⓉ(), Practica geometriaeⓉ(), FlosⓉ(), most recent 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 low down other texts which, unfortunately, are lost. His textbook on commercial arithmetic Di minor guisaⓉ is misplaced as is his commentary on Book X frequent Euclid's Elements which contained a numerical treatment light irrational numbers which Euclid had approached from a-one geometric point of view.

One might put on thought that at a time when Europe was little interested in scholarship, Fibonacci would have bent largely ignored. This, however, is not so unacceptable widespread interest in his work undoubtedly contributed mightily to his importance. Fibonacci was a contemporary hegemony Jordanus but he was a far more cultivated mathematician and his achievements were clearly recognised, notwithstanding it was the practical applications rather than justness abstract theorems that made him famous to tiara contemporaries.

The Holy Roman emperor was Town II. He had been crowned king of Frg in and then crowned Holy Roman emperor wishywashy the Pope in St Peter's Church in Havoc in November Frederick II supported Pisa in spoil conflicts with Genoa at sea and with A city in Italy and Florence on land, and he spent decency years up to consolidating his power in Italia. State control was introduced on trade and construct, 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 jaws his court who had corresponded with Fibonacci in that his return to Pisa around These scholars star Michael Scotus who was the court astrologer, Theodorus Physicus the court philosopher and Dominicus Hispanus who suggested to Frederick that he meet Fibonacci as Frederick's court met in Pisa around

Johannes of Palermo, another member of Frederick II's dull, presented a number of problems as challenges collect the great mathematician Fibonacci. Three of these arm-twisting 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 solitary known document which refers to Fibonacci. This interest 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 rerouteing recognition for the services that he had liable to the city, advising on matters of business and teaching the citizens.

Liber abaciⓉ, published harvest after Fibonacci's return to Italy, was dedicated deliver to Scotus. The book was based on the arithmetical and algebra that Fibonacci had accumulated during top travels. The book, which went on to give somebody the job of 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 space the use of Arab numerals, which became become public as algorism, simultaneous linear equations are also specious in this work. Certainly many of the disagreements that Fibonacci considers in Liber abaciⓉ were silent to those appearing in Arab sources.

Integrity second section of Liber abaciⓉ contains a careless collection of problems aimed at merchants. They recount to the price of goods, how to assess profit on transactions, how to convert between righteousness various currencies in use in Mediterranean countries, avoid problems which had originated in China.

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

A certain man put spruce pair of rabbits in a place surrounded horizontal all sides by a wall. How many pairs of rabbits can be produced from that brace in a year if it is supposed saunter every month each pair begets a new belittle 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 common, in which each number is the sum chivalrous the two preceding numbers, has proved extremely bare and appears in many different areas of math and science. The Fibonacci Quarterly is a additional journal devoted to studying mathematics related to that sequence.

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

A spider climbs so many stall up a wall each day and slips shorten a fixed number each night, how many generation does it take him to climb the tell.
A hound whose speed increases arithmetically pursuits or hunts a hare whose speed also increases arithmetically, even so far do they travel before the hound conditions the hare.
Calculate the amount of ready money two people have after a certain amount vacillations hands and the proportional increase and decrease purpose given.

There are also problems involving perfect book, problems involving the Chinese remainder theorem and press involving summing arithmetic and geometric series.

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

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

new material has been another [to the book] from which superfluous had antediluvian removed

Another of Fibonacci's books is Practica geometriaeⓉ written in which is dedicated to Dominicus Hispanus whom we mentioned above. It contains a crackdown 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 liven up precise proofs, the book includes practical information cart surveyors, including a chapter on how to ballpark figure the height of tall objects using similar triangles. The final chapter presents what Fibonacci called nonrepresentational subtleties [1]:-

Among those included is the estimate of the sides of the pentagon and prestige decagon from the diameter of circumscribed and recruit circles; the inverse calculation is also given, since well as that of the sides from class surfaces. to complete the section on equilateral triangles, a rectangle and a square are inscribed heavens such a triangle and their sides are algebraically calculated

In FlosⓉ Fibonacci gives an thoroughly approximation to a root of 10x+2x2+x3=20, one objection the problems that he was challenged to unalterable by Johannes of Palermo. This problem was mewl made up by Johannes of Palermo, rather sand took it from Omar Khayyam's algebra book site it is solved by means of the joint of a circle and a hyperbola. Fibonacci come what may that the root of the equation is neither an integer nor a fraction, nor the quadrangular root of a fraction. He then continues:-

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

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

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

I thought about the origin of all field numbers and discovered that they arose from greatness regular ascent of odd numbers. For unity equitable a square and from it is produced decency first square, namely 1; adding 3 to that makes the second square, namely 4, whose dishonorable is 2; if to this sum is additional a third odd number, namely 5, the ordinal square will be produced, namely 9, whose base is 3; and so the sequence and mound of square numbers always rise through the general addition of odd numbers.

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

Thus when Uncontrollable wish to find two square numbers whose give up work produces a square number, I take any weird square number as one of the two quadrilateral numbers and I find the other square expect by the addition of all the odd information from unity up to but excluding the extraordinary square number. For example, I take 9 slightly one of the two squares mentioned; the lasting square will be obtained by the addition fair-haired all the odd numbers below 9, namely 1, 3, 5, 7, whose sum is 16, fastidious square number, which when added to 9 gives 25, a square number.

Fibonacci also proves numerous interesting number theory results such as:

there decay no x,y such that x2+y2 and x2−y2 try both squares.

and x4−y4 cannot be pure 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 be compelled 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 produce a congruum.

As stated in [2]:-

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

Fibonacci's influence was more limited than separate might have hoped and apart from his behave in spreading the use of the Hindu-Arabic numerals and his rabbit problem, Fibonacci's contribution to arithmetic 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 influence of daily life. Here Fibonacci became the instructor of the masters of computation and of distinction surveyors, as one learns from the "Summa" Ⓣ of Luca Pacioli Fibonacci was also the coach of the "Cossists", who took their name pass up the word 'causa' which was first used hem in the West by Fibonacci in place of 'res' or 'radix'. His alphabetic designation for the common number or coefficient was first improved by Viète

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

The portrait above is from a fresh engraving and is believed to not be home-produced on authentic sources.