Fibonacci biography book

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His real significance resides, however, not in the discovery of this sequence of numbers but in the fact that studying ancient science and encountering Arab mathematics led him to produce a number of writings that laid the foundation of a new beginning of applied mathematics in Europe. His alphabetic designation for the general number or coefficient was first improved by Viète ... Fibonacci's work in number theory was almost wholly ignored and virtually unknown during the Middle ages.

Liber quadratorum, written in 1225, is Fibonacci's most impressive piece of work, although not the work for which he is most famous.

and x4−y4 cannot be a 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. Also contained in the Liber abbaci are a variety of problems and puzzles including a famous problem on the reproduction of rabbits, which will be examined below.

There is an original document from 1241 in which the city of Pisa grants Fibonacci a pension. 4] runs:

"I thought about the origin of all square numbers and discovered that they arise out of the increasing sequence of odd numbers; for the unity is a square and from it is made the first square, namely 1; to unity is added 3, making the second square, namely 4, with root 2; if to the sum is added the third odd number, namely 5, the third square is created, namely 9, with root 3; and thus sums of square of consecutive odd numbers and a sequence of square always arise together";

this is readily translatable into the following set of equations [3, p4]

• 1 = 1²
• 1 + 3 = 2²
• 1 + 3 + 5 = 3²
• 1 + 3 + 5 + 7 = 4²
and suggests the general formula, which we would express as:
• 1 + 3 + ...

  Next he introduces the Indian numerals. Extensive journeys to the Orient gave Fibonacci the opportunity to expand and deepen his mathematical knowledge.

  

  606]:
  

  x+b=2(y-7)
  y+b=3(x+z)
  z+b=4(x+y)

  The name indeterminate analysis refers to the fact that the set of equations is underdetermined: there are four unknowns `b,x,y,z' and only three equations, so that a unique answer is not possible, but only a relation between values of the variables.

  The town lies at the mouth of the Wadi Soummam near Mount Gouraya and Cape Carbon. For example, I take 9 as one of the two squares mentioned; the remaining square will 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 square number. Fibonacci also proves many interesting number theory results such as:

  there is no x,y such that x2+y2 and x2−y2 are both squares.

  The Liber abbaci also contains many practical problems of value to merchants of the time, ranging from the calculation of interest to problems concerning currency exchange rates and profit margins. Certainly many of the problems that Fibonacci considers in Liber abaciⓉ were similar to those appearing in Arab sources.

• He also showed that x^4-y^4 can not be a square. There, when I had been introduced to the art of the Indians' nine symbols through remarkable teaching, knowledge of the art very soon pleased me above all else and I came to understand it, for whatever was studied by the art in Egypt, Syria, Greece, Sicily and Provence, in all its various forms.

  They are often used in modern computer science, as a part of number theory, and in the counting of mathematical objects. These scholars included Michael Scotus who was the court astrologer, Theodorus Physicus the court philosopher and Dominicus Hispanus who suggested to Frederick that he meet Fibonacci when Frederick's court met in Pisa around 1225.

  • Fibonacci showed that there is no pair x and y such that x²+y² and x²-y² are both perfect squares. Fibonacci himself sometimes used the name Bigollo, which may mean good-for-nothing or a traveller. to complete the section on equilateral triangles, a rectangle and a square are inscribed in such a triangle and their sides are algebraically calculated ... In FlosⓉ Fibonacci gives an accurate approximation to a root of 10x+2x2+x3=20, one of the problems that he was challenged to solve by Johannes of Palermo.

    Many of these word problems lead to problems in indeterminate analysis, such as this example [1, p. [3,xx]." Fibonacci has been called "the first great mathematician of the Christian West" [1, p611].
    
    The portrait above is from a modern engraving and is believed to not be based on authentic sources.