Who was Fibonacci?
Well, Fibonacci was a thirteenth-century Italian mathematician, the first to describe this mathematical sequence. He was also known as Leonardo de Pisa , Leonardo Pisano or Leonardo Bigollo and he was already talking about the succession in 1202, when he published his Liber abaci . Fibonacci was the son of a merchant and he grew up traveling, in an environment where mathematics was of great importance, awakening his interest in calculation immediately.
His knowledge of arithmetic and mathematics is said to have grown enormously with the Hindu and Arabic methods he learned during his stay in North Africa and after years of research, Fibonacci came up with interesting breakthroughs. Some of his contributions refer to geometry, commercial arithmetic and irrational numbers, in addition to having been vital in developing the concept of zero.
What is the Fibonacci sequence?
Have you ever heard of the Fibonacci sequence? Can you imagine an equation capable of mathematically explaining everything in the universe? Do you believe such a thing would be really possible?
Well, of the many mathematical sequences that exist, none is as famous, as interesting and as amazing as the one Fibonacci invented. Over the years, men of science, artists of all kinds and architects have used it to work, sometimes on purpose and sometimes unconsciously, but always with majestic results. I invite you to know the history behind all this matter as today we learn what the Fibonacci sequence is .
The Fibonacci sequence
The Fibonacci sequence , sometimes also known as the Fibonacci sequence or incorrectly as the Fibonacci series, is itself an infinite mathematical sequence. It consists of a series of natural numbers that are added by 2, starting from 0 and 1. Basically, the Fibonacci sequence is carried out by always adding the last 2 numbers (All the numbers present in the sequence are called Fibonacci numbers ) of as follows:
- 0,1,1,2,3,5,8,13,21,34 …
Easy right? (0 + 1 = 1/1 + 1 = 2/1 + 2 = 3/2 + 3 = 5/3 + 5 = 8/5 + 8 = 13/8 + 13 = 21/13 + 21 = 34 .. .) So on, to infinity. As a rule, the Fibonacci sequence is written like this: xn = xn-1 + xn-2.
The Fibonacci Sequence, also called the Golden Succession:
The resulting sequence is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 , … (Fibonacci omitted the first term in “Liber abbaci” ). This sequence, in which each number is the sum of the two numbers that precede it, proved extremely important and is present in many and different areas of mathematics and science. The “Fibonacci Quarterly” is a modern journal aimed at studying mathematics in relation to this sequence.
In the third section, many other problems are raised, including some of these:
- ” A spider climbs many feet on a wall each day and comes back a set number of feet each night, how many days does it take to climb the wall? “
- ” A hunting dog, whose speed increases arithmetic, chases a hare, whose speed also increases arithmetic, how far did they get before the hunting dog could catch the hare? “
Fibonacci treats numbers as the root of 10 in the fourth section, both with rational approximations and with geometric constructions.
In 1228, Fibonacci produced a second edition of “Liber abbaci”, with an introduction, typical of many second editions of books.
Another of Fibonacci’s books is the “Practica Geometrie”, written in 1220 and dedicated to Dominicus Hispanus. It contains a large collection of geometric problems, distributed in eight chapters, together with theorems based on ” Euclid ‘s Elements ” and “On Divisions” also by Euclid. In addition to geometric theorems with precise proofs, the book includes practical information for controllers, including a chapter on how to calculate the height of elevated objects using similar triangles. The last chapter presents what Fibonacci calls geometric subtleties.
“Liber quadratorum” , written in 1225, is the most impressive part of Fibonacci’s work, although it is not the work he is best known for. The name of the book means the book of squares and is a book on number theory which, among other things, examines methods for finding the Pythagorean triple. Fibonacci was the first to note that square numbers could be constructed as sums of odd numbers, essentially describing an inductive procedure and using the formula n ^ 2 + (2n + 1) = (n + 1) ^ 2. Fibonacci writes:
“I thought about the origin of all square numbers and found that they arise from the regular increase of odd numbers. The 1 is a square and from it the first square is produced, called 1; adding 3 to this, we get the second square, 4, whose root is 2; if a third odd number, i.e. 5, is added to this sum, the third square, i.e. 9, whose root is 3, will be produced; hence the sequence and series of square numbers always derive from regular additions of odd numbers “.
He defined the concept of congruum, a number of the form ab (a + b) (ab), if a + b is even, and four times this, if a + b is odd. Fibonacci proved that a congruum must be divisible by 24 and that if x, c such that x ^ 2 + c and x ^ 2-c are both squares, then there is a congruum. He also proved that a congruum is not a perfect square.
Fibonacci’s influence was more limited than could have been hoped and, except for his role in the widespread use of Indo-Arabic numbers and his rabbit problem, his contributions to mathematics were not fully appreciated.
Fibonacci’s work on number theory was almost totally ignored and poorly known during the Middle Ages. Three hundred years later, we find the same results in Maurolico’s work.