NEWSPAPER PRESENTATION

News paper

High School Science "Pasquale Stanislao Mancini", Avellino

GRETA DELL'ORFANO 3Clm

Today we will talk about an extraordinary mathematician, but also a great traveler who introduced cultural elements of enormous importance that changed the culture of Europe and the Western world.

Leonardo Pisano, known as FIBONACCI

We will research his greatest works and delve into them, especially dealing with one of his greatest introductions to the whole world, leading to a real revolution for mathematics: The Fibonacci Succession

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INDEX

01

02

03

Who was Fibonacci?

Fibonacci's works

The Fibonacci succession

Golden Section and the Golden Number

Fibonacci succession in nature

04

05

06

How was it discovered?

Fibonacci and Leonardo da Vinci

07

08

09

In the art...

Curiosity

Fibonacci's works

Fibonacci during his lifetime also wrote important works such as, "Liber Abaci," "LiberQuadratorum," "PracticaGeometriae," and "Flos." Leonardo Pisano contributed much to the spread of Arabic math around Europe and the Western world. Among these texts of notable importance is especially the "Liber Abaci," which brought about a real revolution for the history of math.

Leonardo Pisano, known as FIBONACCI

Born in Pisa in 1170, Leonardo was the son of Guglielmo Bonacci, a merchant and representative of the merchants of the maritime republic of Pisa. Fibonacci followed his father on numerous trading trips to Algeria during which he came into contact with numerous Arab merchants and intellectuals. It was here that Fibonacci studied and learned the Indo-Arabic numerical system. Fibonacci's interest in the Arabic decimal system stemmed mainly from the fact that it was shown to be more practical for carrying out reckoning than the Roman numerical system, and this was of paramount importance commercially; the Roman numerical system in fact presented problems of graphical representation. We also owe to Fibonacci the introduction of the zero to determine the absence of something. Fibonacci died in Pisa around 1240.

The Fibonacci succession

In the twelfth chapter, Fibonacci also introduces a method for deriving a numerical succession: later, this succession will be remembered precisely as the Fibonacci succession. The Fibonacci succession is a sequence of positive integers where each number is the resultant of the sum of the previous two.

How was it discovered?

The Fibonacci succession is said to have originated as a result of solving a problem regarding the reproduction of rabbits during a tournament held in Pisa, where Frederick II of Swabia was also present. The problem went like this, "A certain man puts a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced by that pair in a year, if it is supposed that every month each pair generates a new pair, which from the second month onward becomes productive?"

The story goes that Fibonacci solved the puzzle so quickly that many of the participants accused him of cheating. The answer, 233, came just from his realization that he was dealing with a recursive succession: the total number of pairs generated at the end of each month-the mathematician understood-is obtained by adding up the number of pairs present in the two months preceding it, and thus 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on...

Fibonacci succession in nature

The Fibonacci sequence has also been observed in areas that have little or nothing to do with math. All those in which growth episodes happen, for example, seem to be invested by this particular series. Two examples out of all: -The disposition of leaves along the branch of a plant; -The spiral distribution of the floscules of daisies and sunflower seeds. Looking at the number of repeating elements, we generally come across repeated Fibonacci numbers: 21 and 34 in daisies, 34 and 55 in sunflowers, 5 and 8 in the spiral series of pinecones, 8 and 13 in pineapples, and so on.

Golden Section and the Golden Number

An important property of Fibonacci numbers is, that the ratio of one number to the number immediately preceding it, gets closer and closer to the number 1.6 .....This number is the famous Golden Section or Golden Number, φ PHI in Greek, known since ancient times, in fact Pythagoras and his disciples called it "Divine Proportion." The origin of the Golden Section is not known, but it has been used a lot in architecture, because the ratio between the elements, always 1.6, makes sure that there is a proper proportion. In fact, art history is full of expressions of the golden section, from the facade of the Parthenon in Athens to many works by Leonardo da Vinci.

Fibonacci and Leonardo da Vinci

Leonardo da Vinci represents the harmony of the forms of the human body in Vitruvius' Man in which a person is inscribed in a square and a circle. . Leonardo established that human proportions are perfect when the navel divides the man in a Golden Ratio that is, when dividing the height of the man with the distance of the navel from the base of the square we have as our own value the Golden Section 1.618. In fact, the navel is considered the center of the human body. In the square, the height of the man is equal to the distance between the ends of the hands with his arms extended.

In the human body...

In the human body in many parts we find the golden section. In fact, if we measure the fingers of our hand, we will find that the phalange lengths in the middle and ring fingers are Golden. Also the ratio of the length of the arm to the forearm, between the length of the leg and its lower part gives us the value of the Golden Section. One proof that the Golden Section affects our eye is provided by the human face. In fact, if we examine a face that we call "beautiful," we would find that the distances between the elements that make up the face are related to the Golden Section. In a face if the distance between the two cheeks is 1, then the ideal height is φ

In the art...

Renaissance artists were very fascinated by the golden proportions, one of the first to use it in his paintings was Piero della Francesca, or Sandro Botticelli or even Leonardo da Vinci...

"Birth of Venus" Sandro Botticelli

"Flagellazione di cristo" Piero della Francesca

Another important work that perfectly shows Fibonacci's golden section is...

"The Great Wave of Kanagawa" Katsushika Hokusai

"Mona Lisa" Leonardo da Vinci

Curiosity

On the walls of the dome of the Mole Antonelliana in Turin is Fibonacci's sequence of numbers illuminated in red neon, this work is called "VOLO DEI NUMERI", created and placed on the dome in 2000 by artist Mario Merz.

Thank you very much for your attention

Greta Dell'Orfano 3Clm

From a mathematical point of view

The succession (fn)n∈N is defined by recursion. If we enumerate its elements we get just the succession described by Fibonacci: 1,1,2,3,5,8,13,21,… f3=2=1+1; f4=3=2+1; f5=5=3+2; f6=8=5+3; f7=13=8+5, ... [fn=f(n-2)+f(n-1)]

When do we celebrate Fibonacci days?

Nov. 23 marks Fibonacci Day, the day dedicated to one of the most important mathematicians in history:Leonardo Pisano, known as Fibonacci, who introduced Arabic numerals, and the use of 0, to Italy and the entire West. The date for the celebration does not seem coincidental: Nov. 23 in the Anglo-Saxon world is 11-23, or the first four numbers of the mathematical succession theorized by the Italian genius in which each number is the result of the sum of the previous two.

Today...

The Fibonacci succession is still applied today in the development of bar codes and has contributed to population studies.

"Liber Abaci"

The "Liber abaci," is a textbook on the subject of mathematics. Written in medieval Latin in 1202 by the Pisan mathematician Leonardo Fibonacci, it is a ponderous treatise on arithmetic and algebra by which, in the early 13th century, Fibonacci introduced to Europe the Indo-Arabic decimal number system (which he called "Modus Indorum") and the main methods of calculation, including the four operations, still learned in schools today.