Fibonacci day 2020 - La Spirale Aurea E La Successione Di Fibonacci

Hello guys, in this lesson we will talk about Leonardo Fibonacci, a very famous medieval mathematician for his contribution to arithmetic and for having discovered a succession that takes his name. Fibonacci is also linked to the connections that exist between mathematics, nature and art, and in particular he gave life to what is called the golden spiral. Here in the preview of our lesson you see a sunflower, Fibonacci and the shell of Nautilus. What do a sunflower and the shell of Nautilus have in common? I also add that we could ask ourselves what the sunflower, the shell, the gioconda, the flight of the falcon, the horns of the hare and so on have in common. We will discover it in this lesson. Leonardo Fibonacci is not the real name of our mathematician, but Fibonacci was later attributed in the course of his life to underline the fact that he was the son of Guglielmo Bonacci. He was born in Pisa in 1170 and died in Pisa in 1242. He traveled a lot and in Algeria he studied Arabic arithmetic. In fact, his contribution to Italian mathematics is also due to having brought the contributions of Arabic arithmetic to Italy. He also studied the works of Al-Khwarizmi, a very important Arabic mathematician, because he also gave the name to the word we currently use, algorithm. He also played an important role in algebra. Fibonacci wrote various works, among the most famous we remember the book Rabaci, which deals with arithmetic, another book, Pratica Geometrie, which focuses more on the application of algebra to geometry, and the book Liber Quadratorum. Fibonacci is famous for the succession that takes his name is the one you see here. It starts with 1 1, after which each term, excluding the first two, then excluding 1 and 1, is given by the sum of the two that precede it. In fact, 1 plus 2 gives me 3, 3 plus 5 gives me 8, 8 plus 13 gives me 21, and so on. Each number is given by the sum of the two that precede it. But there is not only this particularity, there is also another feature. The relationship between the pairs of successive terms is very quickly approached to a particular number. The particular number is called the Aurean ratio. Try to calculate the ratio, then the result of the division between successive numbers, and you will realize that it is enough to arrive in this area to see that the result is very close to 1.61803, and so on. 3 divided by 2 is equal to 1.5, then 5 divided by 3, 8 divided by 5, 13 divided by 8, and so on, and you will realize that the result is close to this. What you see here on the right is what takes the name of the Aurean spiral. This spiral originates from this sequence. In fact, if you see here, in small, there are two squares of side 1, 1, 1, and they are 1, 1 of the sequence. Then I build one of side 2, which is the sum of 1 and 1. Then I build the square of side 3, the square of side 5, that of side 8, that of side 13, that of side 21, and so on. You see that in this way you can get this spiral, the Aurean spiral. But how did Fibonacci discover this sequence? He discovered it by studying the reproduction of a pair of rabbits and seeing how the number of rabbits grew over the months. So it started with a pair, this pair then had children, so it counted two pairs, then three pairs, five pairs, and so on. This succession of Fibonacci can also be found in plants, for example in the Roman broccoli, which is what you see represented here, in the sunflower, as we said before, in the petals of other flowers, in the pine trees, in the pineapple, etc. In particular, the Roman broccoli is another example of geometry because its structure is repeated in its small inflorescences, so it is as if it were made up of many miniature broccoli. An application of the succession of Fibonacci can also be found in the phyllotassi, that is, in the arrangement of the leaves along the trunk of a plant. Obviously, the leaves are arranged in a certain way to try to collect as much light and gas as possible, so we are talking about oxygen, carbon dioxide, but look at the particularity, in reality they also follow the succession of Fibonacci. In the animals we find it in the shell of the Nautilus, the golden spiral, and always the spiral in the horns of the net. But we will see this in another lesson.