- Leonardo Fibonacci
O italiano Leonardo Fibonacci foi o primeiro grande matemático na Europa durante a Idade Média. Ele era também conhecido como Leonardo de Pisa. Foi treinado para ser um homem de negócios e começou viajando de Pisa, sua cidade natal, para outros lugares.
Durante essas viagens estudou outros sistemas numéricos e aprendeu o sistema numérico hindu-arábico, que acreditava ser superior ao sistema numérico romano. Ele também estudou álgebra e geometria lendo as obras de Diofante. Por volta de 1200, dedicou seus esforços ao desenvolvimento, à escrita e à aplicação da matemática.
- Número de ouro
O Número de Ouro é um número irracional misterioso e enigmático que nos surge numa infinidade de elementos da natureza na forma de uma razão, sendo considerada por muitos como uma oferta de Deus ao mundo.
A designação adoptada para este número, f (Phi maiúsculo), é a inicial do nome de Fídias que foi escultor e arquiteto encarregado da construção do Parthenon, em Atenas.
Um exemplo desta maravilha é o facto de que se desenharmos um retângulo cujos lados tenham uma razão ente si igual ao número de Ouro este pode ser dividido num quadrado e noutro retângulo em que este tem, também ele, a razão entre os dois lados igual ao número de Ouro. Este processo pode ser repetido indefinidamente mantendo-se a razão constante .
- Mas o que é que o número de ouro tem a ver com a sucessão de Fibonacci?
O número de ouro tem o valor j = ( 1 + Ö 5 )/2 (= 1,618 033 989...).Como se lembram da secção da Sucessão de Fibonacci, temos a seguinte sequência de números 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233....
Se dividirmos cada um destes números pelo seu antecedente, reparamos que essa razão vai tender para um certo valor.
Isto é, se fizermos F2/F1=1; F3/F2=2; F4/F3=1,5; F5/F4=1,6(6); F6/F5=1,6 e se continuarmos assim sucessivamente, obtemos a seguinte sequência de números:
1,000 000; 2,000 000; 1,500 000; 1,666 666; 1,600 000; 1.625 000; 1,615 385; 1,619 048; 1,617 647; 1,618 182; 1,617 978; 1,618 056; 1,618 026; 1,618 037; 1,618 033; ...
Então Fn+1/Fn aproxima-se cada vez mais de j(Phi).
Esta expansão decimal prolongar-se-á sem nunca se repetir (logo é um número irracional).
De fato, quando se prolongam estas "razões de Fibonacci" indefinidamente, o valor gerado aproxima-se cada vez mais do número de ouro.
Postagem feita por Larissa Guerra.
Tradução para Inglês
Post made by Larissa War.
Postagem feita por Larissa Guerra.
Tradução para Inglês
Leonardo Fibonacci
The Italian Leonardo Fibonacci was the first great mathematician in Europe during the Middle Ages. He was also known as Leonardo of Pisa. He was trained to be a businessman and began traveling from Pisa, his home town to other places.
During these trips other number systems studied and learned the Hindu-Arabic number system, he believed to be superior to the Roman numeral system. He also studied algebra and geometry by reading the works of Diophantus. Around 1200, he devoted his efforts to developing, writing and the application of mathematics.
Number of gold
The number of Gold is a mysterious and enigmatic irrational number that comes to us in a variety of elements of nature in the form of a reason, and is considered by many as a gift from God to the world.
The name given to this number, f (capital Phi) is the initial of the name of Phidias, sculptor and architect who was in charge of construction of the Parthenon in Athens.
An example of this wonder is the fact that if we draw a rectangle whose sides have a reason among themselves equal to the number of gold that can be divided into a square and another rectangle in which he has, too, the ratio between the two sides equal tonumber of Gold. This process can be repeated indefinitely keeping the ratio constant.
But what is the number of gold has to do with the Fibonacci sequence?
The number of gold has value j = (1 + Ö 5) / 2 (= 1.618 033 989 ...). As you remember the section of the Fibonacci sequence, we have the following sequence of numbers 1, 1, 2, 3 , 5, 8, 13, 21, 34, 55, 89, 144, 233 ....
If we divide these numbers by each of its antecedent, we note that this ratio will tend toward a certain value.
That is, if we F2/F1 = 1, 2 = F3/F2, F4/F3 = 1.5, F5/F4 = 1.6 (6), F6/F5 = 1.6 and if we continue so, we get the following sequence of numbers:
1.000 000, 2.000 000, 1.500 000, 1.666 666, 1.600 000, 1625 000, 1.615 385, 1.619 048, 1.617 647, 1.618 182, 1.617 978, 1.618 056, 1.618 026, 1.618 037, 1.618 033; ...
Then Fn +1 / Fn approaches increasingly j (Phi)
The decimal expansion will extend never be repeated (so it is an irrational number).
In fact, when they extend "Fibonacci ratios" indefinitely, the value generated close to the increasingly number of gold.
The Italian Leonardo Fibonacci was the first great mathematician in Europe during the Middle Ages. He was also known as Leonardo of Pisa. He was trained to be a businessman and began traveling from Pisa, his home town to other places.
During these trips other number systems studied and learned the Hindu-Arabic number system, he believed to be superior to the Roman numeral system. He also studied algebra and geometry by reading the works of Diophantus. Around 1200, he devoted his efforts to developing, writing and the application of mathematics.
Number of gold
The number of Gold is a mysterious and enigmatic irrational number that comes to us in a variety of elements of nature in the form of a reason, and is considered by many as a gift from God to the world.
The name given to this number, f (capital Phi) is the initial of the name of Phidias, sculptor and architect who was in charge of construction of the Parthenon in Athens.
An example of this wonder is the fact that if we draw a rectangle whose sides have a reason among themselves equal to the number of gold that can be divided into a square and another rectangle in which he has, too, the ratio between the two sides equal tonumber of Gold. This process can be repeated indefinitely keeping the ratio constant.
But what is the number of gold has to do with the Fibonacci sequence?
The number of gold has value j = (1 + Ö 5) / 2 (= 1.618 033 989 ...). As you remember the section of the Fibonacci sequence, we have the following sequence of numbers 1, 1, 2, 3 , 5, 8, 13, 21, 34, 55, 89, 144, 233 ....
If we divide these numbers by each of its antecedent, we note that this ratio will tend toward a certain value.
That is, if we F2/F1 = 1, 2 = F3/F2, F4/F3 = 1.5, F5/F4 = 1.6 (6), F6/F5 = 1.6 and if we continue so, we get the following sequence of numbers:
1.000 000, 2.000 000, 1.500 000, 1.666 666, 1.600 000, 1625 000, 1.615 385, 1.619 048, 1.617 647, 1.618 182, 1.617 978, 1.618 056, 1.618 026, 1.618 037, 1.618 033; ...
Then Fn +1 / Fn approaches increasingly j (Phi)
The decimal expansion will extend never be repeated (so it is an irrational number).
In fact, when they extend "Fibonacci ratios" indefinitely, the value generated close to the increasingly number of gold.
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