The Fibonacci Sequence

by Fibonicci on April 10, 2011


 
The Fibonacci sequence has been named after Leonardo of Pisa also known as Fibonacci (a mix of the words Filius Bonacci, which means son of Bonacci). He first described this sequence in the year 1202 in his book Liber Abaci. Although he is seen as the first who discovered this sequence, It was later discovered that this sequence was already known by Indian mathematicians.

 

The Fibonacci sequence:

0, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 …

 
Each element in the sequence comes by adding the last two elements. For instance, the number 13 is achieved by adding the numbers 5 and 8 and the number 21 is achieved by adding 8 with 13. You might not help wondering why is the sequence so famous? What is Fibonacci? The explanation can be seen if the sequence is depicted visually since then it becomes clear that the sequences describes a growth pattern in nature. See the picture below which explains the fibonacci spiral.
 

the fibonacci sequence explained

 
The number 1 in the sequence stands for a square with each side 1 long. The number 2 stands for a square of 2 by 2 and so on. If the sides of the square are placed next to each other a new side of a larger square forms as explained before, e.g. 2+3 gives 5 and same goes for the squares. This can be repeated till infinity and with each step the squares get larger. Thing that is so special about this sequence can be seen when a line is drawn trough the cross points.
 

examples of the fibonacci sequence in nature

 
With these picture is becomes apparent what the sequence actually represents. This pattern is seen in many natural ophenomeneon, for example in a nautilus or even in the shape of a galaxy, but it doesn end here. The sequence also has a connection with the golden ratio.
 

The life of Fibonacci
Fibonacci in Tool’s song Lateralus

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Leonardo Fibonacci

by Fibonicci on April 10, 2011


 
Leonardo Fibonacci was born in Pisa, Italy around 1170. His father Guglielmo was nicknamed Bonaccio which means “good natured” or “simple”). Leonardo’s mother, Alessandra, died when he was nine years old. Leonardo was posthumously given the nickname Fibonacci (derived from filius Bonacci, meaning son of Bonaccio).

Guglielmo directed a trading post (by some accounts he was the consultant for Pisa) in Bugia, a port east of Algiers in the Almohad dynasty’s sultanate in North Africa (now Bejaia, Algeria). As a young boy, Leonardo traveled there to help him. This is where he learned about the Hindu-Arabic numeral system.

Recognizing that arithmetic with Hindu-Arabic numerals is simpler and more efficient than with Roman numerals, Fibonacci traveled throughout the Mediterranean world to study under the leading Arab mathematicians of the time. Leonardo returned from his travels around 1200. In 1202, at age 32, he published what he had learned in: Liber Abaci which means “Book of Abacus” or “Book of Calculation”, and thereby introduced Hindu-Arabic numerals to Europe.

Leonardo became an amicable guest of the Emperor Frederick II, who enjoyed mathematics and science. In 1240 the Republic of Pisa honored Leonardo, referred to as Leonardo Bigollo, by granting him a salary.

In the 19th century, a statue of Fibonacci was constructed and erected in Pisa. Today it is located in the western gallery of the Camposanto, historical cemetery on the Piazza dei Miracoli.

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Fibonacci in Tool’s Lateralus

April 10, 2011

  The fibonacci sequence can also be found in various artworks throughout history. Fibonacci Sequence + Lateralus Mathematical significance Maynard James Keenan’s vocals during the first few minutes of Lateralus form a Fibonacci sequence. The number of syllables progress to the sixth step, then back down to the first step; up to the seventh step, [...]

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