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The Fibonacci sequence was invented by the Italian Leonardo Pisano Bigollo (1180-1250), who is known in mathematical history by several names: Leonardo of Pisa (Pisano means "from Pisa") and Fibonacci (which means "son of Bonacci").
Fibonacci, the son of an Italian businessman from the city of Pisa, grew up in a trading colony in North Africa during the Middle Ages. Italians were some of the western world's most proficient traders and merchants during the Middle Ages, and they needed arithmetic to keep track of their commercial transactions. Mathematical calculations were made using the Roman numeral system (I, II, III, IV, V, VI, etc.), but that system made it hard to do the addition, subtraction, multiplication, and division that merchants needed to keep track of their transactions.
While growing up in North Africa, Fibonacci learned the more efficient Hindu-Arabic system of arithmetical. It is ironic that, despite his many achievements Fibonacci is remembered today mainly because the 19th century number theorist Edouard Lucas attached his name to a certain infinite set of positive integers that arose in a trivial problem in the Liber Abaci. This celebrated the sequence of integers occurs in nature in a variety of unexpected ways.
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89
For instance, lilies have 3 petals, buttercups 5, marigolds 13, asters 21, while most daisies have 34,55 or 89 petals.
The seeds of a sunflower head radiate from its center in two families of interlaced spirals, one winding clockwise and the other counterclockwise. There are usually 34 spirals twisting clockwise and 55 in the opposite direction.
Fibonacci Sequence seen in a Sunflower
Liber Abaci posed, and solved, a problem involving the growth of a population of rabbits based on idealized assumptions. The solution, generation by generation, was a sequence of numbers later known as Fibonacci numbers. Although Fibonacci's Liber Abaci contains the earliest known description of the sequence outside of India, the sequence had been noted by Indian mathematicians as early as the sixth century.
In the Fibonacci sequence of numbers, each number is the sum of the previous two numbers. Fibonacci began the sequence not with 0, 1, 1, 2, as modern mathematicians do but with 1,1, 2, etc. He carried the calculation up to the thirteenth place (fourteenth in modern counting), that is 233, though another manuscript carries it to the next place: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377.[21][22] Fibonacci did not speak about the golden ratio as the limit of the ratio of consecutive numbers in this sequence.
#Applications
The Fibonacci sequence can also be found in various artworks throughout history.
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, and then back to the fourth step:
The Fibonacci sequence shares a relationship with Phi, the golden ratio. The golden ratio is used to describe spirals, which are mentioned several times in the lyrics: “Swing on the spiral of our divinity and still be human”, “Spiral out, keep going” twice, and “Spiral out, keep going.” five times. Also, Keenan first begins singing 1 minute and 37 seconds into the song, which equates to 1.617 minutes (the golden ratio = approximately 1.618).
The time signatures of the chorus change from 9/8 to 8/8 to 7/8, symbolizing a spiral.
In addition, the number 987 is part of the Fibonacci sequence.
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The famous painting of Mona Lisa has a deep relationship with the Sequence.
The Fibonacci Sequence is rich in itself and is perhaps an answer to many unknown facts of the universe.
If you want to learn more about the richness of this sequence you can visit the following links listed below:
What are some interesting facts about the Fibonacci series