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Fibonacci

            Leonardo Pisano is better known by his nickname, Fibonacci.
             Guilielmo and a member of the Bonacci family. Fibonacci himself sometimes used the name Bigollo, which may mean good-for-nothing or a traveler. Fibonacci was born in Italy but was educated in North Africa where his father held a diplomatic post. His father's job was to represent the merchants of the Republic of Pisa who were trading in Bugia, later called Bougie and now called Bejaia. Fibonacci was taught mathematics in Bugia and traveled widely with his father, and he recognized the advantages of the mathematical systems used in the countries they visited. .
             Fibonacci ended his travels around the year 1200 and at that time he returned to Pisa. There he wrote a number of important texts which played an important role in reviving ancient mathematical skills and he also made significant contributions of his own. He was one of the first people to introduce the Hindu-Arabic number system into Europe - the positional system we use today. His book on how to do arithmetic in the decimal system, called Liber abbaci, was completed in 1202 and persuaded many European mathematicians of his day to use this "new" system. One might have thought that at a time when Europe was little interested in scholarship, Fibonacci would have been largely ignored. However, widespread interest in his work undoubtedly contributed strongly to his importance. .
             In Fibonacci's book he introduces a problem for his readers to use to practice their.
             arithmetic: a pair of rabbits are put in a field and, if rabbits take a month to .
             become mature and then produce a new pair every month.
             after that, how many pairs will there be in twelve months time? .
             He assumes none of the rabbits escape or die. When the problem is solved, the answer involves this series of numbers: , 1, 2, 3, 5, 8, 13, 21, . in which each number is the sum of the previous two. These answers are defined by the following recursive equation: .


Essays Related to Fibonacci

1. Fibonacci Sequence

... two terms immediately preceding it or in an algebratic expression Fk=Fk-1+Fk-2 (Ram, Rajesh). From here we get the beginning of the sequence as 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, Fibonacci sequences have proven useful in number theory, geometry, the theory of continued fractions, genetics, computer science, and many other fields. They also arise in many unrelated phenomena, for example, the ... representation of a number which, when multiplied by itself, is the same as itself plus 1 [ µ2- µ-1=0]. µ = 1.618033989... µ2 = 2.618033989... µ+1 = 2.618033989..." (Conklin). The exact represe...

  • Word Count: 3003
  • Approx Pages: 12
  • Grade Level: High School

2. Leonardo Pisano Fibonacci

... of irrational numbers the Euclid approached from geometric point of view. During the time Europe had little interest in scholars, which would have made Fibonacci being ignored by most. But on the contrary there was much interest in his work, thus making him important. Being a contemporary of Jordanus ... , he was a sophisticated mathematician who was clearly recognized by his many achievements. Fibonacci was famous for his practical applications not for his abstract theorems. Crowned King of Germany in 1212, the Holy Roman Emperor Frederick the ... problems concerned; the price of good,...

  • Word Count: 999
  • Approx Pages: 4
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3. Math in Art

... to 1.618: 1, and its inverse .618: 1, has also been known to show up throughout musical history. Explanations of the Golden Mean can be seen with a brief description of the Fibonacci sequence. The Fibonacci sequence comes up everywhere in nature from the branches and leaves on trees, to the reproductive cycle of certain animals. Numerically shown as 1, 1, 2, 3, 5, 8, 13, 21 with each number being ... nautilus shell. The true growth-curve ratio of a nautilus is slightly higher than the golden ratio by about three percent, so minor deviations may be seen (Fletcher). We find the Fibonacci ...

  • Word Count: 3373
  • Approx Pages: 13
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4. Math in Music

... were found more aesthetically pleasing to the ear. There is even a link between the method used in Gregorian chants and the Fibonacci pattern discovered around that same time in Italy (Garland 51). The Fibonacci pattern consists of 0, 1, 1, 2, 3, 5, 8, 13, 21, etc., and continue with the sum of the two ... numbers prior. Found in many other realms of nature and art, the Fibonacci series is considered to be naturally pleasing to the senses (Garland 13). This idea is translated into the earliest American hymns. Many Appalachain tunes ... of Wolfgang Amadeus Mozart. In his sonorous melodi...

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5. History of the Quadratic Equation

... moneys, weights and measures used in the various Italian states; a treatise on double-entry bookkeeping; and a summary of Euclid's geometry. He admitted to having borrowed freely from Euclid, Boethius, Sacrobosco, Fibonacci, ... The geometrical part of Pacioli's Summa is discussed in detail by Glushkova and Glushkov. The authors write: The geometrical part of L Pacioli's Summa [Venice, 1494] in Italian is one of ... the earliest printed mathematical books. Pacioli broadly used Euclid's Elements, retelling some parts of it. He referred also to Leonardo of Pisa (Fibonacci). Other interest...

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6. Topic Summary - Aesthetics

... has been noted that the painting has an extremely pleasing and harmonious composition, demonstrating the Golden Mean, which gives a pattern that is close to patterns in nature based on the Fibonacci numbers, this is illustrated in the example below, although you can apply the Golden Mean in all four corners of this painting. Meaningful eye states It works no matter how ... ...

  • Word Count: 2825
  • Approx Pages: 11
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  • Grade Level: Undergraduate

7. Arabs

... to the growth of Europe. By the year 800, Arabic mathematicians had learned these tools and the place- valued decimal system from the scholars of India. Four hundred years later, Fibonacci wrote his groundbreaking Liber abaci to introduce modern (Arabic) numerals and the Hindu-Arabic decimal system to a Europe still muddling with Roman numerals. The word 'algebra' is Arabic, from the ... ...

  • Word Count: 695
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8. The Da Vinci Code

... tracking device while Robert and Sophie investigate the crime scene. Robert and Sophie use some of the numbers scribbled by Sanuiere to open a bank vault. The numbers formed the famous Fibonacci sequence. The bank vault contains a box holding a cryptex. Leonardo DaVinci invented the cryptex. A cryptex is a way of keeping a message secret. If a person puts in the wrong password, the cryptex contains ... ...

  • Word Count: 1135
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9. Math and Music

... at a piece of music or listening to music, no one would really associate math with music. Fractions are also involved in harmonies and with what notes sound good together. The Fibonacci sequence is involved aside the Golden Section. Decibels are also involved in music. Basically a decibel is the amount of the music you can hear. Noise ordinances don't allow music over ... ...

  • Word Count: 383
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