The Fibonacci sequence The Fibonacci sequence is a series of numbers developed by Leonardo Fibonacci as a means of solving a practical problem. The original problem that Fibonacci investigated‚ in the year 1202‚ was about how fast rabbits could breed in ideal circumstances. Suppose a newly born pair of rabbits‚ one male‚ one female‚ are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose that
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follow is called a Fibonacci sequence and is often found in nature as well. Many instances in which the Fibonacci Series is present in nature are that a lot of flowers and cone shaped structures have the number of petals as one of the Fibonacci numbers. However some plants such as the sneezewort plant (as seen left) can be seen demonstrating the Fibonacci pattern in succession. It happens on both the number of stems and number of leaves. Another appearance of the Fibonacci Series in nature
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The Discovery of the Fibonacci Sequence A man named Leonardo Pisano‚ who was known by his nickname‚ "Fibonacci"‚ and named the series after himself‚ first discovered the Fibonacci sequence around 1200 A.D. The Fibonacci sequence is a sequence in which each term is the sum of the 2 numbers preceding it. The first 10 Fibonacci numbers are: (1‚ 1‚ 2‚ 3‚ 5‚ 8‚ 13‚ 21‚ 34‚ 55‚ 89). These numbers are obviously recursive. Fibonacci was born around 1170 in Italy‚ and he died around 1240 in Italy
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that Fibonacci investigated (in the year 1202) was about how fast rabbits could breed in ideal circumstances. Suppose a newly-born pair of rabbits‚ one male‚ one female‚ are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose that our rabbits never dieand that the female always produces one new pair (one male‚ one female) every month from the second month on. The puzzle that Fibonacci posed
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the hypothesis was to look for patterns in nature focusing in the Fibonacci sequence as a main and looking for angles. What was first done was to count a pine cone’s pieces‚ a flower’s petals‚ a celery‚ and grapes to find the Fibbonacci sequence which not found only on the celey and on the flower‚ elsewhere the Fibonacci was there. After finishing the experiment I started noticing more patterns relating to the Fibonacci sequence. For example‚ in a tree you start counting by the tree trunk; if you
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particularly that of the Fibonacci sequence and the Golden Ratio. In Debussy’s Nocturne‚ composed in 1892‚ I look into the use of the Fibonacci sequence and the Golden Ratio. Previously it has been noted that composers used the Fibonacci sequence and the Golden Ratio in terms of form‚ however in my analysis I look into the use of it in terms of notation as well. I will explore how the idea of Sonata form is used along with the Mathematical Model of the Fibonacci sequence. It is however important
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Anatolia College | Mathematics HL investigation | The Fibonacci sequence | Christos Vassos | Introduction In this investigation we are going to examine the Fibonacci sequence and investigate some of its aspects by forming conjectures and trying to prove them. Finally‚ we are going to reach a conclusion about the conjectures we have previously established. Segment 1: The Fibonacci sequence The Fibonacci sequence can be defined as the following recursive function: Fn=un-1+
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E-mail: shed30rar@aol.com Leonardo Fibonacci Leonardo Fibonacci was born in Pisa‚ Italy around 1175 to Guilielmo Bonacci. Leonardo’s father was the secretary of the Republic of Pisa and directed the Pisan trading colony. His father intended on Leonardo becoming a merchant. His father enlisted him in the Pisan Republic‚ sending him to various countries. As Leonardo continued to travel with his father‚ he acquired mathematical skills while in Bugia. Fibonacci continued to study throughout his travels
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Assignment: The Fibonacci Sequence Find three examples of the Fibonacci sequence in nature. Write a paragraph describing each example. Include photos or graphics in your explanation. For each example answer the following questions: How does the example relate to the Fibonacci sequence? What portions of each item or situation display the Fibonacci sequence? How could the Fibonacci sequence help you solve a problem involving the item or situation? Document your sources and use the rubric as a guide
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Leonardo Fibonacci was born around 1170 A.D.‚ and died around 1250 A.D. He was born in Pisa‚ Italy and died there too. Leonardo’s mom was Alessandra‚ and she died when he was nine. His father was Guglielmo Bonacci‚ who directed a trading post Bugia‚ Barbary. As a young boy‚ Leonardo traveled there to help him‚ and that’s where he learned about the Hindu-Arabic numeral system. He recognized that arithmetic with Hindu-Arabic numerals is simpler and more efficient that with Roman numerals and so he
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