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, but the exact dates of his birth and death are not known. He played an important role in reviving ancient mathematics and made significant contributions of his own. Even though he was born in Italy, he was educated in North Africa where his father held a diplomatic post. He published a book called Liber abaci, in 1202, after his return to Italy and it was in this book that the Fibonacci numbers were first discussed. It was based on bits of Arithmetic and Algebra that Fibonacci had accumulated during his travels with his father. Liber abaci introduced the HinduArabic placevalued decimal system and the use of Arabic numerals into Europe. Though people were interested, this book was somewhat controversial because it contradicted some of the foremost Roman and Grecian Mathematicians of the time, and even proved many of their calculations to be false.
The Fibonacci sequence is also used in the Pascal triangle. The sum of each diagonal row is a Fibonacci number. They are also in the right sequence.
The Fibonacci sequence has been a big factor in many patterns of things in nature, which is quite fascinating. It's been discovered that the numbers representing the screwlike arrangements of leaves on flowers and trees are very often numbers in the Fibonacci sequence. On many plants, for instance, the number of petals is a Fibonacci number: buttercups have 5 petals; lilies and iris have 3 petals; some delphiniums have 8; corn marigolds have 13 petals; some asters...
...FibonacciSequenceFibonacci, also known as the Leonardo of Pisa, born in the early 1770’s AD in Pisa, Italy, has had a huge impact on today’s math, and is used in everyday jobs all over the world. After living with his dad, a North African educator, he discovered these ways of math by traveling along the Mediterranean Coast learning their ways of math. With the inspiration from the “HinduArabic” numerical system, Fibonacci created...
...the hypothesis was to look for patterns in nature focusing in the Fibonaccisequence 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...
...Anatolia College 
Mathematics HL investigation

The Fibonaccisequence 
Christos Vassos

Introduction
In this investigation we are going to examine the Fibonaccisequence 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 Fibonaccisequence...
...that Fibonacci investigated (in the year 1202) was about how fast rabbits could breed in ideal circumstances.
Suppose a newlyborn 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...
...
The Fibonaccisequence
The Fibonaccisequence 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...
...follow is called a Fibonaccisequence 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...
...SEQUENCE
* In mathematics, informally speaking, a sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements, or terms). The number of ordered elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. Most precisely, a sequence can be defined...
...particularly that of the Fibonaccisequence and the Golden Ratio. In Debussy’s Nocturne, composed in 1892, I look into the use of the Fibonaccisequence and the Golden Ratio. Previously it has been noted that composers used the Fibonaccisequence 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...
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