Introduction: The Fibonacci Series
The Fibonacci Series is a sequence of numbers first created by Leonardo Fibonacci (fibonachee) in 1202. It is a deceptively simple series, but its ramifications and applications are nearly limitless. It has
fascinated and perplexed mathematicians
for over 700 years, and nearly everyone
who has worked with it has added a new
piece to the Fibonacci puzzle, a new tidbit
of information about the series and how it
works. Fibonacci mathematics is a
constantly expanding branch of number
theory, with more and more people being
Yellow flower with 8 petals, a Fibonacci
drawn into the complex subtleties of
Number.
Fibonacci's legacy.
The first two numbers in the series are one and one. To obtain each number of the series, you simply add the two numbers that came before it. In other words, each number of the series is the sum of the two numbers preceding it.
Note: Historically, some mathematicians have considered zero to be a Fibonacci number, placing it before the first 1 in the series. It is known as the zeroth Fibonacci number, and has no real practical merit. We will not consider zero to be a Fibonacci number in our discussion of the series.
Using a piece of graph paper, draw a spiral using the Fibonacci series. Starting in the center of the page, draw a 1 X 1 square, next to it draw another 1 X 1 square,
After, draw 2 X 2 squares touching the last two squares,
Then continue to add on squares until the graph paper is filled. To finish the spiral draw arcs (quarter circles) in each square starting in the center and working outward.
Do you notice any similarity to the spiral you have drawn and the image of the shell?
Fibonacci SeriesActivity 2
Take the Fibonacci sequence listed below and divide each pair of number and record the results in the...
...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...
...
The Golden Number
1.61803 39887 49894 84820 is by no means a number of memorization. However, it is a recognizable one. Never will you find a combination of numbers that is more significant than this one. This ratio is known as the Golden Number, or the GoldenRatio. This mystery number has been used throughout different aspects of life, such as art, architecture, and of course, mathematics. One may wonder where the...
...What is the GoldenRatio?
Most people are familiar with the number Pi because it can be found in so many different math problems and equations. There is, however, another irrational number like Pi. This number isn¡¦t as well known as Pi however. This number is called Phi. This number is also called the goldenratio. The goldenratio is equal to the square root of five plus one, divided by two. If you work...
...Fibonacci sequence in arithmetic sequence
The Fibonacci sequence is a series of numbers in which each number is the sum of the previous two. It starts with 0 and 1, which equals 1. Then 1 plus 2 equals 3, 2 plus 3 equals 5, and so on.
n mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation
With seed values[1]
The Fibonacci numbers are represented practically everywhere....
...info
Source: www.wayfaring.info
BASED ON GOLDENRATIO:
A golden rectangle is a rectangle whose side lengths are in the goldenratio, onetophi, that is, approximately 1:1.618. A distinctive feature of this shape is that when a square section is removed, the remainder is another golden rectangle, that is, with the same proportions as the first. Square removal can be repeated infinitely, which leads to...
...GOLDENRATIO maths project
Index
Serial no. chapter
1  Introduction 
2  History 
3  In nature 
4  In human body 
5  In architecture 
6  In art 
7  In day to day life 
8  SIGNIFICANCE 
ACKNOWLEDGEMENT
I would like to express my special thanks of gratitude to my teacher sonali durgam on the topic goldenratio, which also helped me in doing a lot of Research and I...
...The GoldenRatio
The goldenratio is a number used in mathematics, art, architecture, nature, and architecture. Also known as, the divine proportion, golden mean, or golden section it expresses the relationship that the sum of two quantities is to the larger quantity as is the larger is to the smaller. It is also a number often encountered when taking the ratios of differences in different...
...is the GoldenRatio
The golden ration can occur anywhere. The golden proportion is the ratio of the shorter length to the longer length which equals the ratio of the longer length to the sum of both lengths.
The goldenratio is a term used to describe proportioning in a piece. In a work of art or architecture, if one maintained a ratio of small elements to larger...
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