Golden Ratio and Fibonacci Series

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  • Topic: Golden ratio, Fibonacci number, Fibonacci
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  • Published : October 22, 2012
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Introduction: The Fibonacci Series
The Fibonacci Series is a sequence of numbers first created by Leonardo Fibonacci (fibo-na-chee) 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.

http://library.thinkquest.org/27890/mainIndex.html
Series:
(0,) 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…

EXAMPLE IN NATURE

Fibonacci Series--Activity 1

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 Series--Activity 2
Take the Fibonacci sequence listed below and divide each pair of number and record the results in the...
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