# Golden Ratio and 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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