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 table.
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89
combo
results
1/1
2/1
3/2
5/3
8/5
13/8
21/13
34/21
55/34
89/55
What do you notice?
This is called the golden ratio. (Phi is 1·61803398874...) This is another special number
that appears in the world around us and (as you saw) is related to the Fibonacci series.
Fibonacci Series--Activity 3
Each hand has how many digits?
_______________
Each finger has how many bones?
_______________
Each finger has how many joints between the just
finger bones themselves?
_______________
Each finger has how many finger nails?
What pattern do you see?
_______________
_______________________________
Now pick one finger
Measure the length of each of the three segments; this is the easiest to do if the finger is bent.
Longest
_______________cm
Medium
_______________cm
Shortest
_______________cm
Now divide the longest length by the medium length, what do you get?
________________
Now divide the medium length by the shortest length, what do you get this time? ___________
What is the ratio?
____________________________________