Fibonacci Sequence

Date: 06/18/2001 at 14:30:04
From: brandi barrigher
Subject: Fibonacci  sequence

I need help understanding what the Fibonacci sequence really is. I 
have visited many different Web sites, but they have the same 
information.

Date: 06/19/2001 at 21:25:48
From: Doctor Jodi
Subject: Re: Fibonacci  sequence

Hi Brandi,

The Fibonacci sequence is a sequence of numbers. Specifically, the 
sequence

   1, 1, 2, 3, 5, 8, 13, 21, ... 

How do you get the next term in the sequence? (You add the two 
previous terms.)

The Fibonacci sequence is named for Leonardo Pisano (his nickname was 
Fibonacci), an Italian educated in North Africa who lived around 1200 
A.D. This famous sequence arose in connection with the following 
problem, taken from a book Fibonacci published in 1202:

  A certain man put a pair of rabbits in a place surrounded on all 
  sides by a wall. How many pairs of rabbits can be produced from that 
  pair in a year if it is supposed that every month each pair begets a 
  new pair which from the second month on becomes productive? 

You can read more about Fibonacci's life from the MacTutor History of 
Mathematics archive:

  http://www-history.mcs.st-and.ac.uk/history/   

To find Fibonacci, go first to the Biographies Index and then select F 
from the alphabetical index.

I recommend making a table depicting the first few months of the 
rabbits' lives. Mature rabbits (which will bear a new pair of rabbits 
in the next month) should be colored one color (say red), while the 
newborn rabbits should be colored another (say green). (There's a 
beautiful illustration like this in a book called the _Number Devil_ 
by Hans Magnus Enzensberger.)

The ratios of consecutive pairs of numbers in the Fibonacci sequence 
(1/1, 2/1, 3/2, 5/3, 8/5, etc.) tend to the Golden Ratio. 

You can find more responses to questions about the Fibonacci sequence 
and the Golden Ratio in the high school area of the Dr. Math archives: 

   http://mathforum.org/dr.math/drmath.high.htmll   

and in the links to relevant sites on the Web in the  Dr. Math FAQ:

   http://mathforum.org/dr.math/faq/faq.golden.ratio.html   
 
Thanks for writing us and feel free to write back. 

- Doctor Jodi, The Math Forum
  http://mathforum.org/dr.math/