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### Fibonacci Sequence

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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/
```
Associated Topics:
High School Fibonacci Sequence/Golden Ratio

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