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Q&A #1864


Fibonacci Sequence

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From: Suzanne (for Teacher2Teacher Service)
Date: Aug 12, 1999 at 18:24:37
Subject: Re: Fibonacci Sequence

Amy,

There is a book called Fascinating Fibonacci written by Trudi Hammel Garland.
It is perfect for the late elementary grade student.  It discusses finding
numbers from the Fibonacci sequence in areas of nature--pine cones, sea
shells, artichokes, sunflowers, and many other flowers and plants. It also
explains the connection between this sequence and 0.618034 which is the
golden ratio. All the students need to do is divide each number in the
sequence by the next one and they will see how close they come to the golden
ratio.
EX:  5/8 = .625000
     8/13= .615384
     13/21=.619047
     21/34=.617647
     34/55=.618181
     55/89=.617977

They could then find things that really have these measurements or near to
them, such as index cards 3x5 or 5x8 or pieces of art work.
Students could look for this sequence on the piano.  One (1) octave is made
of 2 black keys, 3 black keys, 5 total black keys, 8 white keys, for a total
of 13 notes.

Of course there is the classic rabbit problem.  How many pairs of rabbits
will there be after one year if it is assumed that every month each pair
produces one new pair, which begins to bear young after two months after its
own birth?  This problem needs to be done in a diagram fashion and it does
not take long to realize that the numbers are the Fibonacci numbers and the
answer is 377 pairs.

  If you want to do a lot with the Fibonacci sequence the book would be
helpful as some of the activities are too difficult to explain without
diagrams.  There is also a book called Historical Connections in Mathematics
Vol. III which is put out by the AIMS Education Foundation.

Good luck.

-Suzanne, for the Teacher2Teacher service

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