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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