Fibonacci Sequence in Nature
Date: 12/08/97 at 17:52:22 From: Naseema Patel Subject: College Algebra I need examples of how the Fibonacci sequence is used in nature. I used the Internet to find examples, but I couldn't find any examples except the one I know: the Rabbit example. I need three more examples. Can you please help me? Thank you.
Date: 12/11/97 at 20:25:33 From: Doctor Steven Subject: Re: College Algebra Here's one. On a tree when a twig comes out from a branch, the next twig to come out from the branch will be slightly farther out on the branch and will be rotated about the branch at some angle. The next twig will come out farther along the branch, rotated at the same angle. Here's the clincher: the number of twigs needed for the last twig to come out of the branch at the same angle as the first twig is always a number that appears in the Fibonacci sequence, no matter what kind of tree it is. An apple tree might need 5 and a pear tree might need 8, but the number needed for any tree will always occur in the Fibonacci sequence. Another example of the Fibonacci sequence can be seen in a Nautilus shell. Those are those shells that curl around on themselves. Inside are little chambers and you guessed it - let's say the first chamber has a volume of 1; then the second chamber has a volume of 2, the third chamber has a volume of 3, the fourth has a volume of 5, and so on: the Fibonacci sequence. Two more examples: pineapples and turtles. One might ask what turtles and pineapples have in common, but the answer is of course the Fibonacci sequence (and their shells/rinds). A pineapple has shapes on its rind, bigger shapes on the bottom of it getting smaller as you go up. If you take one of the shapes on the bottom and go diagonally upward (to your right or left) you see that these shapes are basically the same only scaled to a smaller size as you go up. If we say the bottom has a size of 13, then we'll notice that the shape directly to the upper left (or right) has size 8. The shape to the upper left (or right) of this next shape has size 5, and so on down to one. The size you need to start with depends on the size of the pineapple and how many little shapes are in a sequence. For some turtles basically the same thing happens. Turtles have shells that have what I would call tiles on them (although I know that is not the correct term). These tiles are the same shape but appear in different sizes. The sizes correspond to entries in the Fibonacci sequence. If you want to read more about these examples, I found them in _Applied Combinatorics_ by Fred Roberts. (This book was written to be a graduate level textbook in mathematics.) -Doctor Steven, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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