Chapter 9: Spiral Growth in Nature: Fibonacci Numbers and the Golden Ratio
Internet Excursions


The Fibonacci Numbers And The Golden Ratio In Nature

One of the most impressive things about the Fibonacci numbers is the frequency with which they occur in nature. Fibonacci numbers appear in flowers, in shells, in vegetables, in pine cones, and even in models of the reproduction of rabbits and bees.

An introduction to Fibonacci numbers and the golden ratio in nature can be found by clicking here . Be sure to view the Quick Time animations involving the positions of seeds on flowerheads.

1.  

Suppose each female rabbit took three months to begin reproducing rabbits instead of two. How would you calculate each term in the new sequence? Write down the first ten terms of the new sequence.

2.  

Now suppose that, after the usual two months, each female produces two new pairs per month, instead of one pair. How would you calculate each term in the new sequence? Write down the first ten terms of the new sequence.

3.  

Briefly explain how the Fibonacci numbers occur in populations of bees.

4.  

Why is the pattern produced using a turn of symbol called an optimal packing? Describe the difference between the seed patterns produced using a turn of symbol between successive seeds and a turn of 0.61.

5.  

Predict what the seed pattern would look like using a turn of 0.25 between successive seeds. Then predict what it would look like using a turn of 0.35.


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