10.7. Fibonacci Numbers
Mathematical modeling is not a recent development, as Knuth makes plain in retelling the inquiry, first written by Fibonacci in the year 1202, “How many pairs of rabbits can be produced from a single pair in a year's time?” If the rabbits never die, then the population may grow in each reproductive generation to levels proportional to the integer sequence
1, 1, 2, 3, 5, 8, 13, 21, 34, …
known as the Fibonacci numbers. Centuries later the release of European rabbits in Australia, in the absence of effective predation, indeed led to a runaway population. Modern population biologists of course consider in their mathematical models such additional factors as food supply, predation, and death.
How can the sequence of Fibonacci ...
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