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FIBONACCI NUMBERS

It may be hard to define mathematical beauty,

but that is true of beauty of any kind.

— G.H. Hardy (1877–1947), A Mathematician's Apology

2.1 FIBONACCI'S RABBITS

Fibonacci's Classic work, Liber Abaci, contains many elementary problems, including the following famous problem about rabbits:

Suppose there are two newborn rabbits, one male and the other female. Find the number of rabbits produced in a year if:

  • Each pair takes one month to become mature;
  • Each pair produces a mixed pair every month, beginning with the second month; and
  • Rabbits are immortal.

Suppose, for convenience, that the original pair of rabbits was born on January 1. They take a month to become mature, so there is still only one pair on February 1. On March 1, they are two months old and produce a new mixed pair, a total of two pairs. Continuing like this, there will be three pairs on April 1, five pairs on May 1, and so on; see the last row of Table 2.1.

Table 2.1 Growth of the Rabbit Population

Number of Pairs Jan Feb Mar Apr May Jun Jul Aug
Adults 0 1 1 2 3 5 8 13
Babies 1 0 1 1 2 3 5 8
Total 1 1 2 3 5 8 13 21

2.2 FIBONACCI NUMBERS

The numbers in the bottom row are called Fibonacci numbers, and the sequence c02-math-001 is the Fibonacci sequence. Table A.2 in the Appendix lists ...

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