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|
2.2 FIBONACCI NUMBERS
The numbers in the bottom row are called Fibonacci numbers, and the sequence is the Fibonacci sequence. Table A.2 in the Appendix lists ...