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In the text Liber Abaci written by Fibonacci in 1202, the following question was posed.
A man puts one pair of rabbits in a certain place entirely surrounded by a wall. How many pairs of rabbits can be produced from that pair in a year, if the nature of these rabbits is such that every month each pair bears a new pair which from the second month becomes productive?The number of pairs of rabbits in the nth month begins 1, 1, 2, 3, 5, 8, 13, 21, ... (often denoted u_{1}, u_{2}, u_{3} ...) where each term is the sum of the two terms preceding it. Mathematicians define this sequence recursively as follows: u_{1} = u_{2} = 1 and u_{n+1} = u_{n} + u_{n1} (n > 2)This sequence, now called the Fibonacci sequence, has an amazing number of applications in nature and art; it also has a tremendous number of interesting propertieswhich is reason enough for the journal "The Fibonacci Quarterly" to exist! Here we list just a few of these many properties. Let m and n be positive integers,
See Also: Fibonacci, FibonacciPrime, WallSunSunPrime, LucasNumber Related pages (outside of this work)
Chris K. Caldwell © 19992016 (all rights reserved)
