Revision as of 07:15, 29 December 2007 by imported>Wlodzimierz Holsztynski
In mathematics, the Fibonacci numbers form a sequence defined by the following recurrence relation:
The sequence of fibonacci numbers start: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, ...
Fibonacci numbers and the rabbits
The sequence of fibonacci numbers was first used, to repesent the growth of a colony of rabbits, starting with one pair of rabbits.
Properties
- The quotient of two consecutive fibonacci numbers converges to the golden ratio:
- If divides then divides
- If is a prime number, then is also a prime number.
Direct formula
Let and . Let
Then:
- and
- hence
- hence
for every . Thus for every , i.e.
for every . Furthermore:
It follows that
is the nearest integer to
for every .
Further reading