A FEST for the stupidissimos:
PHI = 1.618
Leonardo Fibonacci who lived in the thirteenth century. In "Liber Abaci" (the best known of his three major works published) the Fibonacci sequence is first presented as a solution to a mathematical problem involving the reproduction rate of rabbits. The number sequence presented is
1,1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, ...
The sequence has a number of interesting properties. The two most noteworthy ones are first, each Fibonacci number is the sum of the two numbers preceding it, thus it is an additive sequence.
For example, 3 and 5 equals 8, 5 and 8 equals 13, 8 and 13 equals 21 etc; and second, the ratio of each Fibonacci number to its preceding number is alternately greater or smaller than the golden ratio. As the sequence continues, the ratio approaches the golden ratio, 1.6180339..., known also as "phi". For example: 144 / 89 = 1.617977, 233 / 144 = 1.618055 etc. The ratio of any number to its higher number approaches .618, after the first four numbers. For example, 144 / 233 = 0.618025 etc. Notice the values of 1.00 (1 / 1), .50 (1 / 2) and .67 (2 / 3) that area also important retracement levels (see "Fibonacci and phi in nature")
Here is a partial list of other intriguing properties of Fibonacci numbers.
- the sum of any ten consecutive Fibonacci numbers is divisible by 11
- every third Fibonacci number is divisible by 3, every fourth is divisible by 5,
every sixth is divisible by 8, etc. (divisors being Fibonacci numbers).
