Quote Originally Posted by Tom View Post
x = sqrt(1 + x)

Pick any number for X. Repeat this about 10 times (using result from equation as new X). You've reached the golden ratio. Repeating 30 times to infinity and the integer remains at 1.618 (golden ratio). Ratios of successive Fibonacci numbers are all solutions to the golden ratio. The following example illustrates the relationship of the second Fibonacci member toward the first one, the relationship of the third member toward the second one, etc:

1:1 = 1.0000, less than phi for 0.6180

2:1 = 2.0000, more than phi for 0.3820

3:2 = 1.5000, less than phi for 0.1180

5:3 = 1.6667, more than phi for 0.0486

8:5 = 1.6000, less than phi 0.0180

The decimal result is of importance here. It is the ratio of the given sequence. As the Fibonacci sequence moves on, each new member will divide the next one, etc coming closer and closer to the unreachable phi.

Fibonacci numbers, while typically dismissed as bunk, are not just numerology and actually common in fields such as architecture and medicine. They're probably pretty useless for betting progression, however
I know. I was just poking fun at your choice of words. Precise statements are important in any discussion of mathematical facts.