Not exactly astronomy, but what the heck.
What you said about the Fibonacci numbers is true, but that's not how you need too look at them. They are defined by an iterative sum:
so if the first number is 1
then the second number is 1
then the third is the sum of first and second: 2
then the fourth is the sum of the 2nd and 3rd: 3
then the fifth is the sum of the 3rd and 4th: 5
and the sixth is the sum of the 4th and 5th: 8, and so on:
so the sequence is:
0,1,1,2,3,5,8,13,21,......
Now their relationship to phi (golden ratio is simple). Instead of adding the successive numbers together, compute their ratios:
2/1 = 2
3/2 =1.5
5/3 = 1.666666
and so on.
Therefore, if the nth fibanocci number is F(n), then phi is given by
limit as n goes to infinity of F(n+1)/F(n).
YOu can check it. Get the list of Fib numbers:
http://en.wikipedia.org/wiki/Fibonacci_numberand just take the ratios of two large, neighboring numbers
for instance:
F_20/F_19 = 6765/4181 = 1.61803, which is pretty close to phi:
http://en.wikipedia.org/wiki/Golden_ratiobut you need to take n to be infinitely large for it to be exact.
Hope this helps!
WHAT? This is exactly true. What you said about pi, is also accurate, both numbers are transcendental, but that doesn't make this wrong! Both numbers pi and phi can be calculated by infinite sums and products. It can be proven by very basic calculus.
So exactly what part did I say is wrong? The fact that they are the sum of the preceding values? Nope, it's true. That's how Fibonacci defined them. About that ratio of successive values? Nope, it was mathematically proven.