Powers of Phi

Curiosity impels me to study the Powers of Phi.

I am trying to discover for myself any more Equations and Correlations.
And here is one.  It is already known,
for I  saw it on Wikipedia after I had figured it out for myself.
Dr Ron Knott's Fibonacci website is famous.
You can find there "what's new" to do with powers of Phi.
He also distinguishes between Phi and phi ( 1.61803 and 0.61803, respectively.)






Here might be something new.
Imagine there are more Golden Means, not only Fn / Fn-1
There is Fn / Fn-2,  Fn /Fn-3, ........Fn / Fn-20,    etc.
I like to call them Phi One,  Phi two,  Phi three,  .... Phi Twenty.......etc.

Compare both Tables.  There are Correlations.

The numbers might be different if taken to 4 decimal places only.

.  I have published back in  "Fibonacci Equations", post Nov 21, 2010  part 8.

The ratio results use many Fibonacci numbers, 

showing how amazingly exact and consistent the values are, especially for larger numbers!

.eg  For Fn / Fn-10         F26 / F16 = 75025 / 610 = 122.9918

F36 / F26 = 9227465 / 75022 = 122.99186

I have to check my  numbers because there were errors in my early calculations for The Fibonacci Series.  We can check with Dr Knott's website-  he has published the first 500 numbers in the series.