What are some examples of exact forms of the golden ratio?

[mesa]

Hello all, I am looking for exact forms (as real number expressions) of the golden ration that are not rewrites of the one we all know and love, i.e.

g.r. = 1/2(5^(1/2)+1)


Searches in Google have yielded nothing so far :P

 

[micromass]

http://en.wikipedia.org/wiki/Golden_ratio#Alternative_forms

 

[mesa]

http://en.wikipedia.org/wiki/Golden_ratio#Alternative_forms

A good link, but I had already seen it. The trigonometric versions are just substitutions of the same expression, ø = 1/2(5^(1/2)+1).

I also checked out Wolfram and I noticed this,

ø=2^(-1/v)(5^(1/2)F_v+(5(F_v^2)-4cos(v∏))^(1/v)

which is a wonderful general form!

Anyone else have anything to add?