Is this equality valid? I just noticed it, and I haven't heard of it before.
$\displaystyle 2cos(\frac{\pi }{5})=\varphi,~where~\varphi~is~the~golden~ratio. $
Found using Google in t < 60 seconds:
http://www.theproblemsite.com/thegol...igonometry.asp
Golden ratio and special angles — The Endeavour