Jim Henderson wrote:
>
> *ding* - light bulb just went on here.  I was trying to figure this one 
> out, and it just intuitively appeared to me.
> 

It's that sort of moment of epiphany that I love about learning this 
sort of stuff.  One moment it seems totally false and the next moment it 
somehow makes sense, a bit it seems obvious!

 > The weird thing is that I can't even explain it, but I understand it.

As for the proof, this site explains it reasonably well i think: 
http://www.math.hmc.edu/funfacts/ffiles/30001.3-4.shtml

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