Apart from pg's and Abigail-II's comments, I couldn't resist golfing these down to: 
1while($x||=3)-($x-=sin$x/cos$x);print"$x\n"

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and: 
1while($x||=2)-($x-=((log($x)-1)*$x));print"$x\n"

[download]

I particularly like the fact that it only uses 1 variable ;-)

Liz

Update:
Golfed some more by losing the seperate initial assignement of $x

In reply to Re: Deriving pi and e by liz
in thread Deriving pi and e by fredopalus

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