25 Jun
2004
25 Jun
'04
9:27 a.m.
----- Original Message -----
From: "Antonio Carlini" <arcarlini(a)iee.org>
To: "'General Discussion: On-Topic and Off-Topic Posts'"
<cctalk(a)classiccmp.org>
Sent: Wednesday, June 23, 2004 11:42 PM
Subject: RE: Modern Electronics (was Re: List charter mods & headcount... ;
I couldn't remember either , but for all those of us who like revisiting old
ground .......
http://www.nist.gov/dads/HTML/squareRoot.html
Gives us the answer. - Yes , I remember now, - it seemed impressive at
the time - still does , It fills me full of admiration for Newton . Remember
that this is only the end product of whatever was going on in his mind -
when you see his elegant proofs for what was the beginning of calculus -
differentiation etc. , you feel extremely humble.
Now , about those pyramids.......................
Geoff.
I've had many an argument with my father over
this. He
insists on using
the binomial expansion. I prefer the Newton iteration, which
converges
very quickly
[ To find sqrt(A)
Set X(0) = A/2 (or some other suitable initial guess)
Repeat
X(N+1) = ( (A/X(N)) + X(N) ) / 2
Unti X(N) and X(N+1) are sufficiently close
Return X(N+1)
]
There's also a method I learnt long ago
that is laid out in the same way as
a long division. I've forgotten it
because it seemed moderately pointless!
I've forgotten it so thoroughly thatI've
even forgotten whether it had a name or not.
Antonio