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If x is an approximation to the square root of n, then (x/2 + n/2x) is a closer approximation.

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drplokta
Nov. 30th, 2007 10:19 pm (UTC)
Clearly untrue. Zero is a (poor) approximation of root 2, and 0/2 + 2/0 is not a closer one.

I suspect it fails in all cases where x < 1. If we take 0.1 as an approximation of root 2, 0.1/2 + 2/0.2 is 10.05, which is considerably further from 1.414....

drplokta
Nov. 30th, 2007 10:23 pm (UTC)
Thinking about it, I now suspect that your formula gives a result that is closer on a log scale rather than a linear one. Neither of my counter-examples would disprove this.

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