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July 29, 2013

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Ray Girvan

This is a bit of a puzzle; I can't see what algorithm he's using. For instance, for sqrt(309), I see how he gets 17 + 10/17 as a first approximation:

309 = 289 + 20 = 17(17 + 20/17)
That gives two terms: 17 is an underestimate, and 17 + 20/17 an overestimate, so their mean 17 + 10/17 is a better approximation than either.

But where does that 6 come from, that he uses to derive the next iteration?


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