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As in the title, when looking at the Wikipedia page, it seems that the more terms the Machin-like formula the better. Could someone explain this to me?

I think it is for two reasons:

  1. It is easier to "split up" the computation. I can compute one term on one computer, another term on another etc. I have tenuous grasp on computational efficiency so I do not know if this makes any difference for computers.
  2. The smaller the numbers are inside arctan the smaller the number of terms needed to evaluate arctan to a given degree of accuracy.

Are my reasons correct? IS there a better reason as to why the formulas used to approximate pi have more and more terms?

2132123
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1 Answers1

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It is mostly the second reason. To be able to use smaller arguments, more terms are in general needed. If the arguments are mostly dyadic powers, then the computation of the series is greatly simplified on a binary computer. So one might accept a few additional terms to get that.

Lutz Lehmann
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