Archimedes' calculations of square roots

Details Archimedes' calculations of square roots Archimedes' calculations of square roots

2011-01-03

arxiv.org/abs/1101.0492v1

Mathematics

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15 pages

Scientific paper

We reconsider Archimedes' evaluations of several square roots in 'Measurement of a Circle'. We show that several methods proposed over the last century or so for his evaluations fail one or more criteria of plausibility. We also provide internal evidence that he probably used an interpolation technique. The conclusions are relevant to the precise calculations by which he obtained upper and lower bounds on pi.

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