Archimedes and the measurement of the circle: A new interpretation

@article{Knorr1976ArchimedesAT,
  title={Archimedes and the measurement of the circle: A new interpretation},
  author={Wilbur Richard Knorr},
  journal={Archive for History of Exact Sciences},
  year={1976},
  volume={15},
  pages={115-140}
}
  • W. Knorr
  • Published 1 June 1976
  • Physics
  • Archive for History of Exact Sciences
In the third propos i t ion of the Dimensio Circuti, ARCHIMEDES established 3-~ as an upper bound , 3~7~ ° as a lower b o u n d for the ra t io of the perimeter to the diameter of the circle. EUTOCIUS remarks that APOLLONIUS derived bounds even more accurate. 1 I shall argue in the present study that ARCHIMEDES himself in t roduced such refinements, yielding bounds at least twenty times more accurate than those in the Dimensio Circuli. A close examina t ion of these computa t ions will affirm… 
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