Archimedes and the measurement of the circle: A new interpretation

  title={Archimedes and the measurement of the circle: A new interpretation},
  author={Wilbur Richard Knorr},
  journal={Archive for History of Exact Sciences},
  • 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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A History of Mathematics.
Origins. Egypt. Mesopotamia. Ionia and the Pythagoreans. The Heroic Age. The Age of Plato and Aristotle. Euclid of Alexandria. Archimedes of Syracuse. Apollonius of Perga. Greek Trigonometry and
Mathematics in Aristotle
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A history of Greek mathematics
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A History of Greek Mathematics, 2 vol., Oxford, 1921
  • 1921