• DOI:10.1007/BF00348496
• Corpus ID: 120954547

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 that the classical Greek mathematics , domina ted by an interest in theoretical geometry, yet included expertise in practical arithmetic. HERO reports as follows of ARCHIMEDES' measu remen t of the circle (Metrica I, 25): Archimedes proves in his work on plinthides and cylinders that of every circle the perimeter has to the diameter a greater rat io than 211875:67441, but a lesser rat io than 197888:62351. But since these numbers are not wellsuited for practical measurements , they are brought down to very small numbers , such as 22: 7. 2