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Approximations for PI

Many different approximations for the actual value of pi have been proposed and used. For each of the following, determine their accuracy to the nearest percent:

  • 256/81 [Egyptian value, 1700 BC]
  • 22/7 [Egyption value, 1000 BC]
  • 3+10/71 < Pi < 3+1/7 [Archimedes' approximation of a circle by a regular 96-gon]
  • SQRT(10) [Ch'ang Hong, China, 125 AD]
  • 31(1/3)
  • 666/212
  • 355/113 Ch'ung-chih, China, 470 AD]
  • 104348/33215
  • One of the roots of 9x4-240x2+1492=0