source file: mills2.txt Date: Thu, 6 Mar 1997 11:32:30 -0800 Subject: Irrationals From: John Chalmers As it happens, I have been reading Neugebauer "The Exact Sciences in Antiquity" and Heath. Archimedes stated that 3 1/7 < pi < 3 10/71, but Heron says that actually Archimedes found that 211872/67441 < pi < 195882/62351, but that these numbers were impractical for computation (the numbers in Heron's text are somewhat corrupt as 211875 and 197888, but Tannery restored the values above) (Heath vol 2, 329). Neugebauer claims that Greek computational methods developed independently from a basis of Babylonian mathematics and were more sophisticate, if less rigorous, than usually thought. However, the Babylonians often used just 3 for pi. --John Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 6 Mar 1997 20:36 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA07981; Thu, 6 Mar 1997 20:36:22 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA07946 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id LAA25003; Thu, 6 Mar 1997 11:34:44 -0800 Date: Thu, 6 Mar 1997 11:34:44 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu