source file: mills2.txt Date: Thu, 27 Feb 1997 15:01:22 -0800 Subject: RE: TUNING digest 998 From: rtomes@kcbbs.gen.nz (Ray Tomes) PAULE wrote: >''The idea of irrational numbers was too >repugnant to the ancient Greeks'' Daniel Wolf >This is simply a false statement. Pythagoreans were said to have known of >the irrationality of the square root of 2, in the 4th century BC, the >''three big problems'' were solved by Menaechmus and Dinostratus with conic >sections and the quadratrix (a transcendental curve), in the golden age of >Greek Mathematics (3rd century BC), all of the great figures (Archimedes, >Apollonius of Perga, Eratosthenes, Happarchus) used irrationals without >repugnance. Originally the ancient greek mathematics was entirely based on rationals and they believed that there were no other numbers. I read that the first guy who proved there were irrationals so upset the applecart that they took him out to sea and drowned him. The problem was that all their proofs assumed that only rational numbers existed and so were completely undermined. Later, they patched it up and were able to cope with irrationals. -- Ray Tomes -- rtomes@kcbbs.gen.nz -- Harmonics Theory -- http://www.kcbbs.gen.nz/users/rtomes/rt-home.htm Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 28 Feb 1997 00:04 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA32406; Fri, 28 Feb 1997 00:04:43 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA32384 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id PAA11421; Thu, 27 Feb 1997 15:02:07 -0800 Date: Thu, 27 Feb 1997 15:02:07 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu