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From: Russell Hendel <rhendel@saber.towson.edu> Date: Mon, 21 Aug 2000 20:43:01 -0400 (EDT) Subject: The Talmud did NOT believe that PI=3 Avi Levi (v33n16) asks, regarding the gmaras derivation from 1Kings7:23 that the ratio of the circumference and diameter of a circle is 3, whether there are similar derivations in the Talmud of empirical facts from verses. I just wanted to clarify a misconception about this "pi=3" gmarra. As tosafot points out no one in the Talmud really believed that pi=3 (See tosafot succah 8 on the talmudic statement that the square root of 2 is 7/5). Rather, the talmudic statement "pi=3" means that in an ***unspecified** sale of a circular plot of land (ie "I sell you a circular plot of land with A diameter of 200 ft at $10.00 a square foot"), in such a sale, we are **allowed** to **approximate** pi as 3 in computing prices. Thus in the cited example if nothing else was stated in the sales contract then I would be allowed to pay for the circular plot of land with radius 100', 3*100*100*$10=$300,000 (and I could not be sued for the extra $14,159). On the other hand (as in all of commercial law) if I stipulate in the contract "sell...at $10.00 a square foot ACCORDING TO THE EXACT AREA OF THE CIRCULAR PLOT") then I would be obligated to use the official value of pi=3.141592 and pay $314159. To answer Avis statement about "other such derivations" the most famous is the Sinaitic tradition that the exact average lunar month is 29 days 12 793/1080 hours. As Prof. Rabbi Sholomo Sternberg points out in his book on Celestial mechanics this is correct to the nearest 1080th of an hour. The Talmud based on a verse in Chronicles, praises the tribe of Yissachar as "excelling in Astronomy". Russell Jay Hendel; Phd ASA Dept of Math; Towson Univ; Rhendel@towson.edu Moderator Rashi is Simple http://www.RashiYomi.Com