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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
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