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<DIV><FONT face=Arial size=2><FONT face="Times New Roman" size=3>RSLK
wrote:</FONT></FONT></DIV>
<DIV><FONT face=Arial size=2><FONT face="Times New Roman" size=3><EM>Should we
lose our respect for the gemara, Rashi and tosafot because their understanding
of geometry was so unsophisticated?</EM> </FONT></FONT></DIV>
<DIV><FONT face=Arial size=2><FONT face=Arial size=2></FONT></FONT> </DIV>
<DIV><FONT face=Arial size=2>CM responds:</FONT></DIV>
<DIV><FONT face=Arial size=2><STRONG>Of course not. A common response is
that they knew that these values were not exact, but only approximations. They
used these values because in halacha these approximations are sufficient. I am
not sure if this answer can be used for all the later meforshim as well as it
may be hard to fit into some of their discussions.</STRONG></FONT></DIV>
<DIV><FONT face=Arial size=2><FONT face="Times New Roman"
size=3></FONT></FONT> </DIV>
<DIV><FONT face=Arial size=2>RSLK:</FONT></DIV>
<DIV><FONT face=Arial size=2><FONT face="Times New Roman" size=3> <EM>Or do
we assume that "nishtaneh ha-tevah" and that the geometric relationships of
circles and squares has changed? </EM></FONT></FONT></DIV>
<DIV><FONT face=Arial size=2><FONT face=Arial size=2></FONT></FONT> </DIV>
<DIV><FONT face=Arial size=2>CM:</FONT></DIV>
<DIV><FONT face=Arial size=2><STRONG>Again, of course not. There is no need for
nishtaneh hatevah as they knew these were only approximations. Besides how do
you apply this to a mathematical concept as opposed to a physical
reality?</STRONG></FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2><FONT face="Times New Roman"
size=3>RSLK:</FONT></FONT></DIV>
<DIV><FONT face=Arial size=2><EM><FONT face="Times New Roman" size=3>Or rather
(my view) that it is perfectly fine for chazal to have dealt with the level of
knowledge at the time, and we need not hold them to account on areas outside the
purview of torah? </FONT><BR></EM></FONT></DIV>
<DIV><FONT face=Arial size=2>CM:</FONT></DIV>
<DIV><FONT face=Arial size=2><STRONG>Actual the Babylonians and Greeks had
better values than the ones used in shas. It is safe to assume that chazal knew
these values that well preceded the time of the mishna and gemara even if
you choose to assume that chazal only knew what the intelligencia of their
day knew in science. They chose to use these rounded values since these
approx. were sufficient halachakly and easier for the less sophisticated hamon
am to use. By the time of Archimedes, who preceded mishna by several centuries,
one could (theoretically) use the circumference of an 2n sided polygon to
approx. a circle. As n grows large this converges (slowly and tediously) to pi.
So they were able to calculate pi to great accuracy if they so
desired.</STRONG></FONT></DIV>
<DIV><STRONG><FONT face=Arial size=2></FONT></STRONG> </DIV>
<DIV><STRONG><FONT face=Arial size=2>BTW there is a well known remez to a better
value in the pasuk about the yam shel Shlomo that ostensibly is the source for
the value of 3 for pi. there is a kri and a ksiv for the word kav with and
without the 'heh.' The ratio of 111/106 (ksiv over kri) when used as a
correction for the approx. value of pi of 3 used in the pasuk gives 3.1415, a
much better value, although not the infinite digits of the
real decimal value. This value is the correct one (infinite places)
truncated to 4 decimal places.</FONT></STRONG></DIV>
<DIV><FONT face=Arial size=2><STRONG></STRONG></FONT> </DIV>
<DIV><FONT face=Arial size=2>KVT</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Chaim Manaster</DIV></FONT></BODY></HTML>