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<DIV><FONT face=Arial size=2><EM>RAM wrote:</EM></FONT></DIV>
<DIV><EM>Geometrically defensible? No way. Sitting in the sukkah's shade is
<BR>dependent on the angle at which the sun is shining, combined with <BR>both
the height of the s'chach and also its horizontal edges. The <BR>simplest
example is that if one is anywhere north of the equator, <BR>sitting against the
southern side of the sukkah is *never* in the <BR>sukkah's shade. (Similar
arguments can be made by Chanuka: Height is <BR>irrelevant. The angle is
significant, and maybe the distance too.)</EM></DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2>CM responds:</FONT></DIV>
<DIV><FONT face=Arial size=2>Actually, the interesting and more revealing cases
are in the far north. I assume there is no p'tur on the mitzvah of Sukkah in the
far north (except maybe mitztaer :-). So let's take someone living at the Arctic
Circle in Alaska and a converted Eskimo living at the North Pole. Since Sukkos
comes out reasonably close to the equinox and the trig functions at the values
we need vary reasonably slowly for our parameters near the equinox the
error will be reasonably small for this simplifying assumption.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>So we can consider our Jewish Eskimo first. He goes
out and throws some sechach over a roofless igloo he made. At the equinox, what
he sees is the sun on the horizon for the full 24 hour day (for the start of the
6 months of night) or close to it depending on how many days Sukkos is
removed from the equinox. So the sun will be near the horizon or slightly BELOW
it, thus the angle is near 90 degrees to the wall or the sun has already set for
six months. Thus the entire Sukkah, no matter how low the walls are, and no
matter how large the LxW dimensions are, will never have tzel sechach AT ANY
TIME and not just immediately south of the wall. Rav Zeira will not be able
to move to the North Pole.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Our Jewish Alaskan on the Arctic Circle has it
somewhat better. For him the sun is at an altitude of 23 1/2 degrees at noon
(since the sun is then overhead at the equator) and he will have close to a 12
hour day or reasonably close to these numbers if Sukkos is a couple of weeks
removed from the equinox. Thus, if our Alaskan builds his Sukkah to
the max kosher height of just under 20 amos, then at local noon his wall will
cast a shadow of approx. y=20 x tan (66.5 deg.) = 20 x 2.3 = 46 amos. Tan
function at these values for the parameter changes very slowly so that the
approximation for a couple of weeks removed from the equinox will be pretty
close. Thus our Alaskan friend will have to build his 20 amos high sukkah AT
LEAST 46 amos long before he gets ANY shade from the sechach just at the
far wall. Tough for Rav Zeira's shita.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Interestingly, if our Alaskan friend builds a
minimum height sukkah of 10 tefachim, then the shadow cast at noon by the wall
will be y=10 x tan (66.5 deg) = 10 x 2.3 = 23 tefachim, which is just short
of 4 amos, which is the minimum dimensions for a sukkah according to Rebbi. I am
not sure if this is just coincidence or something significant in Rebbi's
shita.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>But for RAM's post, I would not have thought to
make these calculations. I hope I have not made any serious mistake. I think it
is pretty straight forward.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Kol Tuv</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Chaim Manaster</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
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