[Avodah] calculation of pi

[Micha Berger]

On Sun, Jan 15, 2012 at 07:17:10PM -0500, Yitzchok Zirkind wrote:
: 2012/1/15 Harvey Benton <harvw613 at yahoo.com>
: > some have complained that the rishonim were not accurate enought  when
: > it came to their description of pi eg, they named it as being3 instead
: > of 3.14 etc.
...
: See Magid Mishna on Ramba"m Hil Shabbos 28:18 D"H Lfichuch im Riboh,
: brought in S"A Horav O"C 399:13. (There are other Nafka Mina's as well)

Yes, one can take the statement to mean that the halachically required
precision for circles is an error of +/- (pi-3)/pi. IOW, 3 is close
enough to be yotzei. And similarly, your tefillin are "square enough"
for halakhah if the diagonal is no more off from sqrt(2) * the sides
than 1.4 is.

RETurkel has posted here similarly a number of times over the years. Here,
though, he argues that Chazal clearly didn't realize just how far off pi
was from 3 because of statements made in a historical context.

To wit, on Mon, Jan 16, 2012 at 07:50:40PM +0200, Eli Turkel wrote:
: The gemara on Baba Batra 14b calculates how much room was left in the ark
: for the sefer torah.
: The gemara end up that there was 2 tefachim left. The gemara then asks that
:  if the space and diameter are both exactly 2 tefachim then it wont fit.
: However if the diameter is 6/3.14 than the sefer torah is less than 2
: tefachim and will fit.

This isn't a question of required precision, but one where they clearly
thought pi was close enough to 3 that the sefer Torah wouldn't fit.

: What does this have to do with emunah?
: R Avraham ben haRambam in other places claims that chazal based their
: science on Greek science and it was wrong.
: Didnt affect his emunah.

Well, there are the usual science and Torah resolutions, of which this
is but one. I must say, though, that nishtanah hateva probably must be
dropped from the list, this time. (Geometry changed?)

While we can argue that agaditos are bederekh mashal, here is doesn't
help. Whatever this is supposed to be a mashal for, the nimshal relies
on the math.

The gemara complains that the Torah is rolled from both ends and therefore
wouldn't fit. And the first answer is that it was rolled from one end
(like a megillah).

The Rashash understands the initial problem being that in order to get
the same volume as a megillah of 2 tefach diameter, you would need nearly
3 tefachim in two circles. Which is true with the correct pi.

But look at the next question and R' Ashi's answer. The gemara knows
that things that measure exactly often don't fit. Perhaps the friction
of parchment compared to its flexibility means that it's difficult to
place a Torah between the badim even with the proper value of pi. One
needs a larger gap just for the logistics of the real world.

The Chasam Sofer asks our question and tells you to add the circumferance
of the eitz chayim. (Or did this Torah have 2 atzei chayim, even though
it was otherwise wound like a megillah?)

Tir'u baTov!
-Micha

-- 
Micha Berger             In the days of our sages, man didn't sin unless
micha at aishdas.org        he was overcome with a spirit of foolishness.
http://www.aishdas.org   Today, we don't do a mitzvah unless we receive
Fax: (270) 514-1507      a spirit of purity.      - Rav Yisrael Salanter