[Avodah] Dimensions of a circular sukkah

[Micha Berger]

On Mon, Sep 16, 2013 at 04:33:31AM +0000, Kenneth Miller wrote:
: I *am* familiar with the concept that we've often discussed here, that a working legal system needs to incorporate estimates and calculations that are feasible to the average person, and must sometimes choose expedient over accurate. Still, this case seems to be rather extreme. Is 3 really an accepted value for pi in halacha l'maaseh, as opposed to the much closer 3 1/6? Can anyone comment?

Yes, three really is close enough to pi halakhah lemaseh. How do I know,
because (as one example):
: The above calculation shows why I was very surprised to find Mishna
: Berurah 634:4 (citing Beis Yosef) giving the circumference of that
: circle as only 29.4 tefachim. In the Shaar Hatziun there, he explains
: the calculation: Seven is multiplied by 1.4 to get the length of the
: diagonal. That is the diameter of the circle, and is multiplied by 3 to
: get the circumference. This calculation gives 29.4.

IOW, why ask a question in surprise rather than take it as your answer?

BTW, saying that 3 is good enough enough for pi has a different weight
than 1-1/5 for sqrt(2). After all, we have a pasuq that uses it.

(In my "observable / existential" way of viewing halakhah, I would
say that it makes sense for pi to be more off than sqrt(2) at only one
digit precision rather than two digit, or 5% off instead of 1%. After
all, people mentally estimate straight lenghts better, and have less
tolerance for calling wavy lines "basically lines" than some hand-drawn
almost circles.)

Tir'u baTov!
-Micha

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