[Avodah] Dimensions of a circular sukkah

[Micha Berger]

On Mon, Sep 23, 2013 at 07:55:15PM +0000, Kenneth Miller wrote:
: Let's suppose I build a sukkah, perfectly circular, of a material
: of negligible thickness, and I measure the circumference to be 29.4 ...

: Later, I start filling in the bulges of the rounded walls, so that
: I'm left with four perfectly flat walls, of equal size and shape...

: Along comes a curious person with a ruler, and finds the diagonal of
: this square (formerly known as The Diameter Of The Circle) to be about
: 9.35831 tefachim. Intrigued, he measures the walls, and finds all of
: them to be only 6.61732 tefachim wide.

: Is the sukkah still kosher?

No, because 6.6 tef isn't 7.

: Was it *ever* kosher?

Yes, because we hold a circular circle doesn't need to be large enough
to circumscribe a square sukkah. We hold it's needs to be large enough
to *approximately* circumscribe one.

To help you accept that approximation (without involving my philosophy
of halakhah):
In terms of area, your minimal 29.4 tef circumference sukkah has an
area of just under 68.8 tef^2, still MUCH larger than the minimal 49
tef^2 area of a square one. And in terms of diameter, the diameter of
just under 9.36 tef is still larger than the minimum length or width.
It is only the idea that a Sukkah must fully contain a length and width at
the same time (and thus a 7 tef x 7 tef square) that is approximate. Both
1D and 2D logical havos amina for shiurim would work.

BTW, a sukkah with straight sides could use the 1.4 for sqrt(2)
approximation to make a squarish trapezoid, and would not contain a
7 x 7 square either.

: If it had been kosher, but is now pasul, then at exactly which point
: did it become pasul?

: Perhaps it is kosher for me, but not for the guy who measured it? Sort
: of like "shavya anafshay chaticha d'isura"?

I would think it became pasul as soon as there were walls that *could*
be measured. Whether or not one actually knows their measurement.

But then, we're back to my phenomenology again... We are accountable for
that which *could* be experienced. Something that could be experienced but
in fact wasn't is where concepts of beshogeig, safeiq, birur in general,
apply. Something that can't be experienced without tools is beyond
those concepts. IMHO.

If so: People have more accurate eyes when it comes to lines than circles,
we are more dependent on tools for precision, so we are allowed to use
a bigger approximation.

Tir'u baTov!
-Micha

-- 
Micha Berger             A pious Jew is not one who worries about his fellow
micha at aishdas.org        man's soul and his own stomach; a pious Jew worries
http://www.aishdas.org   about his own soul and his fellow man's stomach.
Fax: (270) 514-1507                       - Rav Yisrael Salanter