Shalom,

You wrote in the point-by-point summary charts (http://www.dafyomi.co.il/bbasra/points/bb-ps-014.htm) that

5. Summation of question: If the circumference of the Sefer Torah is six Tefachim, the width is (a third of the circumference,) two Tefachim;

i. Since we roll a Sefer Torah from both ends, the width is even more - how can it fit in two Tefachim (according to R. Meir)?

(k) Answer: The Sefer Torah in the Aron (only had one pole and) was rolled to the beginning.

(l) Question: Still, if its width is exactly two Tefachim, it does not fit properly in two Tefachim!

(m) Answer (Rav Ashi): A small amount of parchment was left unrolled (so the width of the rolled part was less than two), it rested above the Torah.

Now -- on what basis does the gemara assume that the scroll couldn't fit into 2 tefachim, when in fact if the hekef was 6 then the width must be 6/3.1415... which is actually less than 2, so it would fit in reality. In fact, a child could even figure this out with a string as a measure.

Please send me your comments.

Thank you.

Simcha

I met this guy who sent me the following regarding this topic.

"The Chasam Sofer admits that a Torah scroll of 6 tefachim in circumference would have less than 2 tefachim in diameter, but then says that the two poles, around which the Torah scroll was rolled, completed the diameter to 2 tefachim. But of course, the Gemara, in its detailed discussion of the subject, makes no mention that the circumference of the Torah scroll would be measured without the poles, while its diameter would be measured with the poles. All that the Gemara does is:

a) Assumes that the circumference of the scroll was 6 tefachim;

b) Takes the ratio of circumference to diameter as 3:1;

c) Obtains in this way the value of 2 tefachim as the diameter of the scroll;

d) Asks, how a space 2 tefachim wide could have been sufficient to place into it a scroll measuring exactly 2 tefachim in diameter;

e) Answers that it was indeed not sufficient, and therefore one had to leave some sheets of the Torah scroll unrolled, placing them above the rolled scroll when the latter was put in the Ark of the Covenant.

"This discussion makes clear that the sages of the Gemara thought the ratio of 3:1 to be an exact one. If they had thought about the possibility of adding or subtracting the width of the poles to the diameter they calculated, they would have no problem to mention this possibility - but they did not. By the way, in the process of discussion the Gemara concludes that the Torah scroll of the Temple was rolled around one pole, not two (differently from the scrolls used in synagogues).

"Regarding the Penei Shelomoh (by R' Shelomoh Ganzfried, the author of Kitzur Shulchan Arukh), he offers a lengthy discussion, with quotations of different Rishonim, about calculating the circumference and the diameter of a Torah scroll rolled around two poles; but all this has nothing to do with the conclusion of the Gemara. Concerning the scroll rolled around a single pole, Penei Shelomoh questions, whether it would still have a second, auxiliary pole (presumably in order to roll part of the scroll around it during a public reading, while before the scroll would be put back into the Ark, it would be rolled again around one pole only). His answer is that the scroll would have a second pole, and that at least according to the Tosafot, the figure for the scroll's diameter would include the width of the poles. This, in fact, fits perfectly the Gemara, where the problem discussed is that of placing a ready-to-use Torah scroll (with poles, one or two) in the Ark of the Covenant. But in any event, Penei Shelomoh does not solve the problem of Pi = 3.