Eruvin 14a Tosfos Vihu'ikah
Tosfos asks on the assumption of our Gemara that the circumference of a circle is exactly 3 times its diameter. The alternative is what Tosfos calls "according to the wise men of measurements", i.e., what we see when we measure, vis. 3.1415...
Tosfos also asks on two stages of the Gemara in Bava Basra.
The first question they ask (before the "vichein") is the Gemara there says that a Sefer Torah with a circumference of 6 fit into a space (width) of 2 tefachim. The Gemara there asks, assuming that the Torah was rolled in the middle then it would be bigger than 2 tefachim wide. Tosfos is bothered by this because the implication is that the ratio of 3 is exact.
How is that implied by the Gemara there? Whether the circumference was 3 or 3.14... the scroll rolled to the middle wouldn't fit in a space of 2, either way!
If it were 3 exactly then the half-way rolled scroll would take up a width of about 2.83.
If it were 3.1415... then the half-way rolled scroll would take up a width of about 2.7.
What does Tosfos mean that the Gemara there implies that 3 is exact?
Bumy Goldson, Beitar Illit, Israel
The first question of Tosfos is that since the circumference of the Sefer Torah is 6 tefachim this means that, to be accurate, the width is less than 2 tefachim. Since the width of the Sefer Torah is less than 2 tefachim it would fit into a space of less than 2, so why did the Gemara Bava Basra 14b ask how could it fit in?
[ see Pnei Shlomo, by Rav Shlomo Ganzfried, on Bava Basra 14b (page 68 of the book) DH VeRaisi beTosfos].
It sounds like you're explaining the last question of Tosfos where the Sefer Torah is supposed to be exactly 2.
I wanted to know the previous question where Tosfos asks on the stage of the Gemara that assumes the Sefer Torah is more than 2.
The Pnei Shlomo you sent me to asks and answers my question.
He says the pshat in the Gemara is that the hekef of 6 is measured after they rolled it into middle, and it is measured as a combination of each individual roll's circumference. So each roll has a diameter of exactly 1 (if we divide by 3) and you can't jam two 1-tefach-wide-objects into a space of 2. However if you divide the circumference by 3.14... then each is slightly less than 1 across and they'll fit.
And he adds, that this is even before assuming the Gemara's next point about tzimtzum since there's a difference between jamming a single 2-tefach-wide-object into a space of 2 and jamming two separate 1-tefach-wide-objects into a space of 2, which is harder.
Thank you, this answers my question.
Bumy, possibly this is an example of "Megalgelin Zechut Al Yedai Zachai". Sometimes things are "Megalgel", they roll around. You look in a sefer for one thing, and then you find just nearby another thing you were looking for!