Truthsharer
4) How much is pi in the gemarah?
I’m assuming you’re referring to the number 3, used in many places in the Gemara to refer to pi.
You missed the Mishna in Eruvin (1:5), which also uses the number 3. You also missed the Rambam’s commentary to that Mishna.
Since I know you probably won’t bother to look it up, here is his comment:
?? ?? ???? ?? ???? ?????? ?????? ?? ????? ???? ??? ???? ??? ???? ???? ?? ????? ???? ?????? ?? ????? ???? ????? ?????? ??? ?????? ?????? ??? ??? ????? ?? ???? ??? ???? ???? ???????? ????? ??? ???? ?? ?????? ???? ???? ???? ??????? ??? ?????? ???? ???? ??????? ?? ????? ?????? ???? ????? ??? ?????? ??? ???? ?????? ???? ?????? ???????? ??? ???? ??? ????? ??????? ??? ????? ????? ??????? ??? ??? ???? ?????? ??? ???? ??????? ?????? ???? ??? ?? ???? ????? ??? ?????? ???? ?? ?????? ????? ????? ?? ??? ?????? ???? ????? ?? ?? ??? ??? ????? ?? ?? ??? ??????? ???? ?? ?????? ?????
Short summary: Pi is a number which is not known; not due to our feeble minds, but because in metzius it is a number which cannot be attained. Therefore, since there will never be a way to write the number in its entirety, the Chachamim chose the whole number “3” to refer to pi.
Basically, why choose a complicated number when you can choose a simple number, when both will anyway be wrong?
The Rambam’s words still hold true 800 years later. We now have all but proven that pi is an irrational number.