Mishnah/Seder Moed/Tractate Eruvin/Chapter 1/5
This mishnah is a continuation of the previous mishnah, which ends with Rabbi Yehuda giving his opinion that to be a valid korah, a beam need not be strong enough to actually hold an ariah (a half brick), but rather it need only be wide enough.
- הייתה של קש או של קנים, רואין אותה כאילו היא של מתכת.
- עקומה, רואין אותה כאילו היא פשוטה.
- עגולה, רואין אותה כאילו היא מרובעת;
- אם יש בהיקפה שלושה טפחים, יש בה רוחב טפח.
- If [the beam] is made out of straw or reeds, view it as if it were made out of metal.
- If [the beam] is bent, view it as if it were straight.
- If [the beam] is rounded, view it as if it were square.
- Anything [round] that is three tefachim in circumference, it has a width of one tefach
Rabbi Yehuda continues his explanation of what a beam needs to count as a valid korah. If the beam is not made perfectly (for example, it is bent or it is made out of a weaker material like straw) we can pretend that it is straight and made out of metal, and would therefore be able to hold an ariah. We can derive from this that rabbi Yehuda is concerned with the fact that the beam is noiceable and looks like it was sufficient to hold an ariah, even if it isn't.
The mishnah then goes on to make a related point, that any round object has a circumference to diamater ratio of 3:1. Today of course we know that the ratio is actually the irrational number known as pi, which is approximately 3.14. This ratio was derived from the tanach, wherein there is a claim that king solomon built a pool which was 10 amot in diameter and 30 amot in circumference. The lack of precision can be attributed to a number of factors, including the fact that the rabbis compiling the mishnah were just rounding off, the fact that they had no standard units of measurement, making such precision difficult and that they were not as mathematically advanced as some other contemporary civilizations. Nehemiah, a late antique Jewish rabbi and mathematician explained this apparent lack of precision by considering the thickness of the pool, and assuming that the thirty amot was the inner circumference, while the ten amot was the diameter of the outside of the pool.