Amah, tefach, and pi

I have a question on Eruvin 14a bottom which says that Shlomo's pool was round, had diameter of 10 amot and thickness 1 tefach, and circumference 30 amot (we learn from this that halachically `pi=3`).

However, next we read (Artscroll 14a4 right column): "but there is still the little bit of thickness..." -- "the circumference is calculated from within". This seems to imply that amoraim knew that `pi>3` and thus they said that diameter of 10 amot was measured outside and the circumference of 30 amot was measured inside.

Thus

``````30 amot = 2 * pi * inner radius = 2 * pi * (5 amot - 1 tefach)
``````

which implies

``````1 tefach ~ 0.225 amot
``````

or

``````1 amah ~ 4.44 tefachim
``````

and not 6 tefachim.

What is my mistake?

• I believe Rashi there says the Gemarra means "had diameter of 10 amot (inside)". pi = 3 Nov 12, 2020 at 19:15
• @robev: the inside/outside is specifically to account for the error in the assumption of pi=3.
– sds
Nov 12, 2020 at 19:17
• But you're asking from the gemarra, which assumes pi = 3 (not factually but halachically). If you're asking on those who suggest the verse doesn't assume pi = 3, I'd cite them and not the gemarra Nov 12, 2020 at 19:18
• the gemara implies that 1 amah ~ 4.44 tefachim; amoraim were quite aware that pi is not 3; they just assumed that it is 3 for halacha. if you assume pi=3, the thickness is 0,
– sds
Nov 12, 2020 at 19:20
• Why is the thickness zero if the diameter and circumference are on the inside? Nov 12, 2020 at 19:20