Wednesday, March 20, 2013

Eiruvin 14a - Relying on 3 for Pi

The Mishna says that the circumference of a circle is 3 times its diameter. The gemara asks how we know that and learns it out from the Yam Shel Shlomo which was a very large mikvah that contained the amount of 150 mikvaos of 40 se'ah. When the pesukim describe the yam shel shlomo, it describes its circumference to be 3 times its diameter.
Rav Shlomo Vilna (Cheishek Shlomo) in the back of the gemara asks, why does the gemara need to figure out the mathematical ratio of circumference to diameter using the yam shel shlomo. This is something that can be easily measured and figured out?

He explains that in truth this number is not precise. As Tosafos points out the mathematicians assume that the circumference is slightly more than 3 times the diameter. The Rambam in the pirush hamishna also says that the circumference is 3 and 1/7 of the diameter (3.14285) recognizing that the number is imprecise.
Actual number is 3.14159265359.
Based on this, the R. Shlomo Vilna explains that the gemara is looking for a source that it is sufficient to use imprecise measurements of pie in calculating the diameter (at least in reference to a korah on a mavuy). From the fact that the pesukim themselves assume the inaccurate ratio of diameter to circumference to be 1:3, we can surely rely on that l'halacha and not have to over compensate for the extra 1/7.

1 comment:

Anonymous said...

3rd masechta daf 14 side 1? 3 - 1 - 4 - 1? :)