Sukkah 8

If you like Mathematics you will likely enjoy the end of yesterday (Sukkah 7b) and much of today’s daf (Sukkah 8a), whereas if you don’t, you may find it a little tricky. This is because the discussion relates to the minimum dimensions of a circular sukkah which requires a journey into the history of pi (π) – i.e. the ratio of a circle’s circumference to its diameter.

Informed by Melachim I 7:23, we are told on Sukkah 7b that ‘whatever has a circumference of 3 tefachim has a diameter of one tefach’ – which approximates pi (π) to 3. However, if this is the case, the calculations presented by Rav Yochanan in today’s daf are, as the Gemara repeatedly notes, לא דק – ‘imprecise’.

Taken at face value, it seems that Rav Yochanan – certainly one of the greatest Amoraim in Israel – simply wasn’t great at Mathematics. However, as Rabbi Shimon Ben Tsemah (1361–1444) – otherwise known by the Tashbetz – explains, (and as has been nicely summarized by Boaz Tsaban and David Garber in their essay ‘On the Rabbinical Approximation of π’ – see, though approximations were used by our Sages when teaching some of these topics (because, as we are taught in Pesachim 3b, “one should always teach his student in the easiest way”), more precise values were used by our Sages when making the halachic calculations.

Given this, and as the Tashbetz explains, it seems clear that Rav Yochanan actually used a very precise (at least for that time) measure of pi of 3 1/7, and this is why his mathematical conclusions differed from the Sages. Thus, while on face value the question in today’s daf relates to the mathematical imprecision of Rav Yochanan, the real question in today’s daf relates to the tension that arises when ideas are presented simply for the sake of explanation, and the more complex reality which those ideas relate to.

In terms of contemporary Judaism this question often arises when school teachers and outreach workers overly simplify complex ideas while, later on in life, those students and learners can be frustrated and confused by the more complex reality which they encounter. This, like the question in today’s daf of squaring the circle, is not easily solved. Still, it is one that must be wrestled with in order to avoid the justified criticism of imprecision.