1)

(a)Rebbi Yochanan requires at least twenty-four people to be able to sit round the inside of the walls of a round Sukah. The Gemara asks that even according to Rebbi, twelve ought to suffice - because of the principle that the diameter of a circle with a circumference of three Tefachim, is one Tefach. Conversely, in our case, since the diameter of the Sukah is four Amos, its circumference is twelve, and a sitting person takes up a square Amah.

(b)We reject this Kashya however, on the grounds that we are talking about a square of four by four, not a circle - and a square is twenty-five per-cent larger than the circle which it surrounds, in which case one would be able to seat sixteen people round the Sukah, and not just twelve. (Note, that we could have arrived at this figure much more directly; however, the Gemara sticks to the method with which it is currently involved: that of the square/circle relationship).

(c)However this is wrong - because it is R. Yochanan's circle that must surround Rebbi's square to be Kasher, and not vice-versa,

(d)Consequently - the diagonal of the square (i.e. the diameter of the circle) will be 5 3/5 Amos (1 2/5 Amah per Amah) giving us an area of 16 4/5 Amos round the inside of the circle.

2)

(a)But this is still not twenty-four, as R. Yochanan maintains. We reject the suggestion that Rebbi Yochanan is only giving a rough measurement - on the grounds that this would be acceptable if the discrepancy was very slight, but not here, where it is almost fifty percent.

(b)Mar Keshisha brei d'Rav suggests that, in fact, three people sit per two Amos (and not one person per Amah, like R. Yochanan). In his opinion, sixteen people will be able to sit in such a Sukah. In his opinion - sixteen people will be able to sit in such a Sukah, and the Sukah will be Kasher if it is sixteen square Amos (instead of 16 3/5 (only a slight discrepancy, which we can accept).

(c)But this too, we refute - on the grounds that it is feasible to accept a slight discrepancy l'Chumra, but not l'Kula.

3)

(a)Rav Asi concludes that a person does indeed take up one Amah space, like R. Yochanan said. To reconcile R. Yochanan with Rebbi, he explains - that when Rebbi Yochanan gave a figure of twenty-four, he was referring to the outside of the circle, whereas our calculations according to Rebbi concerned the inside.

(b)This will reduce the circle's ...

1. ... diameter - from eight Amos to six (one Amah less on each side, due to the fact that a person takes up one Amah space) .

2. ... circumference - from 24 Amos to 18.

(c)Granted, this is slightly more than the 16 4/5 of Rebbi's four by four Amah Sukah. Now however - it is possible to say that Rebbi Yochanan only gave an approximate figure 'l'Chumra (a diameter of six Amos instead of 5 3/5.

(d)The Dayanim of Caesaria have a radical way of answering Rebbi Yochanan - they concede that a square around a circle has a circumference of a quarter more than the circle; but a circle around a square, they say, adds a half to the circumference (and not a third). Consequently, the diameter of the four by four round Sukah of Rebbi will be, not 5 3/5 Amos (as Rebbi Yochanan maintains), but six, just as Rebbi Yochanan said (but in a different context).

(e)We comment on that however - that the Dayanim of Caesaria are mistaken, because a circle that surrounds a square is proven to be a third more than the square, and not a half.

4)

(a)Rebbi Levi citing Rebbi Meir discusses the two potters' huts. The ...

1. ... inner hut - where they lived and where they kept their pots.

2. ... outer one - where they manufactured the pots.

(b)The inner hut was not eligible for a Sukah - because the potter lived there the whole year, and it was not apparent that he was now living there to fulfill the Mitzvah of Sukah.

(c)A gate-house that leads into the house - required a Mezuzah.

(d)The potter's outer hut did not - because (unlike the house into which the gatehouse leads) the inner hut into which it led, was itself not fixed.

5)

(a)Sukas 'Ga'n'ba'ch' is the acronym of four valid Sukos. The 'Gimel' stands for Goyim' and the 'Nun' for Nashim. The ...

1. ... 'Beis' stand for - Behemah.

2. ... 'Chaf' stands for - Kutim.

(b)These Sukos are Kasher - provided the Sechach conforms with the Halachah.

(c)The Sukah of Kutim is not Kasher - because the Chachamim declared them Nochrim in all regards).

(d)They are all Kasher, provided they are constructed in order to give shade.

6)

(a)Sukas 'Mikol Makom', which comes to include 'Sukas 'Ra'k'ba'sh' is Kasher too, under the same condition. The 'Reish stands for 'Ro'im' (shepherds) and the 'Kuf', for Kayatzim - a hut for people guarding figs drying in the field.

(b)'Beis' stands for Burganin and 'Shin', for Shomrei Peiros. 'Burganin' - are little huts for the town guards to rest in.

(c)If two Beraisos had not specifically included each one, we would have thought that, even though 'Sukas ...

1. ... 'Ga'n'ba'ch' is eligible, 'Sukas 'Ra'k'ba'sh' is not - because they are not fixed like those of 'Ga'n'ba'ch'.

2. ... is eligible, 'Sukas 'Ga'n'ba'ch' is not - because the owners are not obligated like those of 'Ra'k'ba'sh'.