THE SHAPE OF A SUKAH [Sukah:shape]
7b - Beraisa - Others: A round Sukah is Pasul.
R. Yochanan: A round Sukah is Kosher only if 24 people can sit along the circumference.
This is like Rebbi, who requires a Sukah to be four Amos by four Amos.
8a - Rav Asi: He holds that a person is one Amah wide (and an Amah thick). He discusses people sitting outside the Sukah (The circumference around the people is 24 Amos, so the diameter is eight, so the diameter of the Sukah itself is six.).
Question: A Sukah contains a square of four Amos by four Amos, whose diagonal is 5.6 Amos, even if its circumference is only (three times as much,) 16.8!
Answer: R. Yochanan was not precise; he was stringent. (Really, even if 23 people can sit around it, it is Kosher.)
Nazir 8b - Beraisa: A round house, or one with two, three or five walls cannot receive Tum'as Tzara'as.
It says "Kiros" twice (superfluously). Each teaches two walls, so we learn that the house must have exactly four.
Rambam (Hilchos Sukah 4:7): A round Sukah is Kosher if it is big enough Lerabe'a (to make a square) seven Tefachim by seven Tefachim inside, even though it has no corners.
Magid Mishnah: The Halachah does not follow Rebbi (who requires four Amos by four Amos). Rather, seven Tefachim by seven Tefachim suffices.
Question: A house that is round, or has more or less than four walls cannot receive Tzara'as because we expound four walls from verses (Nazir 8b). The same should apply to Sukah, for we learn the number of walls from the three occurrences of "ba'Sukos"!
Answer (R. Ezri'el in Shitah Mekubetzes Nazir 8b): 'Sukah' primarily refers to the Sechach. It is only a Drashah to teach about the walls, therefore it does not exclude a Sukah that has more walls or is round.
Rif (Hilchos Mezuzah 6b): The Gemara (Sukah 3a) exempts a house from a Mezuzah if it does not have four by four Amos.
Rambam (Hilchos Mezuzah 6:2): If a house does not contain four by four Amos it is exempt from a Mezuzah. If it is big enough Lerabe'a four Amos by four Amos evenly it is obligated, even if it is round or pentagonal and all the more so if it was longer than it is wide.
Rosh (Hilchos Mezuzah 16): All texts of the Gemara (3a) say that a house must be four Amos. The Rif changes it to say four by four Amos, for less than this is not fit for Dirah. This is unlike the Rambam, who says that if it was longer than it is wide and it is big enough Lerabe'a four by four Amos it is obligated. Every matter mentioned there requires four by four Amos.
Tur (YD 286): The Rambam obligates a Mezuzah as long as the area of the house is no less than that of a square four by four Amos. The Rosh argues and exempts a house unless it contains a square four Amos by four Amos.
Beis Yosef (DH u'Mah she'Chosav): The Halachah follows the Rambam, for only the Rosh argues with him. 'Four by four Amos' does not connote that it holds such a square. It suffices if it holds the area of such a square. Such a house is fitting for Dirah.
Shulchan Aruch (OC 634:1): A Sukah less than seven by seven Tefachim is Pasul.
Shulchan Aruch (OC 634:2): A round Sukah must be big enough Lerabe'a seven by seven Tefachim inside.
Beis Yosef, according to Darchei Moshe (1): The circumference must be 29.4 Tefachim (to fit a square of diameter seven and diagonal 9.8).
Question (Bach DH u'Mah she'Chosav): The Tur requires 'enough Lerabe'a seven by seven.' This connotes like the Rambam, that it does not suffice to enclose the area of such a square. Rather, a square seven by seven must fit inside. The Rambam similarly exempts from Mezuzah unless a square four Amos by four Amos fits inside. However, the Rosh argues and obligates a house with the area of such a square. Why should this be different than Sukah?
Note: The Rosh explicitly says that he argues with the Rambam. However, it is possible to explain the Rambam either way (Divrei Chamudos on the Rosh (50).) Here in Hilchos Mezuzah the Bach does not say that he argues with the Tur, even though the Tur explicitly says that the Rosh is more lenient than the Rambam and obligates only if a square four by four fits inside.
Answer #1 (Bach, ibid.): Perhaps the Tur means (and also the Rosh holds) that it suffices for a Sukah to enclose the area of a square seven by seven. R. Yochanan requires that it enclose an actual square four by four, because he holds like Rebbi who requires Diras Keva. However, the Halachah requires Diras Arai. It is enough if a Sukah fits Rosho v'Rubo. As long as the area is 49 square Tefachim it is Kosher. Tosfos (3a DH Lo) says that Hilmi's Sukah had long compartments that were not seven Tefachim wide (and this is Kosher).
Rebuttal (Taz 1 and Magen Avraham 1): The text of Tosfos should say that the compartments were only seven wide.
Answer #2 (Magen Avraham 1): We hold that a Sukah must house Rosho v'Rubo and his table (so he can eat from it). It does not suffice if it is long and wide. It must enclose a square seven by seven. This is even for us who do not eat reclining. If a big Sukah has a part that is less than seven by seven Tefachim one may not sit there, for it is narrow and uncomfortable.
Bach (ibid.): If the circumference is 24 and three eighths Tefachim, it has the required area. It is possible that the Rambam and Magid Mishnah agree with this. However, in practice one should be stringent. Perhaps R. Yochanan had a tradition from Sinai that it must contain an actual square.
Mishnah Berurah (4): A Sukah with five or more sides must enclose a square seven by seven, just like a round Sukah.
Note: I didn't see anyone discuss how many or how big the walls must be.