Daf Yomi - Sukkah 8 - Four Amos = 5 3/5 Amos All Over

The Pnei Yehoshua quotes Rabbeinu Tam in Eruvin who holds that whenever the Gemora states the measurement of four amos, it means the diagonal of four squared amos, which is five and three fifth's (5 3/5) amos. According to this, the P"Y asks on the question of our Gemora on Rabbi Yochanan's statement.

Rabbi Yochanan rules that a round sukkah is valid providing that it has a circumference that can fit twentyfour people. The Gemora assumes that this is in accordance with Rebbe who maintains that a sukkah must be four squared amos. The Gemora questins this for a person can sit in a one amah space and hence Rabbi Yochanan's required circumference is twentyfour amos. It is known that there is a 3 to 1 ratio between the circumference of a circle and its diameter, which indicates to us that rabbi Yochanan requires the sukkah to be a diameter of eight amos which is substantially larger that Rebbe's opinion of four amos? According to Rebbe, it should suffice with merely twelve amos?

The Pnei Yehoshua therefore asks, Rebbe, who maintains that a sukkah must be four amos squared, according to Rabbeinu Tam would hold that it must be five and three fifth's amos squared. Accordingly, it would be required to have a circumference of twentyfour amos in a circle to contain a square of five and three fifth's amos inside of it and this would be the explanation for Rabbi Yochanan?

The Aruch Lener answers that Rabbeinu Tam was only referring to Shabbos and by sukkah where it states the requirement is four amos, it means four amos literally and not five and three fifth's amos. The Pnei Yehoshua himself hypothesized like that but rejected it with certain proofs.

One of the proofs he cites is from a Taz that riles regarding a house that is three amos by eight amos, it is exempt from a mezuzah. We have learned previously that a house must be four amos squared to be obligated in a mezuzah. The same is true regarding sukkah. One may question as to the logic of that. This house has twentyfour squared amos, which is more that four amos squared? The Pnei Yehoshua states that it must be because it is learned from the possuk al yetzei ish mimkomo, which the sages say that the place of a person is four amos and certainly a house can't be less than that. Just like the place of a person is four amos squared, so too his house or sukkah must be four amos squared. The P"Y extends that analogy and states that just like regarding Shabbos, Rabbeinu Tam maintains that four amos means five and three fifth's amos, so too regarding sukkah as well.