Study Sukkah folio 8A with parallel Hebrew-English text, traditional commentary, and modern study tools. Free access to Babylonian Talmud online.
The Talmud answers: This applies only in the middle of the circle that has a circumference of 12 cubits, as the diameter of the circle is 4 cubits; but in order for a square inscribed within a circle to have a perimeter of 16 cubits, the circle requires a circumference that is more than 12 cubits.
The Talmud asks further: Now, by how much is the perimeter of a square inscribing a circle greater than the circumference of that circle? It is greater by 1/4th of the perimeter of the square. If that is the case, a circle with a circumference of 16 cubits is sufficient. Why, then, does R' Yoḥana
The Talmud answers: This statement with regard to the ratio of the perimeter of a square to the circumference of a circle applies to a circle inscribed in a square, but in the case of a square circumscribed by a circle, the circle requires a greater circumference due to the projection of the corner
The Talmud calculates precisely how much greater the circumference must be in order to circumscribe the 4-by-4-cubit square. Now, in every square whose sides each measure one cubit its diagonal measures one and 2/5ths cubits, and in a circle that circumscribes a square, the diagonal of the square
The Talmud wonders: Say that we say that the Sage was not precise when the difference between the number cited and the precise number is slight; however, when the difference is great, do we say the Sage was not precise? After all, R' Yoḥanan stated that the minimum measure is 24 cubits, a differen