Study Eruvin folio 76B with parallel Hebrew-English text, traditional commentary, and modern study tools. Free access to Babylonian Talmud online.
This measurement applies only to a circle and the ratio between its circumference and diameter, but with regard to a square that must fit entirely within that circle, we require a circle with a larger circumference. In order for a square of 4 by 4 handbreadths to be entirely contained within a circl
The Talmud asks: Now, how much larger is a square than a circle? It is larger by 1/4th. If so, a circle with a circumference of 16 handbreadths at most should suffice.
The Talmud answers: This statement that a square is larger than a circle by 1/4th applies only to a circle circumscribed by a square, but with regard to a square circumscribed by a circle, we require more, and the difference between the square and the circle is greater. What is the reason for this?
The Talmud further objects: Since every cubit in the side of a square is a cubit and 2/5ths in the diagonal, a square of 4 by 4 handbreadths has a diagonal of 5 and 3/5ths handbreadths. And since the diameter of a circle equals the diagonal of the square that it encompasses, the circle circumscribi
The Talmud answers: R' Yoḥanan spoke in accordance with the opinion of the judges of Caesarea, and some say in accordance with the opinion of the rabbis of Caesarea, who say: A circle that is circumscribed within a square is smaller than it by 1/4th; with regard to a square that is circumscribed wi