But what if the opening is circular?
Now we get into issues of geometry:
R. Johanan ruled: A round window must have a circumference of twenty-four handbreadths . . .
Consider: Any object that has a circumference of three handbreadths is approximately one handbreadth in diameter: should not then twelve handbreadths suffice? –
This applies only to a circle, but where a square is to be inscribed within it a greater circumference is required.
But observe: By how much does the perimeter of a square exceed that of a circle? By a quarter approximately; should not then a circumference of sixteen handbreadths suffice? —
This applies only to a circle that is inscribed within the square, but where a square is to be inscribed within a circle it is necessary [for the circumference of the latter] to be much bigger. What is the reason? In order [to allow space for] the projections of the corners.
Draw a circle. Now draw a square around it. Now draw a square within the circle. You see the problem – which square do we use? As always, the problem can be made even more complicated by dealing with diagonal and area:
Consider, however, this: Every cubit in [the side of] a square [corresponds to], one and two fifths cubits in its diagonal; [should not then a circumference] of sixteen and four fifths handbreadths suffice?
R. Johanan holds the same view as the judges of Caesarea or, as others say, as that of the Rabbis of Caesarea who maintain [that the area of] a circle that is inscribed within a square is [less than the latter by] a quarter [while that of] the square that is inscribed within that circle [is less than the outer square by] a half.
R. Johanan seems to be applying the rule relating to area to circumference, requiring the circle to be bigger than necessary.
Circle in the square or circle out of the square?