*eruvs*since they are two separate spaces. But, if there is an opening in that wall with the dimensions of 4 x 4 handbreadths (and less than 10 handbreadths high) the residents can prepare one joint

*eruv*if they chose. This makes sense as an opening that size creates a pass-through so that objects could potentially be shared.

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?

## No comments:

## Post a Comment