What is Talmud Tweets?

What is Talmud Tweets? A short, personal take on a page of Talmud - every day!

For several years now, I have been following the tradition of "Daf Yomi" - reading a set page of Talmud daily. With the start of a new 7 1/2 year cycle, I thought I would share a taste of what the Talmud offers, with a bit of personal commentary included. The idea is not to give a scholarly explanation. Rather, it is for those new to Talmud to give a little taste - a tweet, as it were - of the richness of this text and dialogue it contains. The Talmud is a window into a style of thinking as well as the world as it changed over the centuries of its compilation.

These are not literal "tweets" - I don't limit myself to 140 characters. Rather, these are intended to be short, quick takes - focusing in on one part of a much richer discussion. Hopefully, I will pique your interest. As Hillel says: "Go and study it!" (Shabbat 31a)

Thursday, May 23, 2013

Eruvin 76 – Circle in the Square

The Mishnah describes two courtyards divided by a wall. Normally, these would require two separate 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?

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