Sukkah, Daf Het, Part One

 

Introduction

Today’s section is about the validity of a round sukkah. Just a warning there is a lot of math in this section and in the subsequent sections as well. Good luck!

 

 

אמר רבי יוחנן: סוכה העשויה ככבשן, אם יש בהקיפה כדי לישב בה עשרים וארבעה בני אדם – כשרה, ואם לאו – פסולה.

 

R. Yohanan said: A sukkah which was [round shaped] like a furnace: If twenty-four men can sit around its circumference, it is valid, and if not it is invalid

 

R. Yohanan describes a round sukkah shaped like a furnace. As long as twenty-four men can sit around the circumference of the sukkah it is valid. The Talmud will now discuss how big this actually is.

כמאן – כרבי, דאמר: כל סוכה שאין בה ארבע אמות על ארבע אמות – פסולה.

 

According to whom [is this statement]?

According to Rabbi who says that a sukkah which is not four cubits square is invalid.

 

Earlier in the Talmud we saw three opinions as to how big a sukkah must be: 4 cubits square, large enough for head, most of body and table, or just large enough for head and most of body.

The Talmud assumes that this opinion must match that of Rabbi Judah Hanasi, who says that the sukkah must be four cubits square. This is the largest of the three measures. Obviously, a sukkah that only needs to be large enough to fit his head, most of his body and his table (which would have been small) is far smaller than is necessary to sit 24 people around.

However, as we shall see, the math doesn’t work out that all that well for this.

 

מכדי, גברא באמתא יתיב, כל שיש בהקיפו שלשה טפחים יש בו רוחב טפח, בתריסר סגי! –

 

Since a man occupies the space of a cubit, and where the circumference [of a circle] is three handbreadths its diameter is one handbreadth, it would therefore be enough if only twelve men [can sit around it]?

 

For the rabbis π was 3 and not 3 1/7 . as we now know it is. To remind ourselves the circumference of a circle is diameter multiplied by π (or 2πr). In this case we know the diameter is 4 cubits for it is within a square where each side is 4 cubits. Since the diameter is 4 the circumference is 12, enough space for 12 people to sit around. So why does the sukkah need to be so big that 24 people can sit around the side?

הני מילי בעיגולא, אבל בריבועא – בעיא טפי.

 

That applies only to a circle, but in the case of a square, a greater perimeter is required.

 

Temporarily, the Talmud answers that the previous formula was true only for a circle. However, the perimeter of a square is more than three times its width. The round sukkah must have a circumference that would equal a square that is four cubits wide. So the circumference would indeed have to be more than 12 cubits.

As we shall see in tomorrow’s section, the math is still problematic.