POINT BY POINT SUMMARY
by Rabbi Ephraim Becker
Kollel Iyun Hadaf, Yerushalayim
Rosh Kollel: Rabbi Mordecai Kornfeld
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Previous dafSukah 8
1) A ROUND SUKAH
(a) (R. Yochanan) A round Sukah is Kosher if its circumference
is large enough to contain 24 people.
2) THE GEOMETRICAL FORMULAE OF THE RABANAN D'KESARI
(b) Question: R. Yochanan's requirement aligns with no other
opinion, even the largest opinion (Rebbi, who says that any
Sukah which is not 4x4 Amos is Pasul)!?
1. A person can sit in a space of 1 Amah (thus R.
Yochanan's 24 people must be 24 Amos).
(c) Answer: This relationship between the circumference and
diameter applies only to a circle.
2. But we know that the relationship of the circumference
to the diameter is 3 to 1.
3. Then taking the largest requirement for the width of a
Sukah, Rebbi's (four Amos), it should suffice to have a
circumference of only 12 Amos (not 24)!
1. The perimeter of a square, though, is larger than the
ratio of 3:1.
(d) Question: But that still does not give us 24!?
2. Thus in order to have a circle which has a
circumference equal to the perimeter of a 4 X 4 Amos
square, the circle must be larger than 12 Amos in
1. A square is a fourth (25%) larger than a circle (Rashi:
a circular Amah is surrounded by a 3 Amah
circumference, while a square Amah is surrounded by a 4
(e) Answer: This formula (that a square is 25% larger than a
circle) applies only to a circle which is inscribed within a
2. It should then suffice to have a circumference of only
16 Amos (and still not 24)!
1. The diameter of the inscribed circle is equal to the
length of a side of the square.
(f) Question: But that would still give us only 16 4/5 Amos!?
2. However, the size of a circle which is circumscribed
around a square (i.e. the square is inside the circle,
such that the diameter of the circle is equal to the
diagonal of the square) must be larger, because of the
arcs of the circle.
1. The relationship of a side of a square to its diagonal
is 1 to 1 2/5.
(g) Answer: R. Yochanan was not exact in his number.
2. Thus, the diagonal of the square, which is the same as
the diameter of the circle around it, is 4 X 1 2/5 = 5
3. Since the circumference of a circle is 3 times its
diameter, the circumference of this circle is 5 3/5 X 3
= 16 4/5).
4. It should then suffice to have a circumference of only
16 4/5 Amos (and still not 24)!
(h) Question: We only say that one was not exact in his number
when the difference is small, not when it is so large (24
vs. 16 4/5)!?
(i) Answer (Mar Kashisha): R. Yochanan's number was based on the
assumption that 3 persons fit in 2 Amos (not one person in
(j) Question: If so, R. Yochanan was saying that the size of the
circumference of the round Sukah needs to be only 16 Amos (3
person in 2 Amos = 24 persons in 16 Amos), yet we concluded
that the circle around a square which is 4 X 4 Amos must
have a circumference of 16 4/5 Amos!
(k) Answer: R. Yochanan was not exact in his number.
(l) Question: We only say that one was not exact in his number
when he was rounding off to a figure that would be
1. Here R. Yochanan (who says that the circumference must
be 16) is rounding off to a figure that would be
(m) Answer (R. Asi): R. Yochanan was not including the place
where the person sits, which makes the measured
circumference 18, not 24.
2. This would allow for a smaller Sukah than actually
1. R. Yochanan's number was indeed based on the assumption
that one person fits in one Amah.
(n) Question: But we determined that it is enough to have a
circumference of 16 4/5 Amos (and not 18)!
2. However, R. Yochanan was not including in the size of
the Sukah the place which the sitting person occupies.
3. Rather, the Sukah is measured from *within* (or inside)
the place where the person sits.
4. Hence, if 24 people sit around the Sukah and we do not
include the Amah in which they sit, the circumference
of the circle comes out to be 18 (Rashi: we subtract
two Amos from the diameter of the circle [one Amah on
each 'side' of the Sukah] leaving a diameter of 6. The
circumference of such a circle is 18).
(o) Answer: That is where R. Yochanan was not exact in his
number, and his inexactness was a Chumra.
(a) The circle that comes out from within a square is a fourth
(25%) smaller than the square around it.
(b) The square that comes out from within a circle is one half
(50%) smaller than the circle around it.
3) FULFILLING THE MITZVAH WITH SUKOS BUILT FOR OTHER PURPOSES
(c) Question: This is not so, for we see that the circle
circumscribed around a square is not so much larger.
(Question remains unanswered. See Insights)
(a) (R. Levi citing R. Meir) The inner Sukah of a Potter (used
for residence) is not Kosher as a Sukah, and it requires a
Mezuzah, because it is the place in which he lives all year
(b) The outer Sukah (used as his shop and store) is a Kosher
Sukah, and is exempt from a Mezuzah, because it is not
normally used as his residence.
1. Question: Why is the outer Sukah exempt from a Mezuzah
(it should be like an entrance hall to a house, which
requires a Mezuzah)!?
(c) (Beraisa) The Sukos of GaNVa"CH - The Sukos of Goyim,
Nashim, Behemah, Kusim,- and any Sukah (not made for the
Mitzvah) are Kosher, as long as it has Halachic S'chach.
2. Answer: Since the whole structure is permanent, we only
go as far as to obligate the residence Sukah in
Mezuzah, not to consider the outer Sukah as its
1. Question: What is particular about these as needing
(d) (Beraisa) The Sukos of RaKVa"SH - The Sukos of Ro'im,
Kayatzim, Burganin, Shomrei Peros,- and any Sukah are
Kosher, as long as it has Halachic S'chach.
2. Answer (R. Chisda): The S'chach must have been placed
on the Sukah to provide shade (not only for privacy).
3. Question: What is added by "any Sukah?"
4. Answer: It includes the Sukos of RaKVa"SH, as in the
1. Question: What is Halachic S'chach?
(e) Question: Why did each Tana specify one group of Sukos and
add the other group with "any Sukah?"
2. Answer (R. Chisda): The S'chach must have been placed
on the Sukah for shade (not only for privacy).
3. Question: What is "any Sukah" adding?
4. Answer: It adds the Sukos of GaNVa"CH as we learned in
the earlier Beraisa.
(f) Answer: Each specifies the group of Sukos more likely to be
considered Kosher, and adds the less likely group in the
1. The first Tana held that the Sukos of GaNVa"CH have the
Halachic advantage of being more permanent, compared to
the RaKVa"SH Sukos which are, at times, not even left
standing for seven days, (so he needed to add the
RaKVa"SH Sukos as Kosher).
2. The second Tana held that the Sukos of RaKVa"SH have
the advantage of being used by people who are Chayav in
the Mitzvah of Sukah (and he thus adds the Sukos of
GaNVa"CH which are used by those who are Peturim).