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Eruvin 14

ERUVIN 11-15 - sponsored by a generous grant from an anonymous donor. Kollel Iyun Hadaf is indebted to him for his encouragement and support and prays that Hashem will repay him in kind.


OPINIONS: The Tana Kama in the Mishnah (13b) says that a Korah must be strong enough to hold a brick. Rebbi Yehudah argues and says that even if the Korah is made of straw, we view it "as if it is metal."

The Mishnah continues and says that if the Korah is bent, we view it "as if it is straight," and if it is spherical (lengthwise), we view it "as if it is rectangular."

Is this last statement of the Mishnah a continuation of Rebbi Yehudah's opinion? Or does the Tana Kama agree that "as if" can be applied in this instance?

(a) The ROSH points out that the Gemara uses different phrases when it asks questions on the statements in the Mishnah. First, when citing Rebbi Yehudah's statement that if the Korah was made of straw we view it as if it was made of metal, the Gemara asks, *Mai Ka'mashma Lan* ("What is this statement teaching us" -- Rebbi Yehudah already said that the Korah does not have to be strong). Then, when it cites the statement that if the Korah was bent we view it as straight, the Gemara asks, *Peshita* ("That is obvious"). Later, when it mentions the third statement of the Mishnah that we view a round Korah as if it were square, the Gemara asks *Ha Su Lamah Li* ("Why is it necessary to mention this as well?")

The Rosh explains that the first question addressed specifically the opinion of Rebbi Yehudah. However, the second statement, that we view a bent Korah as if it were straight, is "obvious" -- that is, it is even more logical to apply the "as if" reasoning in this case. If so, the Tana Kama of Rebbi Yehudah may ascribe to it as well. In fact, the Gemara concludes that the Mishnah is teaching a Halachah that was also taught by Rebbi Zeira, and it is logical to assume that Rebbi Zeira was explaining the Halachic opinion (i.e. the Tana Kama rather than Rebbi Yehudah). When the Gemara discusses the thrid statement of the Mishnah, that we view a round Korah as if it were square, the Gemara asks *Ha Su Lamah Li* -- this Halachah is *identical* to the previously mentioned one. That is, here too the Tana Kama applies the logic of "as if." (This is the ruling of the RAMBAM, Hilchos Shabbos 17:26, as well.)

(b) RASHI in our Sugya (DH Peshita) explains that the logic of "as if" applies *equally* to a bent Korah and to a weak Korah. It is Rebbi Yehudah, then, who made both statements, and the Tana Kama *never* applies the logic of "as if." (This is also the approach of Rav Yehonasan m'Lunil; see, however, the Bach there.) The RITVA cites a Yerushalmi that seems to support Rashi's interpretation of the Mishnah.

HALACHAH: The SHULCHAN ARUCH 363:20 rules like the Rosh and the Rambam (a), and applies the logic of "as if" to a bent or round Korah.
QUESTION: The Gemara says that the circumference of a circle is three times greater than its diameter. How do we reconcile this Gemara with the known fact that the ratio of the circumference of a circle to its diameter is slightly more than three (Pi=3.14159...)?
(a) The TOSFOS HA'ROSH explains that the Gemara itself is addressing this issue. Why does the Gemara ask "from where do we learn" that the circumference of a circle is three times greater than the diameter? We do not need a verse to teach us a mathematical fact! The Gemara must be asking from where do we learn that we may use a slightly *inexact* value for determining the circumference of a circle. The Gemara learns from the verse that one may round off the relationship of the diameter of a circle to its circumference for all Halachic purposes, and assume it to be three. This is learned from the verse which describes the circumference of the Yam Shel Shlomo as *three* times its diameter.

Similarly, the RAMBAM (Perush ha'Mishnayos; see also Hil. Tum'as Mes 12:7) writes that Pi is actually an irrational number. "The exact relationship of the diameter to its circumference cannot be known and it is not possible to speak of it... and its actual value cannot be perceived." He writes that the value which is commonly used in calculations is 3 1/7 (3.142857...). The Tana'im of the Mishnah rounded this number and expressed it in terms of the nearest whole integer (3).

(c) It has been said in the name of the Vilna Ga'on (and more reliably, in the name of one Dr. Adler, a Jewish professor of mathematics in Germany) that in the verse (Melachim I 7:23) that the Gemara cites, there is a Kri and a Kesiv; a word is pronounced differently than it is spelled. The word in the verse is written "v'Kaveh" (with a "Heh" at the end), but it is pronounced "v'Kav (with no "Heh"). The Gematria (numerical value) of the word "Kav" is 106, and the Gematria of the word "Kaveh" is 111. The ratio of the K'siv (111) to the K'ri (106), or 111/106, is 1.0471698. This value is an extremely close representation of the relationship of the real value for pi to 3 (111/106 = 3.1415094/3).

Hence, the difference between the actual value of pi and its practical value is expressed by the difference between the Kesiv (the actual, but unread word) and the Kri (the word as we use it) of the verse discussing pi!


OPINIONS: Rava says that a Lechi that was placed over three Tefachim away from the wall is invalid, because "Gedi'in Bok'in Bo," young goats walk though the area.
(a) TOSFOS (10b, DH v'Oseh) seems to explain that the Lechi is invalid when distanced more than three Tefachim from the wall because the rule of Lavud cannot be applied to it, and therefore the Lechi is not connected to the wall.

(b) RAV YEHONASAN M'LUNIL explains that the Lechi is invalid because the airspace on each side of the Lechi is larger than the Lechi, and therefore the Lechi becomes Batel ("Asi Avira d'Hai Gisa u'd'Hai Gisa v'Ka Mevatel Lei").

The difference between these two reasons manifests itself in a case where a wide Lechi (such as one that is four Tefachim wide) was placed a distance of more than three Tefachim away from the wall, such that the distance between it and the wall is less than the width of the Lechi itself. According to Rav Yehonasan, the Lechi will be valid, because the airspace between the Lechi and the wall is smaller than the Lechi. According to Tosfos, though, the Lechi is invalid because Lavud cannot be applied. (Tosfos, ibid., indeed says explicitly that such a Lechi will be invalid because of the problem of Lavud).

The TEVU'OS SHOR brings proof from the Gemara here to the opinion of Tosfos. Tosfos says that the Lechi that is far away from the wall is invalid because Lavud cannot function to connect it to the wall. We see that Tosfos requires the Lechi to be attached to the wall. Rav Yehonasan, on the other hand, does not require the Lechi to be attached to the wall, and that is why he says that the problem is that the airspace on each side of it invalidates it.

According to Rav Yehonasan, why does the Gemara say that the problem is that young goats can walk through the space, thus making it unattached to the wall? It does not have to be attached to the wall according to Rav Yehonasan!

REBBI AKIVA EIGER answers that the reason of "Gedi'in Bok'in Bo" that the Gemara gives is necessary to explain why *Raban Shimon ben Gamliel* invalidates this Lechi. According to Raban Shimon ben Gamliel, Lavud (up to *four* Tefachim) makes it as if there is no airspace between the Lechi and the wall, and thus there is no airspace to annul the Lechi. Why, then, is the Lechi invalid according to Raban Shimon ben Gamliel? Says the Gemara, because young goats walk through that space and thus Lavud cannot work to take away the airspace. Once Lavud is not applied, the reasoning that "air on either side annuls it" can be applied to invalidate the Lechi.

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