who knew??? a jewish math teachers dream! (and a nightmare for everyone else) === What is the halachically required circumference for a round sukkah? The sages set minimal dimensions for a sukkah to be considered serviceable. Thus, for example, according to Rabbi Judah the Nasi the length and width of a square sukkah must be no less than two meters by two meters: A sukkah which is less than four amot by four amot is invalid. One of the scholars, R Yochanan, said that if the sukkah were round, the minimal size must be in keeping with the minimal size of a square sukkah, so its size was set as such that 24 people could sit within its circumference. The scholars asked: Why does a round sukkah have to be so big? The space a person needs to sit is set at a half meter, so the circumference would have to be 12 meters, but for the circumference to match the area of the square, one would have to multiply the length of the square by three, which is the ratio between the diameter and circumference of a circle. If so, the circumference would only have to be 6 meters (2x3=6). The scholars answered that this ratio is between the circles diameter and circumference, but the ratio between the side of a square and its perimeter is four, and is larger than that of a circle. The scholars went on to ask: There still is no need for a circumference of 12 meters, for even with a square all that is needed is a circumference of eight meters. The scholars tried to explain the above sages opinion and argued that the large circumference required is so the round sukkah can contain the square sukkah. The scholars continued to ask: If we measure the diagonal of the square it will be only 2/5 larger than a side. If so, the diagonal is 2.8 meters, multiplied by three to obtain the required circumference, gives us only 8.4 meters. So why did R Yochanan demand a circumference of 12 meters? Answer: R Yochanan was not precise in setting the exact dimensions, and gave only an estimate. The scholars noted: Had R Yochanan set dimensions close to what should be needed, we could say that his measurement was an approximation and not precise, but since the difference is so great, it is not reasonable to attribute it to a lack of precision. Another scholar, Kashisha son of Rav Chida, explained Rabbi Yochanans demand by saying that the space required for a person to sit is not half a meter but only 33 centimeters. According to this calculation, the required circumference is only eight meters (0.33x24=7.92). The scholars asked: Does not the circumference of the circle have to be 8.4 meters? Answer: R Yochanan was not precise in his measurements. The scholars continued to argue that it is inconceivable to accuse R Yochanan of being imprecise and overly lenient. Another scholars, Rav Ashi, supposed that a man takes up half a meter when he sits and the outer circumference of 24 people sitting is indeed 12 meters, but R Yochanan calculated the inner circumference, which is only three meters. If so, the circumference of the sukkah is nine meters. Though 8.4 meters would be sufficient, R Yochanan rounded upwards to nine meters. Other scholars tried to reconcile the matter in a different way. They argued that the required circumference to place a square into a circle is one and a half times the perimeter of the square, so the required circumference of the circle needed to place a two meter by two meter square inside it would be 12 meters (8x1.5=12). Other scholars answered that their words were erroneous, for experience shows one can put a square into a circle whose circumference is smaller than that. (Babylonian Talmud, Tractate Sukkah 7b-8a)
Posted on: Mon, 13 Oct 2014 14:28:00 +0000
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