Tell me more ×
Mi Yodeya is a question and answer site for those who base their lives on Jewish law and tradition and anyone interested in learning more. It's 100% free, no registration required.
up vote 6 down vote favorite
1

In Sepher M'lakhim we read how different measurement was taken. I wonder if this passage (Ⅰ M'lakhim 7:23) is describing an approximation of PI (3.1415...), or was this one of the hidden miracles?

וַיַּעַשׂ אֶת־הַיָּם מוּצָק עֶשֶׂר בָּאַמָּה מִשְּׂפָתֹו עַד־שְׂפָתֹו עָגֹל ׀ סָבִיב וְחָמֵשׁ בָּאַמָּה קֹומָתֹו [וּקְוֵה כ] (וְקָו ק) שְׁלֹשִׁים בָּאַמָּה יָסֹב אֹתֹו סָבִיב׃

Now he made the sea of cast metal ten cubits from brim to brim, circular in form, and its height was five cubits, and thirty cubits in circumference.

share|improve this question
1  
can you define what you mean "one of the hidden miracles"? are you saying that it was a miracle that it was only 30 cubits, instead of the true value it should have been mathematically? – Menachem Jun 6 '12 at 22:48
1  
I'm no believer in biblical literacy, but I've never seen the problem here. It doesn't say "10 cubits to infinity decimal places", it says "5, 10 and 30 cubits" That, to me, suggests that I probably rounded up from nine and a half -- why is that a problem? – Jack V. Jun 12 '12 at 14:30
Thank you all for taking your time answering my questions. It is greatly appreciated. – Millthorn Jun 17 '12 at 15:40
Inner diameter; outer circumference? Or a curved in lip on the bowl with the circumference measured around the middle of the bowl, and the diameter across the top? Frankly, I've never seen the problem here. – TRiG Jul 17 '12 at 18:05
Related: judaism.stackexchange.com/q/18903. – msh210♦ Sep 4 '12 at 3:32

3 Answers

up vote 9 down vote accepted

It's approximating π, as is clear from the g'mara (Eruvin 14:1).

The problem is that that g'mara seems to be saying that it's a pretty precise approximation, and we know it's not. (Tosafos there raise this question and offer no answer.)

But to answer your question, whether it's an approximation of π or a miracle, it's the former.

share|improve this answer
Thank you very much. I had hope for a definite answer. I'm satisfied to know that is is non. I'm satisfied with the explanation you gave. I hope that I can learn form g'mara my self some day. – Millthorn Jun 6 '12 at 16:41
1  
To your question, whether the verse is approximating π or describing (no pun intended) a miracle, I think there is a definite answer: it's approximating π. – msh210♦ Jun 6 '12 at 18:46
IIRC, one of the other tosafos, (Tosafos HaRosh, I think, but I can't find a copy online) rereads the gemara so that it makes more sense. I don't really remember how, though. – jake Jun 6 '12 at 19:32
up vote 7 down vote

Wikipedia has a set of answers in their article on Approximations of pi. That links to a terrific article on rabbinic approximations of π by Boaz Tsaban and David Garber. Tsaban and Garber summarize as follows (pp. 10-11):

  1. The rational-religious approach of Maimonides holds that, since we cannot know the exact values, the Bible tells us that we do not have to worry about this and that is suffices to use the value 3.
  2. The mystical approach of [Matityahu Hacohen] Munk contends that 3 was indeed the ration of the circumference to the diameter in King Solomon's temple: This value is used in order to bridge the gap between our world and the "world of truth." For the sake of consistence, the halachic conditions are applied to the suitable regular polygons.
  3. The practical approach of R' Shimon Ben Tsemah [who learns from other places in Talmud that they used a more precise version of π] asserts the the rough approximations are used when teaching the students, but, when it comes to practice, the calculations are to be done by the experts.

So to answer your question, if you hold by Munk (I don't know who he is), then it's a miracle. If you hold by Rambam or R' Shimon ben Tsemah, it's an approximation

((Aside: two different psaks come out of this for practical reasons like sukkot - either you use the best mathematical approximation (R' Shimon ben Tsemah) or you use 3 (Rambam and Munk). In order to use 3 as π, you can just measure the perimeter of the interior inscribed regular hexagon.))

share|improve this answer
Rabbi Max Munk "three geometry problems in tanach and talmud" (Hebrew), SINAI, 51: 218-227 (Harav Kook Institution, 5722) -- one of the sources used in books.google.co.cr/… -- looks like it's the same – Menachem Jun 6 '12 at 23:17
up vote 4 down vote

The GR"A points out the following:

The word circumference (kav) is spelled קוה but pronounced קו. The gematria of the former is 111 and the latter is 106. The ratio of 111 to 106, multiplied by the approximation of 3, gives you:

(111 / 106) * 3 = 3.1415

Perhaps pi to five digits is a better approximation than 3?

share|improve this answer
1  
So you're taking the approximation side, not the miracle side. – Double AA♦ Jun 6 '12 at 19:06
3  
At what point is pi ever not an approximation? I think five places is pretty good. – yoel Jun 6 '12 at 19:08
Indeed pi is a transcendental number. I'm only pointing out how you try to answer the question, because it wasn't very clear from your post. – Double AA♦ Jun 6 '12 at 19:10
I plead ignore: why do you take the ratio? And then why use the ratio to scale the approximation? Is there any methodology for this? And is there any suggestion that the value 3.1415 should be used in place of 3? Where does the Gra say this? Does he explain it? – Curiouser Jun 6 '12 at 19:23
4  
@Curiouser, Early authorities had already proposed that the reason the "ה" is not extant in the kri is to hint to the fact that the measurement is in fact an approximation and is actually "missing" some length. The Gr"a is merely showing that there is a neat remez that can show how the number was approximated, that is the approximation is essentially a scaling by the ratio of the kri with the ksiv. There is no "methodology". If it would have been easier to hint to e.g. the difference instead of the scaling factor, perhaps it would have. – jake Jun 6 '12 at 19:48
show 2 more comments

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.