# Tag Info

17

Try Pesachim 109a-b where the Gemara (and more elaborately in Rashi and Tosfot) tries to work out the volume of a Reviit in Etzba^3 based on its knowledge of the volume of a Mikva in Amah^3 (ie lots of basic algebra and unit conversion).

13

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.

10

Sefer Sheeris HaNachala mentions in the name of the Sefer HaItim that Rav Hai Gaon said that it is permitted to teach children Arabic and mathematics in order to assist them in learning Torah.

10

Okay, I'll address part of part ("Does it have value to the modern... math-learning audience?") of question 6, and part of question 5, for now. I've read chapter 1 only (and the main text only, not the marginal notes) so far, and it has definitions, postulates, and theorems from elementary plane geometry, lumping postulates and theorems together (i.e., not ...

10

In Hakirah vol. 14, they published an article called "'Learning' Mathematics" which includes examples of different mathematical applications in classical Jewish literature.

9

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): The rational-religious approach of Maimonides holds that, since we cannot know the exact values, the Bible tells us that we do ...

9

Don't take my word on the translation, but Shulchan Aruch 634:2 says: If it's round, it must contain within it a square of seven by seven t'fachim. And MB adds that any other shape has the same rule and that one need not sit in the contained square. You ask about wall length, though. For a circle, a contained square of 7×7 means, Baer Hetev and others ...

9

That is why we say "yesterday was the fourth day" before counting. You do not want to say "today is" in any way because even in an indirect manner you are counting today. Once you have said "today is" then however you say the number, that is still a count. "Code of Jewish Law Ganzfried - Goldin, volume 3 page 52 chapter 120 number 3 (translation of Kitzur ...

8

The MA holds that we split up the 12 hours of a day from Alot HaShachar (the beginning of day) to Tzeit HaKochavim (the end of the day). The Gra holds that the 12 hours are split from sunrise to sunset independent of what is considered day or night. All agree that noon must be when the sun is highest in the sky. (This can be proven from the gemara that says ...

8

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?

8

I remember doing the gemara on Sukkah 8a in high school while I was also in a geometry class in the afternoons. It's pretty basic high-school geometry stuff. Squares and circles. It's the Tosfos there, though, that go all out. It's particularly ingenious how Tosfos (bottom of the page) demonstrates that the ratio of the diagonal of a square to its side (...

8

You might want to show him Rambam Hil. Kiddush HaChodesh and the diagrams in the back, as well as Chazon Ish on Kiddush HaChodesh and the attendant illustrations. At the very end the Chazon Ish even includes a handy sine table! In R' Chaim Kanievsky's Shekel HaKodesh there is an appendix that explains the trigonometric underpinnings of the numbers given by ...

8

In Rava's scenario the entire square is the numerator, so it's not (green/orange), but ((green+orange+gray)/orange). So for your second diagram, the formula should be: BigArea/MigrashArea = ((2(r+1000+1000))^2)/(3(r+1000)^2 - 3r^2) or 3.6x10^7 / 9x10^6 = 4 Abaye, on the other hand, doesn't include the city, so for him it's ((green+orange)/orange). Since ...

7

This might simply have been a confusion of units. Sizes.com claims that a Russian verst is equal to 500 sazheni, but a Moscovy verst is 1000 sazheni. The sazhen was fixed at 7 English feet (2.134m) in both systems way back during the 1700s in Peter the Great's rule. In 397:1, the Aruch HaShulchan says that specifically, he is talking about the Russian ...

6

"ריש חזית" means "the beginning of מדרש חזית". The Midrash Rabbah on Shir Hashirim and Kohelles is often called מדרש חזית because it begins with derashos on the pasuk "חָזִיתָ אִישׁ, מָהִיר בִּמְלַאכְתּוֹ" (Mishlei 22:29). The author of the introduction you are reading begins by quoting Shir Hashirim Rabbah (1:8).

6

The Rambam here is giving an easy way to calculate the moment of conjunction for future months. A (lunar synodic) month, as you stated, is 29 days 12 hours and 793/1080 hours. Since 28 days is exactly 4 weeks (bringing us back to the same point in the week), the next conjunction will occur 1 day 12 hours and 793/1080 hours later in the week relative to the ...

6

This might refer to Deut. 4:2. There is the advice not add or remove commands. http://ohr.edu/this_week/its_not_quite_that_simple/5926 So associating this advice with maths and numbers might actually remove the context. Or in other words: This might add somthing by substracting.

6

I'd say if an average human, using an average human brain and eye, can't figure out the pattern, that's good enough. Rabbi Asher Weiss discusses the criteria of "does an unaided human notice it?" with regards to triggering some change deep instead some semiconductor someplace that I'd never notice. He points out that I may not drag a heavy bench on shabbos ...

6

The sefer Shmiras Shabbos K'Hilchasah (16:33) paskens without reservation that dice games for recreation (not gambling) are fully permitted on Shabbos. No qualification is made for fear of writing by accident. A strict opinion (which not all hold like as Halachah) is brought by the Chayey Adam (Shabbos 11:38). He holds that any game which usually involves ...

5

I think that the point is being missed here. There are not that many places where there is a difference between the written word (k'siv) and the way the word is pronounced (kri). This is especially true where the written word would be pronounced the same way. The reason is generally that neither is quite correct. The "real" word should be some combination. ...

4

Amazing what you can see when you look. Irv Bromberg at the University of Toronto discusses an adjustment. Currently there are 13 months in 7 years out of every 19; the new formula would involve 130 leap years out of every 353. As he clarifies, witnesses only determined when exactly the new month would start; the Sanhedrin could decide whether to make it a ...

4

There is a very slightly different account here, which places the story in the context of religious persecution and Rav Moshe's ostensible motivations for leaving Russia. But something tells me by "details about this story" you mean "specific contents of the calculus problem", in which case this is no help. . .

4

Not sure these quotes exactly answer your question, however they do show some of the major times when math was taught and introduced into Jewish schools. The last one seems particularly on topic. It was published in 1906, and reads: "On the 31st March 1805 members of the High German Jewish community in Altona formed an association with the purpose of ...

4

R. Abarbanel (in his Zevach Pesach) explains: The magicians had tried to replicate the first three plagues, but were unsuccessful with the third, lice, which proved to them retroactively that all three had indeed been God's finger, as would any remaining plagues be. That's why they didn't bother trying to replicate the remaining plagues, and why Pharaoh didn'...

3

According to MA day lasts from Dawn till Tzeis Hakochavim of R.Tam. It looks like Sunset on MyZmanim is calculated by other shita than R.Tam (maybe GR"A). That's why it looks like Plag Haminha of MA is 2 minutes before sunset. Here is a source that also states this. In paragraph: השעות הזמניות ודיניהן.

3

A couple examples in Eruvin come to mind. 14a brings proof that for halachic matters, pi = 3, and then continues to explain the dimensions of Solomon's pool. This contains some prealgebra and simple geometry. Also 23b discusses the difference between 7.666 and sqrt(5000), with Rashi giving an interesting way of calculating the square root of 5000.

3

Contemporary poskim discuss how to approach statistics -- we tend to work with concepts of mi'ut hamatzui -- a "commonly occurring though less than 50% event", for which we do need to check; vs. mi'ut sh'eino matzui -- a rare event, for which we don't. Many poskim treat 10% as the cutoff line for mi'ut sh'eino matzui, based on a fascinating application from ...

2

With regards to the short Amah, Rashi in Sukkah 5b (s"v Hanicha) says that there are three types of amos: 5 tefachim (20 etzba'os), 6 tefachim (24 etzba'os) and 6 tefachim + 1/2 etzbah (24 1/2 etzba'os). So when he says, "these four are really three" maybe he means that using the small amah of 5 x 4 = 20 tefachim. Using the regular medium amah 6 x 3 = 18 ...

2

assuming that a kezayit is 25.6 grams (as per http://www.chabad.org/search/keyword_cdo/kid/10951/jewish/Kezayit.htm) and that in all purpose white flour, there are 100 calories in 30 grams (http://caloriecount.about.com/calories-gold-medal-all-purpose-flour-i116037) there are, then, about 86 calories in a kezayit (I'm liberal arts also so my math is inexact)....

2

You may be interested in my Sefer which includes the Sugyos Eruvim Daf 14,57,76, Pesachim 109, Succos 7,8. It explains Gemara, Rashi, Tosfos, Marsha, Maharom, Gra, others, and presents every step in equation form and diagrams; it also makes corrections and clarifications on diagrams found in the Shas. It includes an Appendix on Basic Algrebra, 21 definitions ...

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