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15

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).


11

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

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


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 ...


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 ...


8

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 ...


7

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 ...


7

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 ...


7

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 ...


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 ...


7

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 ...


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 ...


5

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?


4

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 ...


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 ...


3

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. . .


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

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 ...


3

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 ...


2

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. ...


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 ...


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 ...


2

Yaskil Avdi (vol. 1 Orah Haim siman 7) permits it (he was asked by Rabbi Masliah Mazuz). As well as Sis Eliezer (vol. 9 siman 15). See the aforementioned Yabia Omer 7:21. I found in Yalkut Yosef vol. 2 pg. 255 אין לערוך הרצאות של חול בבית הכנסת, וכל שכן לערוך שם קונצרטים וכיוצא בזה. אלא אם כן ההרצאה כוללת גם דברי חיזוק ועידוד לשמירת התורה והמצוות (כגון ...


2

Since your need seems to be to figure out "when to start saying ותן טל ומטר in diaspora", I'll just focus on that (and ignore the mention of the tekufah in the title): To simplify things, start with the date November 21. You will then need to adjust based on two rules: If the following year is a Gregorian leap year, push the day off by one (i.e. November ...


1

Here's a very partial answer: In the United States in 2012, 1,570,976 of the 3,952,841 live births, or 39.7%, were the first live birth to that mother. Among mothers listed as non-Hispanic and white (which I mention only because I think the vast majority of Jews in the States are so listed and the category is available to me), 895,171 of the 2,134,044 live ...


1

This past tekufat tishrei was October 7, 2011 at 9 PM. To calculate the next tekufat tishrei: add six hours to the previous year's time, while subtracting 24 hours for every civil leap year passed in between tekufot tishrei. Source To generalize, tekufat tishrei for future years is on October 7 at time: ((6 hours*(year mod 4)) - 3 hours) + (24 hours * ...


1

http://www.hebrewbooks.org/pdfpager.aspx?req=20713&st=&pgnum=4 this link shows the Haskamos on the Sefer איל משולש. In the haskomos it mentions how it is worthy to publish this Sefer to show that the Jews are the true Chachomim. The name of the Sefer is Ayil Meshulash



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