Questions tagged [mathematics]

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Will the real Shas Kattan please stand up

There is an old tradition commonly referenced in the yeshiva community that Masekhet Ketubot is the "Shas Kattan" of Talmud Bavli, that is, it contains ideas that connect to just about every ...
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Midpoint of each Sefer

I am looking for sources that tell what word, letter and verse is at the midpoint of each Sefer, meaning 5 midpoints if considering the Torah containing 5 books or if you want, 7 as the Talmud states ...
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187 views

Chazal using calculus

We see various math issues that show up in Chazal, but I don't usually see calculus. Thus, I was surprised to see the same topic in two places in Maseches Mikvaos, and in both I think you need ...
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117 views

Amah, tefach, and pi

I have a question on Eruvin 14a bottom which says that Shlomo's pool was round, had diameter of 10 amot and thickness 1 tefach, and circumference 30 amot (we learn from this that halachically pi=3). ...
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Can "round" refer to an ellipse, in the case that ratio of circumference to length is 3:1?

As quoted in Eruvin 14a, from Kings I 7:23, we know that Shlomo's pool was round, measuring 10 across and 30 around. There have been discussions about how the ratio of these (3:1) is only an ...
596 views

Maggid Mishnah on relying on approximations for π and √2

In a previous discussion, it was stated: The Maggid Mishnah in Hilchos Shabbos (17:26) says that one may rely on π=3, but he says in Hilchos Eiruvin (3:2) that one may not rely on √2=1.4. I can't ...
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579 views

Why are there different versions of what Chazon Ish says is the size of an Amah?

Different sources have different information regarding the size of an Amah (all measurements are attributed to Chazon Ish): Halachipedia - 24 in. / 60.96 cm Dafyomi.co.il - 22.72 in. / 57.72 cm Daat....
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231 views

Changing from Base-10 to Base-7 in sefiras haomer

I saw years ago a fascinating idea regarding the counting of sefiras haomer. The source was discussing the change in counting between the days and the weeks. We first start counting in base-10: "...
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169 views

What is R. Chananel's/R. Bachye's calculation of the years in Egypt?

In this answer I collected the opinions of various biblical commentators as to how many years the Israelites actually spent in Egypt. One of those views was that expressed by R. Chananel, as recorded ...
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1 vote
127 views

Mathematical functions in Jewish Halacha [closed]

What mathematical operators, functions, and constants are mentioned in the Halachah besides addition, subtraction, multiplication, and division? For example: powers and square or other roots, Pi etc....
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Why does the date for the prayer for rain change from one century to the next?

My due diligence: Praying for rain in the Diaspora How to calculate 60 days from tekufat tishri for any given year? On which evening should we start saying “V'tein tal u'matar li'vrachah”? I see ...
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1 vote
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Translation (or searchable version) of *Sefer Elim* of Rabbi Joseph Solomon Delmedigo

Does there exist any translation of the Sefer Elim of Rabbi Joseph Solomon Delmedigo into a European language? If not, does there at least exist a text-version of the original Hebrew version (all I ...
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וקמת ועלית - how did they measure Jerusalem's highest point?

On the Pasuk (Deut 17,8): כִּי יִפָּלֵא מִמְּךָ דָבָר ... וְקַמְתָּ וְעָלִיתָ אֶל־הַמָּקוֹם אֲשֶׁר יִבְחַר ה' א' בּוֹ׃ If a case is too baffling for you to decide, ... you shall promptly ascend to ...
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How the irrational number Pi can be derived from the Torah?

Some traditions say, based on a Gemmorah in Taanis 9a (also מדרש רבה נשא י' ו', זוהר פנחס רכ"א א, and more): "ליכא מידי דלא רמיזא באורייתא" "There is nothing that is not alluded ...
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112 views

Polygons in Tanach/Gemara

Is there a source that compiles the different times that polygons and other non-polygons that come up in tanach/gemara? I'm looking to fine any place where quadrilaterals, pentagons, hexagons etc. ...
148 views

Why does Yisro recommend so many judges?

In Shemos 18:21 Yisro tells Moshe that he shouldn't judge Bnei Yisrael himself, instead he should appoint: וְאַתָּ֣ה תֶחֱזֶ֣ה מִכָּל־הָ֠עָם אַנְשֵׁי־חַ֜יִל יִרְאֵ֧י אֱלֹהִ֛ים אַנְשֵׁ֥י אֱמֶ֖ת ...
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Source for the "gra's" calculation of pi

I am looking for a textual source for this famous GRA which corrects the מקרא calculation of Pi from 3 to 3.1415 based on the kri and ksiv of קו vs קוה. Based on my research there may not be a written ...
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Why are some dates off by one day?

The Hebrew calendar works on a 19-year cycle of leap years and a 247-year cycle of varying types of years. This is discussed more fully in Shvili d'Rakia, printed in all Mishnayos containing Tiferes ...
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אצבע אלוקים היא - *how* many? [duplicate]

We all know the part of the seder in which we talk about how many makot were part of an אצבע (10) and how many were part of a יד (50). But wait a minute. The phrase אצבע אלוקים היא was not told at ...
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Probabilities vs תמים ? Weather forecast etc

There is an issur to ask astrologers (Pess. 113; Shul.Ar. YD 179,1). And Rashi says (Dev. 13, 18) התהלך עמו בתמימות ותצפה לו ולא תחקור אחר העתידות So, is then a problem to ...compute probabilities? ...
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Mathematical books of the Ibn Ezra [closed]

I am interested in studying one of the mathematical compositions of the Ibn Ezra. Is anyone familiar with the easiest book that he wrote? Thanks
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1 vote
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Sefeikos and Mathematical Modelling

I heard from a colleague that there exists a Sefer where the conclusions of Chazal on the status of certain Sefeikos can be represented in the form of probability models1. Could anyone verify if ...
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Can one rely on rounded irrational numbers?

Chazal often talk about irrational numbers in their math discussions. For instance, Sukkah 7b-8a uses both √2=1.4 and π=3 in its discussion, and Eiruvin 76a-b uses the same numbers in an almost ...
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1 vote
115 views

How many people are needed to (virtually) eliminate a person's sickness?

(Alright, how many ben gilo's.) The Gemara in BM 30b says that each ben gilo visitor to a sick person eliminates 1/60 of their sickness by taking it upon himself. Presumably this means 1/60 of what's ...
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How complicated can a vesst pattern be?

Background: In the laws of niddah there is something called a vesst haflaga, which is a period that occurs at some consistent interval. If a woman establishes a pattern for some amount of consecutive ...
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Rolling dice on shabbat?

I was told that when rolling dice [for a game, such as backgammon] on shabbos one should roll one di, move the pieces, and then roll the other di [and move the pieces]. The reason for this, I was told,...
303 views

Game theory in the Tanaim

I read an article a while back (maybe over a year ago?) in the Mishpacha English Magazine (I'm pretty sure, although it may have been in the Ami) that discussed a certain machlokes Tanaim about how to ...
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What is the hallachic definition of randomness?

A new Shabbat-friendly technology, KosherSwitch, uses randomly timed light pulses to create various safeks, so that flipping the switch does not hallachically count as switching the light on, even in ...
205 views

Why do all of them say that there were 5 times more plagues at the sea, instead of 1.5 times?

In the Haggadah it says: (text from WikiSource) רַבִּי יוֹסֵי הַגְּלִילִי אוֹמֵר: מִנַּיִן אַתָּה אוֹמֵר שֶׁלָּקוּ הַמִּצְרִים בְּמִצְרַיִם עֶשֶׂר מַכּוֹת וְעַל הַיָּם לָקוּ חֲמִשִּׁים מַכּוֹת? ...
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More Maaser and Tax Math

Let's say your income before taxes and contributions was \$1,111, and your tax rate is 10%. Ordinarily, you would pay \$111.10 in taxes, and have \$999.90 left over, which would be eligible for maaser. ...
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If the Torah tells you not to add or subtract, what does it imply for behaviour?

If the Torah forbids addition and subtraction, what does it imply for Jews, and for ultra orthodox jews, regarding practical life? It is a baffling rule. Can you you use money at all? can you not ...
288 views

Today is the square-root of 25th day of the omer

If you haven't counted sefirat haomer yet that night, you're not supposed to say the current day (for example, 'today is the 5th day') before making the bracha. But what about saying what today is in ...
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Slide Rule on Shabbos/Yom Tov

May a slide rule (mechanical device before calculators) can be used on Shabbos for Gemara calculations?
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What is considered a Safek?

I've been learning all these laws about Sekefot-doubts, but I'm coming up shy on a basic point. What is considered a Safek? Example:if there are 100 pieces of lettuce and I check all of them and only ...
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How can we explain the growth of Israelite population in Egypt?

Jacob and his family went to Egypt numbering (approximately) 70 people. After approximately 200 years, 600,000 men between the ages of 20-60 (if I'm not mistaken). So probably 2 million total got ...
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Aruch Hashulchan's moon-distance estimate

Aruch Hashulchan (1829–1908), Orach Chayim 397:1, says that a מיל is the same as a Russian верста (verst) or 500 сажен (sazhen), which comes to 1066.8 meters. In 426:2, he says the distance to the ...
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How does this math work out?

The Gemara Eiruvin 56b said that the Migrash (the orange area) is one quarter of the area of the sados (the green area). Let's look at the math. (This is how I understood the maskana) greenArea = (2r+...
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What does ריש חזית mean?

I'm reading(/trying to read) the introduction to the Vilna Gaon's איל משולש (his geometry textbook). The first two words are ריש חזית. What does ריש חזית mean? If it helps, the phrase is immediately ...
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How many calories are in a KeZayith of flour?

I've often wondered how I can be sure I've eaten a KeZayith of flour when I eat something small but complete - like one cookie - and struggle with the decision of whether or not to eat more in order ...
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Rambam's method for calculating the conjunction of the moon (and sun)

I think I'm missing something basic here... The Rambam, in Hilchot Kiddush Hachodesh (6:3) says that the interval between one conjunction to the next is is 29 full days, 12 hours of the 30th day, and ...
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An improved Jewish calendar after this one expires?

Conventional wisdom has it that about 1600 years ago, the latter Hillel utilized his Sanhedrin to sanctify the Hebrew calendar as we know it today until the year 6000. (Presumably by that point we'll ...
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High School Math in the Talmud

I'm currently tutoring someone in math that has an atitude of "what's the point of all this... why would I ever need this..." (which is typical of many high-schoolers). To try to pique his interest, I ...
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Pidyon HaBen rate

About how many pidyon haben ceremonies are required to be performed per 1000 Jewish births in the past few decades? The requirements for a pidyon haben are: Both parents are Israel, not Kohen or ...
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Mikvah Math for the Sea of Shlomo

In calculating the number of Mikvas that the "Sea of Shlomo" could hold, the Gemara (Eruvin 14b) calculates that it would hold 150. The Gemara asks, that being that the Sea was round, and the area/...
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Is the passage describing an approximation of pi or is it one of the miracles of Bais Hamikdash?

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? ...
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How to calculate 60 days from tekufat tishri for any given year?

I'm trying to pin down an algorithm for calculating when to start saying ותן טל ומטר in diaspora. (In Israel it begins 7 Cheshvan.) I've gotten that we need to know how many centuries passed since ...
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349 views

Mathematics in Cheder

I recall reading that their is a pesak/teshuvah/report by a major posek, perhaps an early "later" Acharon, (Rabbi Akiva Eiger zt"l) which noted that at least elementary arithmatic or mathematics was ...
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Magen Avraham - Practically no Plag HaMinḥah or just no Plag HaMinḥah in winter?

Calling all science and math-oriented Judaism.SE-ers! According to the website MyZmanim.com, today's Halachic times where I work are as follows (only a handful of times are shown because the question ...
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How big does a pentagonal Sukkah have to be?

What is the minimum length requirement for each of the walls of a 5-sided sukkah? What about 6 sides? What about 7? ... What about ∞ sides (i.e. a circle)?
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