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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 figured it would be great if I could provide him with examples from the Gemara that actually make use of some of the regent-level math he's learning.

So my question is what are some examples from the Talmud (Rashi and Tosfos included) that make use of (or refer to) high school level math?

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How about ways one would use math practically for Halachic purposes? – Isaac Moses Dec 19 '12 at 3:52
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I recommend you look through the archives of cheshbon.weeklyshtikle.com – Isaac Moses Dec 19 '12 at 3:54
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If that won't impress him, you can tell him about this guy you know through an internet forum who frequently has to divide fractions at work for reasons that are difficult to explain in a comment box. :) – Seth J Dec 19 '12 at 4:08
Really, if a person doesn't find math intrinsically beautiful, it's probably hard to make a specific case for learning past arithmetic, given that most math is abstracted away from us in 21st c. Western society. Might want to look at the remarkable manifestations of math constructs in nature. Basic algebra is certainly related to logic though, so a good foundation in that is a good thing WRT Talmud. He should be able to cross over from e.g. kal va-chomer and represent that quasi-algebraically (if a > b etc.) – yitznewton Dec 19 '12 at 5:50
See Igros Moshe Choshen Mishpat 2:30 for why you need to treat secular subjects seriously. – Curiouser Dec 19 '12 at 11:57

4 Answers

up vote 12 down vote

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).

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It gets pretty complicated, so be warned. – Double AA♦ Dec 19 '12 at 3:24
Good stuff. I find the hardest part about it to be the terminology, while in terms of math concepts it is right up there at high school level. – WAF Dec 19 '12 at 4:45
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@WAF Makes you glad we have a decimal system! – Double AA♦ Dec 19 '12 at 5:00
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Yeah it's actually not that bad to take a calculator and verify the Gemara's result of "how many cubic fingers make a quarter-log of volume?" The problem is tracking the way various medieval commentaries do the math -- they use some very convoluted methods to avoid fractions until the bitter end! (And then Tosfos says the Yerushalmi has a different number, it meant a round cup instead of a cubed one ...) – Shalom Dec 19 '12 at 8:46
up vote 10 down vote

In Hakirah vol. 14, they published an article called "'Learning' Mathematics." Right now, only the first two pages are available online to non-subscribers, but they provide a few examples already. The full article will become visible when the next issue of Hakirah is published. (I personally don't subscribe to Hakirah so I can't tell you what's in the article beyond those two pages.)

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up vote 5 down vote

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 the Rambam.

The Mirkeves HaMishneh wrote a kuntres called Breichos B'Cheshbon (included in some editions of Mirkeves HaMishneh) which provides advanced mathematical explanations for various sugyos. About 30 years ago it was translated into English and explained, in a book called Approaching Infinity. It was a fascinating read, but I don't know where you could find it now. Perhaps interlibrary loan or such?

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Approaching Infinity seems to be on re-order from this site. I guess you could get it there later (or on Barnes & Noble now, but I doubt you want to pay $73) – b a Dec 19 '12 at 4:37
Another good book on this topic is Di Shemaya, by Alex Schutz. I bought a copy of it retail a few years ago in a bookstore in Baltimore. – Isaac Moses Dec 19 '12 at 4:45
@IsaacMoses Indeed it contains some interesting ideas. – Double AA♦ Dec 19 '12 at 4:50
@DoubleAA Indeed! :) – Isaac Moses Dec 19 '12 at 5:03
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@IsaacMoses If anyone is looking for a copy of Di Shemaya, I still have a few boxes stored in my garage. (Alex asked me to be his Lakewood "distribution" point back when he published.) – LazerA Dec 19 '12 at 6:48
up vote 5 down vote

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 (which we know is sqrt(2)) is not exactly 7/5 as the gemara asserts.

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Here's a fantastic article about this: aishdas.org/asp/2010/08/r-dr-eliezer-ehrenpreis-zl.shtml – Dave Jan 2 at 4:51

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