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Some traditions say, based on the Gemmorah in Taanis 9a (also מדרש רבה נשא י' ו', זוהר פנחס רכ"א א, and more):

"ליכא מידי דלא רמיזא באורייתא" (Is there anything that is written in the Writings that is not alluded to in the Torah at all?)

that everything can be derived from the written Torah (the Pentateuch of 304,805 letters, and Gr"a adds from Parashat Bereshis alone etc). Many tried (and succeeded) to find certain integers, such as numbers and dates.

In what way can the irrational and infinite number Pi be derived from the written Torah?

(to clarify, the question is not about approximation of Pi, it is about the possibility to derive an irrational number from a list of letters)

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    Just because it can be done in principle doesn't mean anyone knows how to do it in practice. – Heshy Jul 30 '18 at 5:38
  • Are you accepting answers from Nach? In that case it’s trivial - the Gemara already discusses it. – DonielF Jul 30 '18 at 5:39
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    @DonielF well, math textbooks define it in a finite number of characters. – Heshy Jul 30 '18 at 7:02
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    Gemara Eruvin. Pi was not irrational in theire mind. The discovery of rational-irrational concept is posterior – kouty Jul 30 '18 at 11:37
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    Just because PI is irrational (and even transcendental), doesn't mean you cannot describe it accurately in a finite number of syllables. Just as an example, there are numerous infinite series that converge to Pi. E.g. en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80 – Nic Jul 30 '18 at 14:11
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Pi can be derived from the Torah by rolling up a Torah scroll and measuring the end's diameter and circumference. The ratio between them will be pi.

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    No joke! See Bava Batra 14a – Double AA Jul 30 '18 at 11:41
  • it is about the possibility to derive an irrational number from a list of letters - I guessed he asked for it! :-D – Danny Schoemann Jul 30 '18 at 11:59
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    Technically this would be a linear spiral, but you have my upvote. – Nic Jul 30 '18 at 14:08
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    Hah! One of the great Ma'asei Hashem! No matter who rolls a Torah, no matter how loosely or tightly it's rolled and no matter what the sixe of the Torah is, you get the same number by dividing the circumference by its diameter. Seems like a nes (miracle) to me! Who needs Euclid? – DanF Jul 30 '18 at 14:23
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    This answer is being discussed on meta. – Monica Cellio Jan 21 at 17:40

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