How the irrational number Pi can be derived from the Torah?

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)

• 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
• @DonielF well, math textbooks define it in a finite number of characters. – Heshy Jul 30 '18 at 7:02
• Gemara Eruvin. Pi was not irrational in theire mind. The discovery of rational-irrational concept is posterior – kouty Jul 30 '18 at 11:37
• 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