Who knows irrational numbers?
?מספר אי-רציונלי - מי יודע
In the spirit of the song "Echad", please post interesting and significant Jewish facts about irrational numbers. I tried dealing with them, but it's just impossible ... They're completely irrational. Who knows? Maybe YOU do!
Please, no lazy gematria about these numbers. I'm looking for something clever.
Answer
- It is "e efshar" to write irrational numbers as fractions.
- Understanding the basic concept might be easy as "pi," but mastering it "transcends" logic.
- Going all the way around the square can be difficult, but √2 made the cut.
- He who spareth the "log" hateth the child.
- "Phi" fie fo fum
- These puns are getting a bit "irrational," so I'll skip to the serious part now.
The Mishnah in Eiruvin 1:5 says that the ratio of the circumference to the diameter is 3:1. Peirush HaMishnayos to that Mishnah notes that three is imprecise; the number (which the Tiferes Yisrael denotes as פ״י) actually goes on forever. Since no matter what value you use will be imprecise, the Tanna cut it off after the first digit.
The Tosfos HaRosh to Eiruvin 14a explains the Gemara's question of "how do we know this ratio of 3:1" as "how do we know that we can rely on this imprecise approximation?" We answer it from the passuk in Melachim 1:7:23 that claims the circumference of the ten-amah-diameter kiyor was thirty amos.
Tosfos to Sukkah 8a prove πr^2.
This topic of irrational mi Yodeya has been breached before: take a look here and at the links quoted in that discussion.
Check out my discussion here regarding relying on approximations to irrational numbers in Halacha, and my discussion here involving logarithms regarding taking away 1/60 of a sick person's disease.
No comments:
Post a Comment