Pi is one of the most famous irrational numbers. Kids encounter it around the fifth grade when they learn about the area and circumference of a circle. There’s a fun song about pi, to the tune of Don McLean’s “American Pie”. Several different versions are out there, so I’m giving you links to a couple.
For a quick (1:15 min) sample, this has the first verse and chorus with some clever graphics. The lyrics are printed below the YouTube player. Speaking of the ancient Greeks, the song says,
I can’t be certain if they cried
when irrationality was realized,
but something deep within them died
the day they discovered pi.
In case you’re hooked, here’s another, longer (4:50) version that has more verses and nice graphics.
Apparently, the song is by Lawrence Mark Lesser, the Mathemusician. Here’s his page with two versions of the lyrics. There’s a verse about a bill in Indiana that aimed to legislate a rational value for pi! Apparently it passed the House unanimously but the senators didn’t go for that sort of irrationality and didn’t pass it.
This version of the lyrics adds more historical details through 1999. I’m not vouching for the accuracy, but I will say, you might be surprised at how interesting and dramatic the history of math is!