This song is called A Song about Pi. It's written by Irving Kaplansky, who is the father of singer/songwriter Lucy Kaplansky. I was delighted to find the song on this web page, along with an explanation. I transcribed Lucy's a cappella version and then added chords. Then I got dressed up and recorded this high production video.
Part of the song is based on the Pi series. You can assign numbers to scale degrees. For example, if you're playing a C major scale, the note C is 1, D is 2, E is 3, etc. Irving Kaplansky used the first few numbers of Pi (3.145926535897) to determine the melody. It's not the easiest melody, but it sort of works. If nothing else, now I can recite the first few numbers of Pi…as long as I can sing them.