"Musique concrète (French; literally, "concrete music"), is a style of avant-garde music that relies on natural environmental sounds and other non-inherently-musical noises to create music."
For example, here is the first "musique concrète" piece. It was composed by Pierre Schaeffer in 1948 using train sounds. To do so, he used magnetic tape recordings. He experimented with "playing sounds backwards, slowing them down, speeding them up and juxtaposing them with other sounds".
Pierre Schaeffer was inspired by Luigi Russolo. He "emphasized the importance of 'playing' (in his terms, jeu) in the creation of music. Schaeffer's idea of jeu comes from the French verb jouer, which carries the same double meaning as the English verb play: 'to enjoy oneself by interacting with one's surroundings', as well as 'to operate a musical instrument'. This notion is at the core of the concept of musique concrète." (quoted from Wikipedia)
The theme of your composition should be related to the ideas of Pythagoras, Plato, etc. and the various proportions as described in the "Squaring the Circle" handout.
If you play a musical instrument, you may incorporate sounds that follow these proportions.
Or, make the lengths of clips used follow these proportions.
Experiment with different possibilities on paper first. Be creative, be original.
In addition to your music, you should include a short report to explain how your piece was put together and how these proportions are manifested in it.
You can find great recorded sounds (audio files) here: