“What of invisible beauty? There are patterns in the air. Sound waves that can make our spirits rise.”

That quote is from a short video clip on videos.howstuffworks.com. One segment describes how Pythagoras discovered the mathematics of music after passing by a blacksmith’s shop: hammers of different weights would create different sounds when dropped, the differences of each corresponding to a mathematical ratio.

One of the people interviewed in this clip, Frederick Turner, uttered a curious sentence:

“…and so there’s this wonderful

threefold connection between a human mind…, the mathematics themselves, and the physical world.”

You should note that Pythagoras’ most famous theorem happens to apply to triangles, and that the minimum amount of notes necessary to create a chord is three.

Perhaps it’s true, as ancient Roman poet Virgil once wrote, that **“the gods delight in odd numbers.”**