THE MUSIC OF THE SPHERES

Hunched over your paper, you try to concentrate. This is the worst kind of assignment.

- Ratios rock

It’s nothing but fractions! And you’re not supposed to use a calculator. Ear buds pump your favorite tunes directly into your brain. Is 37/74 reduced to its simplest form? Yes? No? Argh . . . ! Don’t get frustrated. Try to relax. Let the soothing sounds of fractions ease your pain.

That’s right: The soothing sounds of fractions. Those tunes that are massaging your mind are composed of the same fractions that are hurting your head. You can thank the Greek mathematician Pythagoras for discovering that fact. Are you familiar with his right triangle theorem, A² + B² = C²? Well, according to legend, that same Pythagoras once spent an afternoon listening to blacksmiths hammering away at their anvils. He noticed that some clanging sounds rang together in a pleasing chorus. Other clangs clashed in a cacophony of noise. Pythagoras decided to investigate this curious phenomenon. He discovered that it didn’t matter which of the blacksmiths did the hammering. Nor did it matter how light or heavy handed their hammering was. The pleasantness of any clang combo depended only on the weight ratio of the hammers involved. And please note, “ratio” is the fancy name for a fraction.