Mathematics
Fourier Series: Decomposing Periodic Functions into Harmonics
Quick fact
Fourier showed that even a discontinuous function like a square wave can be represented as an infinite sum of continuous sine waves, converging at every point of continuity.
Why this is interesting
You can build almost any repeating shape—from a square wave to a sawtooth—by stacking just the right combination of smooth sine and cosine waves. How is that possible?