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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?