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Mathematics

Fourier Series

Quick fact

Joseph Fourier introduced these series in 1822 while studying heat transfer, but the idea that any periodic function can be built from sines and cosines was initially controversial. Today it's essential in everything from JPEG compression to MRI scans.

Why this is interesting

You know how a single musical note sounds pure, but a chord feels rich? What if I told you that even a sharp square wave or a jagged sawtooth can be built from pure notes? How can simple sine waves combine to create such different shapes?