Fourier
The Fourier transform is usually taught as a wall of integrals, and most people come out the other side never quite seeing it. These demos take the opposite route: everything here is geometry you can watch move. First-year university level — but no calculus required to get the idea.
The big idea, in one sentence: any repeating shape — no matter how jagged — is just a sum of smooth sine waves of different speeds. The Fourier transform is the recipe that tells you how much of each. Start with the first demo and build one yourself.
Start here
Build a Wave
Fourier series
Stack sine waves with sliders and watch a jagged square, sawtooth or triangle wave appear out of smooth curves. The gateway idea: complicated shapes are sums of simple tones.
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The "aha"
Epicycles
Circles on circles
Take those same sine waves and draw each as a spinning circle riding on the last one. The tip of the final arm traces your wave — the picture that makes Fourier finally click.
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The payoff
The Winding Machine
The transform itself
The reverse trick: given a wave, wrap it around a circle and watch its centre of mass spike exactly at each hidden frequency. This is the Fourier transform integral ∫g(t)e^(−2πift)dt, shown as a picture you can drag.
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On your own voice
Your Voice's Spectrum
Live microphone FFT
Hum, sing or whistle and watch a real Fourier transform of your own voice in real time — the frequencies you're making, with the note names. The same maths, running live in your phone. (Audio never leaves your device.)
Open the mic →