Fourier series click when students see them move. PathAnimator gives you live figures you can drive in class: add circles one at a time, mute a single frequency, or let students draw their own shape and watch it converge.
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The computer measures your drawing with a Fourier transform and turns it into circles, biggest first. The bars below are those circles: height is size, position is speed and direction. Click a bar to remove that circle.
1Start with Fourier Visualized: five short steps from adding sine waves to drawing any shape with circles.
2Switch to classroom mode on the projector. Press the arrow keys to add circles while the class predicts what happens next.
3Let students draw their own shapes on their phones or laptops, then compare how many circles each one needs.
Tips
Ask the class to predict the shape at 1, 2 and 3 circles before you press the arrow key.
Mute the biggest bar in the spectrum to show that one circle carries most of the shape.
Compare a smooth shape (infinity, 6 circles to get close) with a cornered one (pi, 29): corners need high frequencies.
The square-wave figure shows the Gibbs overshoot at the jumps, a good bridge to convergence.
Questions
What age is this for?
The explainer needs no formulas, so it works from about age 14 as an intuition builder. University students can connect it to complex exponentials, the discrete Fourier transform and Parseval's theorem, which the page's last figure uses.
Does it work on school devices?
Yes. Everything runs in a modern browser on laptops, Chromebooks, tablets and phones, with no account, install or sign-in. Classroom mode goes full screen with the F key.