Fourier Series
Interactive simulation — adjust parameters and watch the visualization update in real time.
How it works
Finite **Fourier sums** approximating periodic targets: **square** (odd sines), **sawtooth**, and **triangle** (odd sines with 1/k²). Raise the term count to see convergence; near jump discontinuities you still see **Gibbs overshoot** (square/saw). The dashed curve is the ideal limit; cyan is the partial sum. Toggle **animate** to slide phase in time.
Key equations
Square: (4/π) Σ sin((2k−1)t)/(2k−1)