Draw and Fourier
Draw a periodic curve with the mouse and watch the Fourier series rebuild it coarse-to-fine in animation — partial sums and spectrum live.
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Fourier analysis Learn interactively.
Grasp Fourier synthesis, frequencies and spectra visually
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Fourier epicycles (3D)
Every closed curve as a sum of rotating vectors — Σ cₙ·eⁱⁿᵗ. The tip traces the curve, time unrolled as a 3D helix. Presets (heart, star, treble clef, …) or draw your own curve freely.
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Fourier Synthesis
11 free coefficients (a₀/2 + a₁..a₅ + b₁..b₅) — ghost curves per term, live sum and spectrum, build any periodic function by hand.
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Fourier Series — 5 Functions
Five classic periodic functions (square, triangle, half-sine, pulse 80/20, sawtooth) — slider for the partial-sum degree, magnitude spectrum and KaTeX coefficient formula.
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Sine Orthogonality
Two integer-frequency sines, the integral ∫sin(nx)·sin(mx)dx filled live — KaTeX shows 0 (orthogonal) or π (identical n=m), the heart of Fourier coefficients.
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Sine Anatomy
Three sliders for amplitude A, angular frequency ω and phase φ in f(t) = A·sin(ωt + φ) — markers for A, period T and phase shift, plus a KaTeX addition-theorem decomposition.
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