Labs / Mathematics
Fourier Epicycles
Each spinning circle is one sine wave — a single harmonic — and stacking them tip-to-tip adds those waves together. Add more circles to sharpen the traced shape, or drag the canvas to hand-crank the whole machine and watch the pen draw the wave.
terms 6A₁ 1.273RMS err 0.000
What to try
- With one circle you get a pure sine. How many harmonics does a square wave need before its edges look truly flat?
- Why do the wiggly overshoots near each jump never fully disappear, no matter how many terms you add?
- Switch between square, sawtooth, and triangle — why do the circles shrink so much faster for the triangle?
- Watch the RMS error as you drag the harmonics slider. Does doubling the terms halve the error?
- Which wave's reconstruction gets closest to ideal with the fewest circles, and what does that say about how "smooth" it is?