Fourier epicycles are a fascinating way of visualizing Fourier series, which express complex periodic shapes as sums of simple circular motions. Imagine tracing a point on the rim of a small circle that itself rotates around another circle, which rotates around yet another, and so on. Each circle represents a sine or cosine term with a specific frequency, amplitude, and phase. By combining many of these rotating circles, we can recreate intricate paths and curves, even those that look nothing li