Fourier series allow us to approximate complex periodic functions, like the square wave, by summing simple sine waves. As more terms (harmonics) are added to the series, the approximation becomes increasingly accurate. The square wave, which has sharp transitions, can be closely mimicked by combining enough sine waves with carefully chosen frequencies and amplitudes. This process beautifully demonstrates how smooth functions can build up sharp, structured patterns. 📌Support us - Like/Share/Foll

From Circles to Squares - This animation shows how a Fourier series builds a square wave. Starting smooth and wavy, each added harmonic sharpens the shape until it forms the classic square wave. | The Brain Maze

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