Why can spinning circles draw anything? (Fourier Transforms)

A handful of circles, each just spinning at a steady speed, can draw any shape you like: your signature, a heart, even a face. That single idea quietly runs JPEG, MP3, and MRI scanners. It's called the Fourier transform, and it's far more beautiful than school ever let on. In this video we build it from nothing: we start with one circle and watch a sine wave appear, stack circles until a smooth motion grows sharp corners, chain them together to draw a heart, and then answer the real question: given any drawing or sound, how do you find the circles hiding inside it? That's the Fourier transform, and you'll see exactly what it does and why it works, no formulas-first required. Made with ManimGL. Pure black, take your time, watch the circles. ⏱️ Chapters 0:00 Circles that draw a star 0:39 One circle = one sine wave 1:07 Stacking circles → a square wave 1:40 The chain that draws a heart 2:09 How to FIND the circles (the winding trick) 2:50 The aha: every signal is a sum of circles 3:09 Where it all shows up — and what's next 🔭 If this rewired something for you, the channel is one long argument that the impossible-looking ideas in maths are actually the inevitable ones. Subscribe and stick around. 💬 Question for the comments: what shape should the circles draw next?