I recently read the book “Infinite Powers” by Steven Strogatz. In chapter 10 he told the story of Joseph Fourier and why he initially cared about approximating functions with a mixture of sine and cosine waves.
His objective was to solve the “heat problem”. How does heat distribute in in a rod (or regarding circuits: in a wire). For some backgrounds see the section “background”.
The following section contains a demo of such a wire that can cool down. By clicking on the first wire you can draw heat patterns which are smoothed with a Fourier transformations (actually by setting the higher order coefficients to zero). In the case that the “simulate” check-box was active, then the simulation will start after clicking on the wire.
Input (click on the left half of the bar):
Heat flow simulation:
FFT coefficients: 1… … 400
Initially I wanted to write a little bit about this but I found that 3b1b just published a video about this topic: