![Fourier expansion of simple geometries [+MWE Python code] @animations_ag](https://i.ytimg.com/vi/V6bQoEjnCKk/maxresdefault.jpg)
Uploaded July 2021 | Updated September 2026, 2 weeks ago
Shown is some simple geometries drawn by epicycles, i.e., represented by Fourier series. See pinned comment for a minimal working example code (Python).
The ellipse of course only needs two rods to coincide with the exact solution. However, I was a bit surprised that the square and the triangle were so well approximated using only two rods. When representing the three (disconnected) geometries by a single basis set the number of basis functions must be large. The discontinuities naturally induce Gibb's phenomenon. I've cheated a bit here, and removed a small portion of the traces in connection with the discontinuities.
Reuse of the fantastic song Vanessa, made by @gpcbass. See youtube.com/watch?v=yE8G0kmfzjc for the full version.
Shown is some simple geometries drawn by epicycles, i.e., represented by Fourier series. See pinned comment for a minimal working example code (Python).
The ellipse of course only needs two rods to coincide with the exact solution. However, I was a bit surprised that the square and the triangle were so well approximated using only two rods. When representing the three (disconnected) geometries by a single basis set the number of basis functions must be large. The discontinuities naturally induce Gibb's phenomenon. I've cheated a bit here, and removed a small portion of the traces in connection with the discontinuities.
Reuse of the fantastic song Vanessa, made by @gpcbass. See youtube.com/watch?v=yE8G0kmfzjc for the full version.
![Fourier expansion of simple geometries [+MWE Python code]](https://i.ytimg.com/vi/V6bQoEjnCKk/mqdefault.jpg "Fourier expansion of simple geometries [+MWE Python code]
Shown is some simple geometries drawn by epicycles, i.e., represented by Fourier series. See pinned comment for a minimal working example code (Python).
The ellipse of course only needs two rods to coincide with the exact solution. However, I was a bit surprised that the square and the triangle were so well approximated using only two rods. When representing the three (disconnected) geometries by a single basis set the number of basis functions must be large. The discontinuities naturally induce Gibbs phenomenon. Ive cheated a bit here, and removed a small portion of the traces in connection with the discontinuities.
Reuse of the fantastic song Vanessa, made by @gpcbass. See https://www.youtube.com/watch?v=yE8G0kmfzjc for the full version.")
