Uploaded April 2021 | Updated September 2026, 2 weeks ago
Here is shown a ray starting with a varying start vector (thick white line) crossing a focal point very slowly, the ray being reflected approximately 60 times against the boundary of the ellipse, demonstrating some drama at the focal point.
This is de-prioritized visual material from the making of the video youtube.com/watch?v=-VjbYI-eaTQ&t=92s
Music by @gpcbass! A further developed full version of this song, Stella by starlight (Victor Young cover) can be found here: youtube.com/watch?v=iaxV6lG6uqg
Here is shown a ray starting with a varying start vector (thick white line) crossing a focal point very slowly, the ray being reflected approximately 60 times against the boundary of the ellipse, demonstrating some drama at the focal point.
This is de-prioritized visual material from the making of the video youtube.com/watch?v=-VjbYI-eaTQ&t=92s
Music by @gpcbass! A further developed full version of this song, Stella by starlight (Victor Young cover) can be found here: youtube.com/watch?v=iaxV6lG6uqg
![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.")
