How to distinguish an icosikaipentagon from a circle
Channel: Nils Berglund
Date: 20/05/2021

It is quite easy, really: simply fill your container with a superfluid, such as Helium 4 at a few degrees Kelvin. Then let a drop of fluid fall in the center of the container. If the container is a circle, then it will create a pulsating, perfectly circular wave front. If you get patterns as in this simulation, in means that your container is a regular polygon with 25 sides, also known as an icosikaipentagon. The more sides the polygon has, the longer will the wave front stay close to a circle. As one can see here, 25 sides is far from being enough to keep the circular shape for much longer than the first collision with the boundary.

Music: Exotics by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 licence. https://creativecommons.org/licenses/by/4.0/
Source: http://incompetech.com/music/royalty-free/index.html?isrc=USUAN1100233
Artist: http://incompetech.com/

Current version of the C code used to make these animations: https://github.com/nilsberglund-orleans/YouTube-simulations
https://www.idpoisson.fr/berglund/software.html

Some outreach articles on mathematics:
https://images.math.cnrs.fr/_Berglund-Nils-1343_.html
(in French, some with a Spanish translation)