The Vitruvian pond: wave front in a 5-pointed star
This shape is not strictly speaking a pentagram, but I hope it is close enough to make all pentagram enthusiasts happy. Similarly to the video • The redemption of the pentagon the shape is obtained by replacing the sides of a regular pentagon by circular arcs curving inward. The radius of the arcs has been chosen in such a way that the angles at the corners are of 45°. The simulation shows an expanding wave front reflected on the sides, in the idealized situation where there is neither dissipation nor interference between waves. Because the angles at the corners divide 180°, the wave front remains intact, even though here the wave front starts slightly above the center of the shape. The concave sides cause strong dispersion, which makes the billiard chaotic, and also causes numerical issues. However I managed to make the representation more symmetric, by changing the way the front is drawn: the segments are drawn in the order given by their color.
Music: "Lights" by TrackTribe@TrackTribe
Current version of the C code used to make these animations: https://github.com/nilsberglund-orlea...
https://www.idpoisson.fr/berglund/sof...
Some outreach articles on mathematics:
https://images.math.cnrs.fr/_Berglund...
(in French, some with a Spanish translation)
