4 ms·
The only constraint on the polygon is that the angles are rational multiples. There all kinds of crazy non-convex shapes that satisfy this constraint, which is
by ironSkillet 7y ago
The only constraint on the polygon is that the angles are rational multiples. There all kinds of crazy non-convex shapes that satisfy this constraint, which is why the result is noteworthy.
- readams 7y agoRational angles and only a finite number of points are not illuminated. You can still get points that are dark, but not regions.
- anonytrary 7y agoI think this is also interesting when it comes to physics. A dark "point" physically means that the electromagnetic fields permeate the entire room except over a finite set of Dirac delta functions. If you were to try and put something physical in the dark point, you'd quickly turn this into a quantum mechanics problem. I don't think the dark points matter in real life because confining yourself to a single point would require infinite momentum. This theorem assumes perfect mirrors and Newtonian light. In real life, I predict that the entire room would be illuminated. There's a path of least action for the light to take, but there is a probability of taking other paths. Scattering is not precise. I would think that would add a fudge factor to the paths.