Opus 5.5 visualizes the 17-lighthouse math proof
After seven years, the author solved a problem about 17 point-sized lighthouses covering the plane, and used Claude Opus 5.5 to make a visualization showing any lighthouse layout can illuminate the whole plane.
It took me 7 years to solve this problem: There are 17 point-sized light-houses in the plane. Assume that each of these lighthouses can shine light in any direction with an angle of 2*pi/17. Prove that no matter the position of each lighthouse, it is always possible to choose the angles at which they shine their light such that every point in the plane is illuminated (point-sized lighthouses don’t cast shadows). I finally got the solution after thinking about it on and off for for a long time (in fact, with the key idea coming to me on a psychedelic state - I've talked about this on some podcast or another). Now thanks to Opus 5.5 I can show you guys how this is actually true for any configuration of lighthouses. In fact, it's true for any n :D I won't share the proof so you also have a chance to think it through ;-)