Still excited about these 3Blue1Brown-style videos generated by AI. Here’s a beautiful illustration of a classic analysis problem: Let f be convex, nonnegative on [0,∞), with f(0)>0 and f(x)→0 as x→∞. Place a light source at (0,b) with 0<b<f(0). Rays reflect off the graph of f and the x-axis following the usual laws of optics. Question: can any ray escape to +∞, or do all trajectories eventually come back? Prompt to video
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The longest thick curve on a sphere. Put a rope of prescribed thickness on the unit sphere. How long can it be without overlapping itself? Surprisingly, the answer is known only for thickness sin(π/2n)
