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  • $\begingroup$ Sounds interesting. The Wikipedia article for the Worm problem lists known upper and lower bounds for the area as 0.260437 and 0.232239, respectively. Do you hope for tighter bounds, an explicit solution for the area or even the shape? $\endgroup$ Commented Oct 1, 2015 at 8:18
  • $\begingroup$ I think that simply trying to do better with those bounds is not so easy. it would interesting to start with the lost in a forest problem. This was recently solved for the equilateral triangle. Can it be solved for all triangles? What triangle gives the best bound for Moser's problem? What about other simple shapes? Also are there any general statements that might be made about the shape of paths when the forest is a polygon? Will it always be a polyline? etc. $\endgroup$ Commented Oct 1, 2015 at 9:44
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    $\begingroup$ For a convex cover, the lower bound would be 0.270911861. The current lower bound is proved by trying to estimate the minimal area of a convex shape containing a segment, a triangle and a rectangle. We can try to add more shapes to tighten the lower bound, but I am not sure if it will be analytically or computationally feasible. $\endgroup$ Commented Oct 2, 2015 at 9:03
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    $\begingroup$ One approach to this kind of problem is to first try to compute the answer without any attempt to prove the result, so monte carlo methods are fine. The hope is that when you see the answer you can formulate some conjectures and try to prove them. The computation is then just scaffolding that might be removed from the final analysis. This requires collaboration between programmers and problem solvers. $\endgroup$ Commented Oct 2, 2015 at 12:01
  • $\begingroup$ This strikes me as a reformulation of the traveling salesman problem. $\endgroup$ Commented Jul 6, 2018 at 7:56