For an agent starting anywhere in the plane, the optimal search-and-rescue strategy on the x-axis is either to go directly to the origin or to first visit a checkpoint at a closed-form distance, with the choice changing abruptly at about 15.6 degrees.
Israel Journal of Mathematics2(4), 221– 228 (1964)
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Search and Rescue on the Plane
For an agent starting anywhere in the plane, the optimal search-and-rescue strategy on the x-axis is either to go directly to the origin or to first visit a checkpoint at a closed-form distance, with the choice changing abruptly at about 15.6 degrees.