Bellman's Lost-in-a-Forest Problem for the Golden Gnomon
Prior state unknown→proved
Bellman's problem for general regions remains open
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geometry-topology / Convex geometry
Bellman's Lost-in-a-Forest Problem for the Golden Gnomon
What is the shortest curve guaranteed to reach the boundary of the golden gnomon - the isosceles triangle with equal sides $1$ and apex angle $108^\circ$ - from an unknown starting position and heading? The optimum is a symmetric seven-piece path of segments, circular shoulders and tangents, of exactly determined transcendental length $C = 1.282676\ldots$ - the first proved exact optimum for an isosceles triangle with base angle below $45^\circ$.
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What is the shortest curve guaranteed to reach the boundary of the golden gnomon - the isosceles triangle with equal sides $1$ and apex angle $108^\circ$ - from an unknown starting position and heading? The optimum is a symmetric seven-piece path of segments, circular shoulders and tangents, of exactly determined transcendental length $C = 1.282676\ldots$ - the first proved exact optimum for an isosceles triangle with base angle below $45^\circ$.
Bellman's problem for general regions remains open
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