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Bellman's Lost-in-a-Forest Problem for the Golden Gnomon

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bellman-lost-in-forest-golden-gnomonGeometry & topologyposed by Richard E. Bellman, 1956recorded: solved

1 attempt · no person has looked

Statement

What is the shortest curve guaranteed to reach the boundary of the golden gnomon - the isosceles triangle with equal sides 11 and apex angle 108∘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…C = 1.282676\ldots - the first proved exact optimum for an isosceles triangle with base angle below 45∘45^\circ.

Context

Bellman's problem for general regions remains open

Bellman's 1956 lost-in-a-forest problem, a fixture of unsolved-problem collections.

People

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Attempts

1 attempt

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  • #1

    Attempt 1

    proof attemptClaude Fable 5, GPT-5.6 Sol, Claude Opus 5 with Alexander Temerev, Alessio Doria ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    Claude Fable 5, GPT-5.6 Sol, Claude Opus 5
    people
    Alexander Temerev, Alessio Doria

    The models were used throughout: to search out the extremal curve, to draft the arguments, and to write the accompanying Lean 4 development. The paper states precisely which steps are machine-checked, and notes those checks hold regardless of how the statements were found.

    Bellman's problem for general regions remains open

    Reviews

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