A Shape Proposed

The Prompt

Design and draw (or compute) a connected planar shape that can navigate a unit-width L-shaped hallway, and calculate or estimate its area. Compare your shape's area to Hammersley's constant (π/2 + 2/π ≈ 2.2074) and to Gerver's shape (≈ 2.2195). You may use any construction technique — geometric, parametric, or computational optimisation. Record your shape, its area, and what the construction process taught you about the constraints of the problem.

Completion Criteria

A drawing or computed rendering of the shape, its area (exact or estimated), a comparison to known shapes, and a one-paragraph note on what the construction revealed.

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