From Moser to Romik

The Prompt

Explain the moving sofa problem to a reader who knows basic geometry. State the problem; describe the progression from the semicircle through Hammersley's shape to Gerver's 1992 construction. Cite Moser (1966), Hammersley (1968), and Gerver (1992). Mention Romik's 2018 ambidextrous variant. Explain why Gerver's shape is believed to be optimal but the proof remains elusive.

Completion Criteria

A short essay (three or four paragraphs) with at least three citations and a clear explanation of why optimality remains unproven.

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