A legendary geometry puzzle asks for the largest 2D sofa that can round a right-angle hallway corner. We trace the journey from Moser and Hammersley’s early bounds to Gerver’s iconic handset-shaped sofa, and finally Jin-Hyun Baek’s 2024 proof using enclosing shapes that pin down the exact maximum at 2.2195 square units. Along the way, we connect this centuries-spanning debate to modern motion planning in robotics and medicine, showing how a stubborn hallway can reveal fundamental limits of movement.

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