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The Moving Sofa Problem (in Turkish: Taşınan Kanepe Problemi) is a geometric optimization problem formulated in two-dimensional Euclidean space. Its exact solution remains unknown to this day. The problem seeks to determine the two-dimensional shape—resembling a sofa—that has the largest possible area and can be maneuvered around a right-angled hallway corner. In this context, the “sofa” refers to any two-dimensional shape that can be both rotated and translated. The problem was first formulated