The area-stationary sofa for a corner of interior angle α, and its motion through the bend. Everything (shape, area, motion) is computed live by integrating the optimality ODEs — nothing is precomputed.
Corner interior angle α90.0°
sharp turnstraight
Area—
Motion (scrub)enter → turn → exit
Entry hallway length—
minimalextended
Exit hallway length—
minimalextended
Zoom—×
scroll to zoom · drag to pan
Computing the solution family…
Unit-width corridors; turn angle ϕ=π−α. At α=90° this is Gerver's sofa (area ≈ 2.2195).
The sofa is drawn in a fixed corridor; as it turns, its pose is Tt(S)=R−t(S−x(t)), which provably stays inside the walls for all t.
This is the locally-optimal (stationary) shape, not a proven global optimum.