What is the sofa of greatest area which can be moved around a right-angled hallway of unit width?
Hammersley (Croft et al. 1994) showed that
(OEIS A086118). Gerver (1992) found a sofa with larger area and provided arguments indicating that
it is either optimal or close to it. The boundary of Gerver's sofa is a complicated
shape composed of 18 arcs. Its area
can be given by defining the constants , , , and by solving