1968: John Hammersley proved that the upper bound of the area of a sofa that can be moved around an L-shape corner of width 1 unit is 2Ö2=~2.2074 square units. He designed such a sofa consisting of two quarter-circles with 1 1-unit radius connected by a rectangle of length 4/π.

1992: Joseph Gerver slightly improved Hammersley’s solution. The area of Gerver’s “sofa” is ~2.2195 square units.

2016: Romik presents a complete solution to the problem of moving a sofa around two opposite corners.

2017: Dan Romik and Yoav Kallus found (using a computer) a lower upper bound to the sofa moving problem, which is 2.37 square units.

To the MNS presentation