Symmetryplus No. 63

Number 63 Summer 2017 SO FAR WITH THE SOFA! The ‘Moving Sofa problem’ has been around for more than 50 years. It asks ‘What is the largest shape that can move around a 90 ° turn?’. Now the Gerver sofa (shown here in red) is the largest found so far that will fit round a single turn. Its area, or ‘sofa constant’ is 2.22 square units where one unit corresponds to the width of the hall along which it is moving. However, the challenge is not only finding the largest sofa, but proving it to be the largest. Professor Dan Romik has been working on this problem and extended it to a problem where there are two 90 ° turns as shown here with the new (blue) sofa. He has recently published his results in Experimental Mathematics . You can find out more and see some animations by searching on the web under ‘moving sofa problem’. Recent News SPIRALS This is the spiral staircase in the monument to the Great Fire of London. There are 311 stairs. How many revolutions do you think you make if you ascend it?