Research report: moving sofa's

The PDF reflects work I did the last month based on a problem that was mentioned as "unsolved". It is likely solved, even if that took about 40 years.

Nevertheless, I started blind, deliberately not looking into the papers. You can find the ones that matter most in the reference section. My approach was really blind, in the sense that I did not assume any form or anything that is not inherent in the problem setting. 

The pretty good solution of Hammersley emerged from this blind sort-of brute force search. It was not the expected "final" solution of Gerber. There was an extra level of freedom hiding that I missed. Introducing it did allow to find the Gerber solution, or something close to it. To find the optimal one costs too much computer time, but anyone can try based on the approach. It will confirm or not what the optimal solution is.

This result was somewhat disappointing, so I decided to extend the problem to any angle instead of just 90° angles. Some places have unusual forms, don't they? I retained the constraint to only consider Hammersley-style solutions.  The solutions for all angles are based on "solid" mathematics. The surface calculations forced me to use numerical integration and numerical maximum computation. The solution for 90° angles just comes out of the general solution for the problem, and is indeed the Hammersley solution (as it should be).

In the end I added a form that is certainly not optimal, but provides more insight in the optimalization Gerber did, as well as providing a nice alternative.

While it might help furniture designers or movers, an alternative useful case is not clear. I suggest a gadget-like set-up, that might be useful.

There is no security advice here. On safety: The basic square will crush you, for the others the corner may save you.