I have seen a claim that for the sofa problem, an upper bound for the area of a sofa is $2 \sqrt 2$, and that this can be proved by a "simple" argument. But I can't find a proof. What that argument?
(The articles and papers I found all seem to point back to On the enfeeblement of mathematical skills by modern mathematics and by similar soft intellectual trash in schools and universities, but that paper gives this bound as a problem, and I can't find the solution.)