The animation shows Hammersley’s sofa, not Gerver’s. [Never mind - BBS view playing tricks on me, yet again.]
Although it hasn’t been proven optimal, Philip Gibbs did a search of possible shapes using numerical methods, and the optimal solution found had an area the same as Gerver’s sofa up to 8 decimal places.
Of course, to a theoretical mathematician, that’s just a hint that you’re on the right path. The proof’s the thing!
