Gerver Sofa? Why did noone suggest anything better yet?

So i was playing Surviving Mars and listening to youtube videos in the background. Among others, some numberphile videos - i was subscribed to them on an older account but that was suspended so i missed a lot.
The Gerver Sofa currently being believed to be the sofa with the largest surface area that can make the turn.
The most easiest describable improvement would be anything but straight lines where it is flat at the top - as long as the highest it extends to is where the top is now, itll fit and the surface area will be larger. As anyone vaguely familiar with the coastline problem will be able to tell you, you can improve on that allmost infinately.