The first thing you’ll notice about Gerver’s sofa is that, well, it doesn’t look much like the one in your living room. The first was confirming that the optimal shape for maximizing the area of the sofa was indeed the traditional telephone-like shape of Gerver’s sofa. In other words, if you took a Gerver’s sofa of a certain length and width, it would always fit within a simplified sofa of the same dimensions. This result means that the lower and upper bounds on the optimal sofa were the same, so Gerver’s sofa is the largest possible sofa that could fit around a corner. “I still want a physical Gerver’s sofa at the corner of my office that I can actually sit on!”