Gerver's Sofa | Moving Sofa Problem

The Moving Sofa Problem:

The Moving Sofa Problem is a famous unsolved problem in mathematics that seeks to determine the largest two-dimensional shape that can navigate through an L-shaped corridor of unit width. In 1992, mathematician Joseph Gerver proposed a solution—now known as the Gerver Sofa—which has an area of approximately 2.2195 square units. This intricate shape is composed of 18 distinct curved sections and represents the largest known solution to the problem. Just a few months ago, a study that claimed the Gerver Sofa to be the optimal solution was published, which is what prompted me make this model.

This model does work just as expected and is abled to slide perfectly around the corner, even with no extra tolerance on the hallway. To make it perfectly smooth, some tolerance is advised, which is why i have a 1mm tolerance version available as well.

Print Settings:

You can scale the model to your liking and use pretty much any settings you like; this model is not demanding at all. I do recommend ironing and maybe a textured PEI plate to make the appearance a bit neater.

Making Of:

I exported this desmos modeling of the sofa as an svg into Fusion360, since Fusion natively does not support the complex formulas used to describe the 18 subsections. After a bit of fiddling and cleaning up the imperfections of the exported svg, I had a Fusion sketch that approximates the original sofa quite well, with a unit size (or corridor width) of 50mm.

The gif shows a prior, non-optimal solution, the Hammersley Sofa, to demonstrate the problem.