Most people dread moving homes or even changing the interior layout of their existing house. Despite all the excitement and optimism that comes with a fresh start, moving furniture upstairs, downstairs, through narrow openings and tight spaces can be exhausting and stressful. Especially when you are stuck in the hallway with a lovely (as your girlfriend says) sofa that is too big or long to turn the corner. You may be surprised that the question of finding the largest possible figure which can maneuver past a right-angle turn has also bothered scientists and scholars for nearly a century. 

The Sofa Formula

People come up with a vast range of solutions to solve their “sofa problem,” and scientists have their way – the mathematical way of course. Dan Romik, a Professor of Mathematics and the Chair of the Department of Mathematics at UC Davis, is one such scientist. He designed a couple of sofa models to a relatively big size which can easily fit through a corridor with a 90-degree corner, and to take it one step further, he also added a second angle to his theoretical hallway. 

As a true expert in combinatorics (a branch of mathematics dealing with combinations of objects), Prof. Romik started with abstract figures and by drawing on previous “sofa problem” research and derived the formula of the figure that can achieve the goal. The final product consists of 18 distinct pieces which we must admit, looks a little weird.

He also used a 3D printer to make physical prototypes of his innovative and ambidextrous sofa. “I’m excited by how 3D technology can be used in math. Having something you can move around with your hands can really help your intuition,” he says.

Dan Romik published the entire study in the Experimental Mathematics Journal, where he also added CAD files of the hallways and sofa models that are free to download.

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