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New twist to the Sofa Problem

Most of us have struggled with the mathematical puzzle known as the "moving sofa problem." It poses a deceptively simple question: What is the largest sofa that can pivot around an L-shaped hallway corner?

For years, this mathematical problem has puzzled mathematicians and furniture movers. Mathematician Dan Romik has extended this problem to a hallway with two turns. He has shown that an infinity shaped sofa is the largest so far found that can move down such a hallway.

The largest area that will fit around a corner is called the "sofa constant". It is measured in units where one unit corresponds to the width of the hallway. To solve the problem, Romik has used the 3-D print technology. 3-D prints of both, the hallway and a sofa have been redesigned to get a shape that can easily crossover an L- shaped hallway.

“It is amazing how 3D print technology can be used to derive solutions to one of the biggest mathematical problems,” says Romik.



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