Hobby 3-D Printing Leads to New Insights into Moving Sofa Problem
By Becky Oskin
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?
A mover will tell you to just stand the sofa on end. But imagine the sofa is impossible to lift, squish or tilt. Although it still seems easy to solve, the moving sofa problem has stymied math sleuths for more than 50 years. That’s because the challenge for mathematicians is both finding the largest sofa and proving it to be the largest. Without a proof, it’s always possible someone will come along with a better solution.
The largest area that will fit around a corner is called the “sofa constant” (yes, really). It is measured in units where one unit corresponds to the width of the hallway.
Inspired by his passion for 3-D printing, Romik recently tackled a twist on the sofa problem called the ambidextrous moving sofa. In this scenario, the sofa must maneuver around both left and right 90-degree turns. His findings are .
Romik, who specializes in combinatorics, enjoys pondering tough questions about shapes and structures. But it was a hobby that sparked Romik’s interest in the moving sofa problem—he wanted to 3-D print a sofa and hallway. “I’m excited by how 3-D technology can be used in math, ” said Romik, who has a 3-D printer at home. “Having something you can move around with your hands can really help your intuition.”