The moving sofa math problem: still unsolved 50 years later

Ever try to move a sofa down a hallway that has a corner? The underlying math behind it inspired a math problem that's been a puzzler since 1966. Gerver's Sofa above shows the parameters: a U-shaped sofa moving around a 90-degree corner in an even-width hallway. Gerver's got the record so far, and it is likely the optimal sofa.

Per the American Mathematical Society:

This question was first published by Leo Moser in 1966. The animation above, made by Claudio Rocchini, shows one attempt to solve this problem. It's called the Hammersley sofa, since it was discovered by John Michael Hammersley in 1968… But it's not the best known solution! In 1992, Joseph Gerver found a shape of area […] that fits around the bend in the hallway. Basically Gerver rounded off some of the corners of Hammersley's sofa. The resulting shape has a boundary consisting of 3 straight line segments and 15 curved segments.

AMS has a good detailed illustration of the Gerver Sofa, too.

Moving Sofa Problem (Wolfram)

Gif: Hammersley Sofa via Wikimedia Commons