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The Most Famous Sofa in Mathematics… Finally Has Its Place!

24/11/2024|2 min read

The Most Famous Sofa in Mathematics… Finally Has Its Place!

We are kicking off with exciting news for the world of mathematics: the historic sofa problem, first posed in 1966 and a source of bewilderment for mathematicians around the globe for decades, has finally been solved.

What Is the Sofa Problem?

At first glance, it seems like a practical logic challenge: Imagine an L-shaped hallway with two straight segments joined by a 90° corner. The question is: What is the largest-area object that can pass through the hallway and turn the corner without being deformed? You cannot lift, tilt, or alter the shape in any way—only slide it.

You might think the best option is a square that fits precisely within the width of the hallway. But mathematics—as so often happens—invites us to think beyond.

A Bit of History

Since mathematician Leo Moser formulated the problem in 1966, multiple solutions have been proposed. In 1992, Joseph Gerver designed an extremely precise—and unintuitive—shape that seemed to be the best candidate. It had a curved, symmetrical, and complex form, with several smoothly connected parts—almost like a piece of abstract art.

A Solution, at Last!

In 2024, mathematician Jineon Baek successfully proved that the shape proposed by Gerver is indeed the optimal solution to the sofa problem. This means there is no larger shape that can exceed that area and still turn the hallway corner without difficulty.

As shown in the image, the optimal shape has an area approximately 2.21 times larger than that of a square with the same width as the hallway.