Compressed sofa is the shape with the largest area that can maneuver around a right-angled (90-degree) corner in a hallway of a specific width. It is the solution to a famous mathematical puzzle known as the "Moving Sofa Problem."

The Core Problem

Imagine you are moving a sofa through an L-shaped hallway. The hallway has two corridors, each one unit wide, that meet at a right angle. The question is:

What is the largest-area sofa that can be moved around this corner?

A "compressed sofa" isn't a single, fixed shape. Instead, it refers to the idea of finding this optimal shape, which is a product of mathematical optimization.

TermMeaningCompressed SofaThe general concept of the largest shape that can fit around a corner. It's the answer to the "Moving Sofa Problem."Moving Sofa ProblemThe mathematical problem of finding the above shape in a hallway of unit width.Sofa ConstantThe exact area of the largest possible sofa. Its value is unknown but lies between ~2.2195 and ~2.37.Gerver's SofaThe current best-known solution (since 1992), with an area of ~2.2195.

In short, a compressed sofa is the solution to a classic geometry optimization problem, representing the ultimate shape for moving around a tight corner. It's a fun and intuitive puzzle that leads to deep and unsolved mathematical questions.

Key Features and Benefits:

• Space Saving: This is the #1 benefit. It can free up enormous floor space for other activities during the day.

• Multi-Functional: Many models are also sofa beds. Once expanded, you can often pull out a hidden mattress from within the seat, providing sleeping space for guests.

• Ease of Use: They are typically designed to be lightweight and easy to move and transform without requiring great physical strength.

• Modern Design: They often feature a sleek, minimalist, and modern aesthetic that fits well with contemporary small-space decor.