Friday, 25 April 2025

MOVING SOFA PROBLEM

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The Moving Sofa Problem is a classic unsolved problem in mathematics (specifically in geometry and optimization). Here's a breakdown for quick understanding:


🛋️ Moving Sofa Problem – Explained

Aspect Details
Problem Statement What is the largest possible area of a 2D shape (like a sofa) that can be moved around a right-angled corner in a hallway of unit width?
Originator Formulated by Leo Moser in 1966.
Constraints The "sofa" must stay within the boundaries of a hallway that’s shaped like an L: both arms are unit-width corridors at a right angle.
What’s Being Maximized The area of the shape (sofa) that can make the turn.
Current Best Known Shape The "Gerver Sofa", found by Joseph Gerver in 1992, has an area ≈ 2.2195. It’s the best known candidate, but not proven optimal.
Upper Bound The largest provable upper bound is slightly over 2.37, so the true answer lies between 2.2195 and 2.37.
Why It's Hard It’s a problem in geometric optimization under motion constraints and has no known general technique for exact solutions.
Related Problem The Rotating Sofa Problem — same setup, but now the sofa can rotate arbitrarily while moving.

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