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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. |
Would you like a simple diagram or infographic explaining this visually?
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