Optimality of Gerver's Sofa
Jineon Baek's paper "Optimality of Gerver's Sofa" resolves the moving sofa problem, demonstrating Gerver's construction achieves a maximum area of approximately 2.2195, contributing to metric geometry and optimization.
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The paper titled "Optimality of Gerver's Sofa" by Jineon Baek addresses the moving sofa problem in metric geometry. The author demonstrates that Gerver's construction, which consists of 18 curve sections, achieves the maximum area of approximately 2.2195. This result resolves a long-standing question in the field regarding the optimal shape for a sofa that can be maneuvered around a right-angled corner while maximizing area. The paper spans 119 pages and includes 21 figures to illustrate the findings. The work falls under several mathematical classifications, including metric geometry, combinatorics, and optimization.
- The paper resolves the moving sofa problem.
- Gerver's construction is shown to have the maximum area of approximately 2.2195.
- The study includes 119 pages and 21 figures.
- The research contributes to the fields of metric geometry and optimization.
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- Many commenters express excitement about the resolution of a long-standing mathematical problem, with some noting its historical significance.
- There are inquiries about the proof's peer review status and its practical applications, indicating a desire for validation and real-world relevance.
- Some users share personal anecdotes or humorous takes related to the sofa problem, highlighting its accessibility and relatability.
- Comments also touch on the technical aspects of the proof, including the use of computer assistance and the complexity of the shape's definition.
- Several users question the practicality of the findings, suggesting that real-world furniture moving involves additional dimensions and considerations.
19 commentshttps://www.mdpi.com/symmetry/symmetry-14-01409/article_depl...
I kinda want one...
I wonder how the result varies if one of the corridors (the second one for simplicity) is given a variable width. And if the angle of turn is variable.
It seems there is no closed-form solution. I saw this paper is maybe easier to follow for the definition:
https://www.math.ucdavis.edu/~romik/data/uploads/papers/sofa...
Quote:
It is worth noting that Gerver’s description of his shape is not fully explicit, in the sense that the analytic formulas for the curved pieces of the shape are given in terms of four numerical constants A, B, φ and θ (where 0 < φ < θ < π/4 are angles with a certain geometric meaning), which are defined only implicitly as solutions of the nonlinear system of four equations
The difficulty of extending the definition to 3 dimensions is that the restriction to 2 separates two classes of constraint: being able to move the sofa round the corner, and the shape of the sofa being comfortable to sit on.
After showing them a youtube video about the problem they saw clearly how the organizer is a sofa and even made a joke about it a few days later.
Relatable math is pretty great. Also really cool is showing how academia translates to enriching our lives in benign ways.
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